#+PROPERTY: header-args :session finite_temp :kernel python :pandoc t :async yes * Setup ** Jupyter #+begin_src jupyter-python %load_ext autoreload %autoreload 2 %load_ext jupyter_spaces #+end_src #+RESULTS: : The autoreload extension is already loaded. To reload it, use: : %reload_ext autoreload : The jupyter_spaces extension is already loaded. To reload it, use: : %reload_ext jupyter_spaces ** Matplotlib #+begin_src jupyter-python import matplotlib import matplotlib.pyplot as plt #matplotlib.use("TkCairo", force=True) %gui tk %matplotlib inline plt.style.use('ggplot') #+end_src #+RESULTS: ** Richard (old) HOPS #+begin_src jupyter-python import hierarchyLib import hierarchyData import numpy as np from stocproc.stocproc import StocProc_FFT import bcf from dataclasses import dataclass, field import scipy import scipy.misc import scipy.signal import pickle from scipy.special import gamma as gamma_func from scipy.optimize import curve_fit #+end_src #+RESULTS: ** Auxiliary Definitions #+begin_src jupyter-python σ1 = np.matrix([[0,1],[1,0]]) σ2 = np.matrix([[0,-1j],[1j,0]]) σ3 = np.matrix([[1,0],[0,-1]]) #+end_src #+RESULTS: * Model Setup Basic parameters. #+begin_src jupyter-python class params: T = 2 t_max = 15 t_steps = int(t_max * 1/.05) k_max = 10 N = 4000 seed = 100 dim = 2 H_s = σ3 + np.eye(dim) L = σ2 #1 / 2 * (σ1 - 1j * σ2) ψ_0 = np.array([0, 1]) s = 1 num_exp_t = 4 wc = 1 with open("good_fit_data_abs_brute_force", "rb") as f: good_fit_data_abs = pickle.load(f) alpha = 0.8 # _, g_tilde, w_tilde = good_fit_data_abs[(numExpFit, s)] # g_tilde = np.array(g_tilde) # w_tilde = np.array(w_tilde) # g = 1 / np.pi * gamma_func(s + 1) * wc ** (s + 1) * np.asarray(g_tilde) # w = wc * np.asarray(w_tilde) bcf_scale = np.pi / 2 * alpha * wc ** (1 - s) #+end_src #+RESULTS: ** BCF and Thermal BCF #+begin_src jupyter-python @dataclass class CauchyBCF: δ: float wc: float def I(self, ω): return np.sqrt(self.δ) / (self.δ + (ω - self.wc) ** 2 / self.δ) def __call__(self, τ): return np.sqrt(self.δ) * np.exp(-1j * self.wc * τ - np.abs(τ) * self.δ) def __bfkey__(self): return self.δ, self.wc α = bcf.OBCF(s=params.s, eta=1, gamma=params.wc) I = bcf.OSD(s=params.s, eta=1, gamma=params.wc) #+end_src #+RESULTS: *** Fit We now fit a sum of exponentials against the BCF. #+begin_src jupyter-python from lmfit import minimize, Parameters def α_apprx(τ, g, w): return np.sum( g[np.newaxis, :] * np.exp(-w[np.newaxis, :] * (τ[:, np.newaxis])), axis=1 ) def _fit(): def residual(fit_params, x, data): resid = 0 w = np.array([fit_params[f"w{i}"] for i in range(params.num_exp_t)]) + 1j * np.array( [fit_params[f"wi{i}"] for i in range(params.num_exp_t)] ) g = np.array([fit_params[f"g{i}"] for i in range(params.num_exp_t)]) + 1j * np.array( [fit_params[f"gi{i}"] for i in range(params.num_exp_t)] ) resid = data - α_apprx(x, g, w) return resid.view(float) fit_params = Parameters() for i in range(params.num_exp_t): fit_params.add(f"g{i}", value=.1) fit_params.add(f"gi{i}", value=.1) fit_params.add(f"w{i}", value=.1) fit_params.add(f"wi{i}", value=.1) ts = np.linspace(0, params.t_max, 1000) out = minimize(residual, fit_params, args=(ts, α(ts))) w = np.array([out.params[f"w{i}"] for i in range(params.num_exp_t)]) + 1j * np.array( [out.params[f"wi{i}"] for i in range(params.num_exp_t)] ) g = np.array([out.params[f"g{i}"] for i in range(params.num_exp_t)]) + 1j * np.array( [out.params[f"gi{i}"] for i in range(params.num_exp_t)] ) return w, g w, g = _fit() #+end_src #+RESULTS: *** Plot Let's look a the result. #+begin_src jupyter-python class bcfplt: t = np.linspace(0, params.t_max, 1000) ω = np.linspace(params.wc - 10, params.wc + 10, 1000) fig, axs = plt.subplots(2) axs[0].plot(t, np.real(α(t))) axs[0].plot(t, np.imag(α(t))) axs[0].plot(t, np.real(α_apprx(t, g, w))) axs[0].plot(t, np.imag(α_apprx(t, g, w))) axs[1].plot(ω, I(ω).real) axs[1].plot(ω, I(ω).imag) #+end_src #+RESULTS: [[file:./.ob-jupyter/9f05a1fbf06920c271f0667db664ce2972415437.png]] Seems ok for now. ** Hops setup #+begin_src jupyter-python HierachyParam = hierarchyData.HiP( k_max=params.k_max, # g_scale=None, # sample_method='random', seed=params.seed, nonlinear=True, normalized=False, # terminator=False, result_type=hierarchyData.RESULT_TYPE_ALL, # accum_only=None, # rand_skip=None ) #+end_src #+RESULTS: Integration. #+begin_src jupyter-python IntegrationParam = hierarchyData.IntP( t_max=params.t_max, t_steps=params.t_steps, # integrator_name='zvode', # atol=1e-8, # rtol=1e-8, # order=5, # nsteps=5000, # method='bdf', # t_steps_skip=1 ) #+end_src #+RESULTS: And now the system. #+begin_src jupyter-python SystemParam = hierarchyData.SysP( H_sys=params.H_s, L=params.L, psi0=params.ψ_0, # excited qubit g=np.array(g), w=np.array(w), H_dynamic=[], bcf_scale=params.bcf_scale, # some coupling strength (scaling of the fit parameters 'g_i') gw_hash=None, # this is used to load g,w from some database len_gw=len(g), ) #+end_src #+RESULTS: The quantum noise. #+begin_src jupyter-python Eta = StocProc_FFT( I, params.t_max, α, negative_frequencies=False, seed=params.seed, intgr_tol=1e-3, intpl_tol=1e-3, scale=params.bcf_scale, ) #+end_src #+RESULTS: #+begin_example stocproc.stocproc - INFO - non neg freq only stocproc.method_ft - INFO - get_dt_for_accurate_interpolation, please wait ... stocproc.method_ft - INFO - acc interp N 33 dt 9.38e-01 -> diff 2.83e-01 stocproc.method_ft - INFO - acc interp N 65 dt 4.69e-01 -> diff 8.53e-02 stocproc.method_ft - INFO - acc interp N 129 dt 2.34e-01 -> diff 1.76e-02 stocproc.method_ft - INFO - acc interp N 257 dt 1.17e-01 -> diff 3.92e-03 stocproc.method_ft - INFO - acc interp N 513 dt 5.86e-02 -> diff 9.52e-04 stocproc.method_ft - INFO - requires dt < 5.859e-02 stocproc.method_ft - INFO - get_N_a_b_for_accurate_fourier_integral, please wait ... stocproc.method_ft - INFO - J_w_min:1.00e-02 N 32 yields: interval [0.00e+00,6.47e+00] diff 9.83e-03 stocproc.method_ft - INFO - J_w_min:1.00e-03 N 32 yields: interval [0.00e+00,9.12e+00] diff 8.12e-03 stocproc.method_ft - INFO - J_w_min:1.00e-02 N 64 yields: interval [0.00e+00,6.47e+00] diff 1.11e-02 stocproc.method_ft - INFO - increasing N while shrinking the interval does lower the error -> try next level stocproc.method_ft - INFO - J_w_min:1.00e-04 N 32 yields: interval [0.00e+00,1.17e+01] diff 1.32e-02 stocproc.method_ft - INFO - J_w_min:1.00e-03 N 64 yields: interval [0.00e+00,9.12e+00] diff 1.22e-03 stocproc.method_ft - INFO - J_w_min:1.00e-02 N 128 yields: interval [0.00e+00,6.47e+00] diff 1.14e-02 stocproc.method_ft - INFO - increasing N while shrinking the interval does lower the error -> try next level stocproc.method_ft - INFO - J_w_min:1.00e-05 N 32 yields: interval [0.00e+00,1.42e+01] diff 1.94e-02 stocproc.method_ft - INFO - J_w_min:1.00e-04 N 64 yields: interval [0.00e+00,1.17e+01] diff 2.57e-03 stocproc.method_ft - INFO - J_w_min:1.00e-03 N 128 yields: interval [0.00e+00,9.12e+00] diff 8.98e-04 stocproc.method_ft - INFO - return, cause tol of 0.001 was reached stocproc.method_ft - INFO - requires dx < 7.123e-02 stocproc.stocproc - INFO - Fourier Integral Boundaries: [0.000e+00, 1.251e+02] stocproc.stocproc - INFO - Number of Nodes : 2048 stocproc.stocproc - INFO - yields dx : 6.107e-02 stocproc.stocproc - INFO - yields dt : 5.023e-02 stocproc.stocproc - INFO - yields t_max : 1.028e+02 #+end_example The sample trajectories are smooth. #+begin_src jupyter-python %%space plot ts = np.linspace(0, params.t_max, 1000) Eta.new_process() plt.plot(ts, Eta(ts).real) #+end_src #+RESULTS: :RESULTS: | | [[file:./.ob-jupyter/10385a90753d7683d5740b88622cc4274de9c86a.png]] :END: And now the thermal noise. #+begin_src jupyter-python EtaTherm = StocProc_FFT( spectral_density=bcf.OFTDens(s=params.s, eta=1, gamma=params.wc, beta=1 / params.T), t_max=params.t_max, alpha=bcf.OFTCorr(s=params.s, eta=1, gamma=params.wc, beta=1 / params.T), intgr_tol=1e-3, intpl_tol=1e-3, seed=params.seed, negative_frequencies=False, scale=params.bcf_scale, ) #+end_src #+RESULTS: #+begin_example stocproc.method_ft - INFO - acc interp N 129 dt 2.34e-01 -> diff 3.20e-03 stocproc.method_ft - INFO - acc interp N 257 dt 1.17e-01 -> diff 7.67e-04 stocproc.method_ft - INFO - requires dt < 1.172e-01 stocproc.method_ft - INFO - get_N_a_b_for_accurate_fourier_integral, please wait ... stocproc.method_ft - INFO - J_w_min:1.00e-02 N 32 yields: interval [0.00e+00,4.10e+00] diff 2.00e-02 stocproc.method_ft - INFO - J_w_min:1.00e-03 N 32 yields: interval [0.00e+00,5.82e+00] diff 4.75e-02 stocproc.method_ft - INFO - J_w_min:1.00e-02 N 64 yields: interval [0.00e+00,4.10e+00] diff 7.88e-03 stocproc.method_ft - INFO - J_w_min:1.00e-04 N 32 yields: interval [0.00e+00,7.50e+00] diff 8.51e-02 stocproc.method_ft - INFO - J_w_min:1.00e-03 N 64 yields: interval [0.00e+00,5.82e+00] diff 1.01e-02 stocproc.method_ft - INFO - J_w_min:1.00e-02 N 128 yields: interval [0.00e+00,4.10e+00] diff 7.56e-03 stocproc.method_ft - INFO - J_w_min:1.00e-05 N 32 yields: interval [0.00e+00,9.16e+00] diff 1.04e-01 stocproc.method_ft - INFO - J_w_min:1.00e-04 N 64 yields: interval [0.00e+00,7.50e+00] diff 1.78e-02 stocproc.method_ft - INFO - J_w_min:1.00e-03 N 128 yields: interval [0.00e+00,5.82e+00] diff 2.38e-03 stocproc.method_ft - INFO - J_w_min:1.00e-02 N 256 yields: interval [0.00e+00,4.10e+00] diff 7.48e-03 stocproc.method_ft - INFO - increasing N while shrinking the interval does lower the error -> try next level stocproc.method_ft - INFO - J_w_min:1.00e-06 N 32 yields: interval [0.00e+00,1.08e+01] diff 1.22e-01 stocproc.method_ft - INFO - J_w_min:1.00e-05 N 64 yields: interval [0.00e+00,9.16e+00] diff 2.81e-02 stocproc.method_ft - INFO - J_w_min:1.00e-04 N 128 yields: interval [0.00e+00,7.50e+00] diff 4.17e-03 stocproc.method_ft - INFO - J_w_min:1.00e-03 N 256 yields: interval [0.00e+00,5.82e+00] diff 7.86e-04 stocproc.method_ft - INFO - return, cause tol of 0.001 was reached stocproc.method_ft - INFO - requires dx < 2.272e-02 stocproc.stocproc - INFO - Fourier Integral Boundaries: [0.000e+00, 7.064e+01] stocproc.stocproc - INFO - Number of Nodes : 4096 stocproc.stocproc - INFO - yields dx : 1.725e-02 stocproc.stocproc - INFO - yields dt : 8.895e-02 stocproc.stocproc - INFO - yields t_max : 3.642e+02 stocproc.stocproc - INFO - non neg freq only stocproc.method_ft - INFO - get_dt_for_accurate_interpolation, please wait ... stocproc.method_ft - INFO - acc interp N 33 dt 9.38e-01 -> diff 6.53e-02 stocproc.method_ft - INFO - acc interp N 65 dt 4.69e-01 -> diff 1.47e-02 stocproc.method_ft - INFO - acc interp N 129 dt 2.34e-01 -> diff 3.20e-03 stocproc.method_ft - INFO - acc interp N 257 dt 1.17e-01 -> diff 7.67e-04 stocproc.method_ft - INFO - requires dt < 1.172e-01 stocproc.method_ft - INFO - get_N_a_b_for_accurate_fourier_integral, please wait ... stocproc.method_ft - INFO - J_w_min:1.00e-02 N 32 yields: interval [0.00e+00,4.10e+00] diff 2.00e-02 stocproc.method_ft - INFO - J_w_min:1.00e-03 N 32 yields: interval [0.00e+00,5.82e+00] diff 4.75e-02 stocproc.method_ft - INFO - J_w_min:1.00e-02 N 64 yields: interval [0.00e+00,4.10e+00] diff 7.88e-03 stocproc.method_ft - INFO - J_w_min:1.00e-04 N 32 yields: interval [0.00e+00,7.50e+00] diff 8.51e-02 stocproc.method_ft - INFO - J_w_min:1.00e-03 N 64 yields: interval [0.00e+00,5.82e+00] diff 1.01e-02 stocproc.method_ft - INFO - J_w_min:1.00e-02 N 128 yields: interval [0.00e+00,4.10e+00] diff 7.56e-03 stocproc.method_ft - INFO - J_w_min:1.00e-05 N 32 yields: interval [0.00e+00,9.16e+00] diff 1.04e-01 stocproc.method_ft - INFO - J_w_min:1.00e-04 N 64 yields: interval [0.00e+00,7.50e+00] diff 1.78e-02 stocproc.method_ft - INFO - J_w_min:1.00e-03 N 128 yields: interval [0.00e+00,5.82e+00] diff 2.38e-03 stocproc.method_ft - INFO - J_w_min:1.00e-02 N 256 yields: interval [0.00e+00,4.10e+00] diff 7.48e-03 stocproc.method_ft - INFO - increasing N while shrinking the interval does lower the error -> try next level stocproc.method_ft - INFO - J_w_min:1.00e-06 N 32 yields: interval [0.00e+00,1.08e+01] diff 1.22e-01 stocproc.method_ft - INFO - J_w_min:1.00e-05 N 64 yields: interval [0.00e+00,9.16e+00] diff 2.81e-02 stocproc.method_ft - INFO - J_w_min:1.00e-04 N 128 yields: interval [0.00e+00,7.50e+00] diff 4.17e-03 stocproc.method_ft - INFO - J_w_min:1.00e-03 N 256 yields: interval [0.00e+00,5.82e+00] diff 7.86e-04 stocproc.method_ft - INFO - return, cause tol of 0.001 was reached stocproc.method_ft - INFO - requires dx < 2.272e-02 stocproc.stocproc - INFO - Fourier Integral Boundaries: [0.000e+00, 7.064e+01] stocproc.stocproc - INFO - Number of Nodes : 4096 stocproc.stocproc - INFO - yields dx : 1.725e-02 stocproc.stocproc - INFO - yields dt : 8.895e-02 stocproc.stocproc - INFO - yields t_max : 3.642e+02 #+end_example The sample trajectories are smooth too. #+begin_src jupyter-python %%space plot ts = np.linspace(0, params.t_max, 1000) EtaTherm.new_process() plt.plot(ts, EtaTherm(ts).real) #+end_src #+RESULTS: :RESULTS: | | [[file:./.ob-jupyter/20d0cdb5d62012a02c6ac14bc39a3b9fe59968ce.png]] | | [[file:./.ob-jupyter/6d082076097694cb45a42d4608ed411592bfcd3e.png]] :END: * Actual Hops Generate the key for binary caching. #+begin_src jupyter-python hi_key = hierarchyData.HIMetaKey_type( HiP=HierachyParam, IntP=IntegrationParam, SysP=SystemParam, Eta=Eta, EtaTherm=EtaTherm, ) #+end_src #+RESULTS: Initialize Hierarchy. #+begin_src jupyter-python myHierarchy = hierarchyLib.HI(hi_key, number_of_samples=params.N, desc="calculate the heat flow") #+end_src #+RESULTS: : /home/hiro/Documents/Projects/UNI/master/masterarb/python/richard_hops/hierarchyLib.py:1058: UserWarning: sum_k_max is not implemented! DO SO BEFORE NEXT USAGE (use simplex).HierarchyParametersType does not yet know about sum_k_max : warnings.warn( : init Hi class, use 2002 equation Run the integration. #+begin_src jupyter-python myHierarchy.integrate_simple(data_path="data", data_name="energy_flow_therm_new_again_less.data") #+end_src #+RESULTS: #+begin_example (10, 300, 1001) samples :0.0% integration :0.0% samples :0.1% integration :0.0% samples :0.1% integration :23.7% samples :0.2% integration :22.3% samples :0.3% integration :49.7% samples :0.4% integration :68.0% samples :0.4% integration :96.7% samples :0.5% integration :19.7% samples :0.6% integration :39.3% samples :0.7% integration :58.0% samples :0.8% integration :88.0% samples :0.9% integration :20.7% samples :0.9% integration :44.0% samples :1.0% integration :64.0% samples :1.1% integration :83.3% samples :1.2% integration :5.0% samples :1.2% integration :86.3% samples :1.2% integration :4.3% samples :1.3% integration :99.7% samples :1.3% integration :95.7% samples :1.4% integration :20.3% samples :1.5% integration :79.7% samples :1.6% integration :12.0% samples :1.7% integration :31.7% samples :1.7% integration :62.0% samples :1.8% integration :88.0% samples :1.9% integration :99.7% samples :2.0% integration :25.3% samples :2.1% integration :54.0% samples :2.1% integration :80.3% samples :2.2% integration :4.0% samples :2.3% integration :21.3% samples :2.4% integration :23.3% samples :2.5% integration :45.7% samples :2.5% integration :40.0% samples :2.6% integration :54.7% samples :2.6% integration :75.3% samples :2.7% integration :16.3% samples :2.8% integration :45.0% samples :2.8% integration :99.7% samples :2.9% integration :94.7% samples :2.9% integration :99.0% samples :3.0% integration :44.7% samples :3.1% integration :54.7% samples :3.1% integration :48.3% samples :3.2% integration :50.0% samples :3.3% integration :47.0% samples :3.3% integration :67.7% samples :3.4% integration :75.0% samples :3.5% integration :19.7% samples :3.5% integration :25.3% samples :3.6% integration :33.3% samples :3.7% integration :57.3% samples :3.8% integration :47.0% samples :3.8% integration :99.7% samples :3.9% integration :35.7% samples :4.0% integration :42.7% samples :4.0% integration :17.7% samples :4.1% integration :24.3% samples :4.2% integration :99.7% samples :4.2% integration :66.7% samples :4.3% integration :78.0% samples :4.3% integration :80.7% samples :4.4% integration :87.0% samples :4.5% integration :76.0% samples :4.6% integration :19.3% samples :4.7% integration :0.0% samples :4.7% integration :51.3% samples :4.8% integration :67.3% samples :4.9% integration :75.7% samples :4.9% integration :67.3% samples :5.0% integration :86.3% samples :5.0% integration :99.7% samples :5.1% integration :17.0% samples :5.1% integration :24.3% samples :5.2% integration :84.7% samples :5.3% integration :14.7% samples :5.3% integration :99.7% samples :5.4% integration :79.0% samples :5.5% integration :82.0% samples :5.6% integration :9.3% samples :5.7% integration :7.0% samples :5.7% integration :99.7% samples :5.7% integration :48.0% samples :5.8% integration :65.0% samples :5.9% integration :3.3% samples :5.9% integration :23.3% samples :6.0% integration :99.7% samples :6.0% integration :98.3% samples :6.2% integration :7.3% samples :6.2% integration :51.3% samples :6.3% integration :45.7% samples :6.3% integration :50.7% samples :6.4% integration :41.0% samples :6.5% integration :49.3% samples :6.5% integration :25.7% samples :6.6% integration :50.0% samples :6.7% integration :65.7% samples :6.8% integration :45.3% samples :6.8% integration :66.0% samples :6.9% integration :99.7% samples :7.0% integration :89.0% samples :7.0% integration :75.3% samples :7.1% integration :12.3% samples :7.2% integration :8.0% samples :7.2% integration :93.3% samples :7.3% integration :77.0% samples :7.3% integration :79.0% samples :7.4% integration :91.3% samples :7.5% integration :85.0% samples :7.5% integration :85.7% samples :7.6% integration :3.3% samples :7.7% integration :92.3% samples :7.8% integration :44.0% samples :7.8% integration :54.3% samples :7.9% integration :63.7% samples :8.0% integration :83.3% samples :8.1% integration :10.7% samples :8.1% integration :99.7% samples :8.2% integration :4.0% samples :8.3% integration :25.0% samples :8.3% integration :99.7% samples :8.3% integration :84.3% samples :8.4% integration :97.0% samples :8.5% integration :25.7% samples :8.6% integration :45.0% samples :8.6% integration :80.7% samples :8.7% integration :98.7% samples :8.8% integration :99.7% samples :8.8% integration :98.7% samples :8.9% integration :11.0% samples :9.0% integration :70.7% samples :9.0% integration :53.0% samples :9.1% integration :53.0% samples :9.2% integration :94.3% samples :9.2% integration :93.0% samples :9.3% integration :99.7% samples :9.3% integration :24.3% samples :9.4% integration :19.7% samples :9.5% integration :70.0% samples :9.6% integration :45.7% samples :9.6% integration :99.7% samples :9.7% integration :89.0% samples :9.8% integration :83.7% samples :9.8% integration :32.3% samples :9.9% integration :29.0% samples :10.0% integration :99.7% samples :10.0% integration :64.7% samples :10.1% integration :63.3% samples :10.1% integration :99.7% samples :10.2% integration :32.0% samples :10.2% integration :99.7% samples :10.3% integration :59.7% samples :10.4% integration :62.7% samples :10.4% integration :64.7% samples :10.5% integration :84.3% samples :10.6% integration :99.7% samples :10.7% integration :14.0% samples :10.8% integration :31.0% samples :10.8% integration :31.7% samples :10.9% integration :50.7% samples :10.9% integration :65.3% samples :11.0% integration :65.0% samples :11.1% integration :76.7% samples :11.1% integration :99.7% samples :11.2% integration :85.7% samples :11.3% integration :84.7% samples :11.3% integration :28.7% samples :11.4% integration :32.3% samples :11.5% integration :99.7% samples :11.6% integration :70.0% samples :11.6% integration :79.7% samples :11.7% integration :92.7% samples :11.8% integration :89.3% samples :11.8% integration :85.0% samples :11.9% integration :34.3% samples :12.0% integration :47.7% samples :12.0% integration :63.7% samples :12.1% integration :87.7% samples :12.2% integration :99.7% samples :12.2% integration :6.0% samples :12.3% integration :17.7% samples :12.4% integration :30.7% samples :12.4% integration :42.7% samples :12.5% integration :58.0% samples :12.6% integration :72.0% samples :12.7% integration :72.7% samples :12.7% integration :99.7% samples :12.8% integration :0.0% samples :12.9% integration :21.7% samples :12.9% integration :20.7% samples :13.0% integration :27.0% samples :13.1% integration :99.7% samples :13.1% integration :35.0% samples :13.2% integration :48.7% samples :13.2% integration :49.0% samples :13.3% integration :25.7% samples :13.4% integration :44.3% samples :13.5% integration :55.0% samples :13.6% integration :58.7% samples :13.6% integration :54.0% samples :13.7% integration :57.0% samples :13.8% integration :61.3% samples :13.9% integration :66.0% samples :13.9% integration :82.3% samples :14.0% integration :8.3% samples :14.1% integration :19.7% samples :14.2% integration :41.7% samples :14.2% integration :99.7% samples :14.2% integration :42.0% samples :14.3% integration :48.0% samples :14.4% integration :76.0% samples :14.4% integration :98.3% samples :14.5% integration :27.3% samples :14.6% integration :59.0% samples :14.7% integration :73.0% samples :14.8% integration :96.7% samples :14.9% integration :14.7% samples :14.9% integration :37.0% samples :15.0% integration :54.0% samples :15.1% integration :70.7% samples :15.2% integration :91.0% samples :15.3% integration :1.7% samples :15.3% integration :99.7% samples :15.3% integration :44.7% samples :15.4% integration :59.0% samples :15.5% integration :27.7% samples :15.6% integration :53.3% samples :15.6% integration :0.7% samples :15.7% integration :11.7% samples :15.8% integration :24.7% samples :15.8% integration :59.7% samples :15.9% integration :78.0% samples :16.0% integration :96.0% samples :16.1% integration :3.3% samples :16.2% integration :11.3% samples :16.2% integration :27.0% samples :16.3% integration :50.0% samples :16.4% integration :62.7% samples :16.4% integration :77.3% samples :16.5% integration :96.7% samples :16.6% integration :18.7% samples :16.7% integration :49.3% samples :16.8% integration :56.7% samples :16.9% integration :72.0% samples :16.9% integration :94.0% samples :17.0% integration :99.7% samples :17.0% integration :99.7% samples :17.0% integration :92.0% samples :17.1% integration :84.3% samples :17.2% integration :13.0% samples :17.3% integration :32.7% samples :17.3% integration :53.0% samples :17.4% integration :71.7% samples :17.5% integration :92.7% samples :17.6% integration :12.7% samples :17.7% integration :31.0% samples :17.8% integration :51.3% samples :17.8% integration :68.7% samples :17.9% integration :88.7% samples :18.0% integration :17.0% samples :18.1% integration :99.7% samples :18.1% integration :99.7% samples :18.1% integration :70.3% samples :18.2% integration :81.7% samples :18.2% integration :97.3% samples :18.4% integration :24.3% samples :18.4% integration :47.3% samples :18.5% integration :68.7% samples :18.6% integration :87.0% samples :18.6% integration :99.3% samples :18.8% integration :22.3% samples :18.8% integration :44.7% samples :18.9% integration :57.3% samples :19.0% integration :14.0% samples :19.1% integration :20.3% samples :19.1% integration :32.0% samples :19.1% integration :99.7% samples :19.1% integration :99.7% samples :19.2% integration :97.7% samples :19.2% integration :91.0% samples :19.3% integration :94.0% samples :19.4% integration :0.3% samples :19.5% integration :4.0% samples :19.5% integration :90.0% samples :19.6% integration :66.3% samples :19.6% integration :81.3% samples :19.7% integration :91.0% samples :19.8% integration :8.3% samples :19.8% integration :99.7% samples :19.9% integration :19.0% samples :20.0% integration :38.7% samples :20.0% integration :41.7% samples :20.1% integration :70.3% samples :20.2% integration :86.7% samples :20.2% integration :82.7% samples :20.3% integration :3.7% samples :20.4% integration :0.0% samples :20.4% integration :14.3% samples :20.5% integration :32.7% samples :20.6% integration :46.0% samples :20.6% integration :56.0% samples :20.7% integration :99.7% samples :20.8% integration :72.0% samples :20.8% integration :89.0% samples :20.9% integration :26.3% samples :21.0% integration :57.0% samples :21.1% integration :80.0% samples :21.1% integration :43.7% samples :21.2% integration :69.3% samples :21.2% integration :70.7% samples :21.3% integration :93.0% samples :21.4% integration :99.7% samples :21.5% integration :22.0% samples :21.6% integration :44.7% samples :21.6% integration :27.3% samples :21.7% integration :59.0% samples :21.8% integration :84.3% samples :21.8% integration :2.7% samples :21.9% integration :36.0% samples :21.9% integration :99.7% samples :22.1% integration :23.7% samples :22.1% integration :30.0% samples :22.2% integration :55.0% samples :22.2% integration :85.0% samples :22.3% integration :87.7% samples :22.4% integration :76.0% samples :22.5% integration :93.3% samples :22.6% integration :0.0% samples :22.6% integration :22.3% samples :22.7% integration :99.7% samples :22.7% integration :99.7% samples :22.8% integration :4.7% samples :22.9% integration :0.7% samples :22.9% integration :23.7% samples :23.0% integration :49.0% samples :23.1% integration :6.0% samples :23.2% integration :19.7% samples :23.2% integration :36.3% samples :23.3% integration :44.7% samples :23.4% integration :58.3% samples :23.4% integration :82.0% samples :23.5% integration :98.7% samples :23.5% integration :99.7% samples :23.6% integration :3.7% samples :23.7% integration :8.0% samples :23.8% integration :53.7% samples :23.8% integration :60.0% samples :23.9% integration :99.7% samples :23.9% integration :77.0% samples :24.0% integration :94.3% samples :24.1% integration :32.3% samples :24.1% integration :48.0% samples :24.2% integration :70.7% samples :24.3% integration :30.3% samples :24.4% integration :41.3% samples :24.4% integration :67.3% samples :24.5% integration :89.0% samples :24.6% integration :13.3% samples :24.6% integration :93.3% samples :24.8% integration :19.0% samples :24.8% integration :31.7% samples :24.9% integration :54.3% samples :24.9% integration :83.3% samples :25.0% integration :99.7% samples :25.1% integration :2.3% samples :25.1% integration :5.3% samples :25.2% integration :24.7% samples :25.3% integration :41.3% samples :25.4% integration :27.3% samples :25.4% integration :45.7% samples :25.5% integration :99.7% samples :25.6% integration :75.3% samples :25.7% integration :87.7% samples :25.7% integration :97.0% samples :25.8% integration :11.7% samples :25.9% integration :99.7% samples :25.9% integration :46.7% samples :26.0% integration :70.3% samples :26.1% integration :52.0% samples :26.2% integration :68.3% samples :26.2% integration :79.0% samples :26.3% integration :99.0% samples :26.4% integration :18.3% samples :26.4% integration :30.0% samples :26.5% integration :50.0% samples :26.6% integration :72.3% samples :26.6% integration :58.7% samples :26.7% integration :88.0% samples :26.8% integration :99.7% samples :26.8% integration :99.0% samples :26.9% integration :31.3% samples :27.0% integration :34.7% samples :27.1% integration :47.3% samples :27.1% integration :99.7% samples :27.2% integration :78.3% samples :27.3% integration :98.0% samples :27.3% integration :82.3% samples :27.4% integration :9.7% samples :27.5% integration :99.7% samples :27.6% integration :28.7% samples :27.6% integration :44.3% samples :27.7% integration :60.0% samples :27.8% integration :72.7% samples :27.8% integration :87.3% samples :27.9% integration :5.7% samples :28.0% integration :34.7% samples :28.1% integration :4.0% samples :28.1% integration :33.0% samples :28.2% integration :56.7% samples :28.2% integration :70.0% samples :28.3% integration :82.3% samples :28.4% integration :99.7% samples :28.5% integration :9.0% samples :28.5% integration :41.7% samples :28.6% integration :14.3% samples :28.7% integration :32.3% samples :28.7% integration :99.7% samples :28.8% integration :60.0% samples :28.9% integration :66.3% samples :28.9% integration :90.7% samples :29.0% integration :99.3% samples :29.1% integration :99.7% samples :29.1% integration :71.0% samples :29.2% integration :90.0% samples :29.3% integration :63.3% samples :29.3% integration :84.3% samples :29.4% integration :13.3% samples :29.5% integration :31.7% samples :29.6% integration :62.3% samples :29.6% integration :18.0% samples :29.7% integration :37.7% samples :29.8% integration :66.3% samples :29.9% integration :52.3% samples :29.9% integration :75.3% samples :30.0% integration :99.7% samples :30.1% integration :0.0% samples :30.2% integration :14.0% samples :30.2% integration :30.7% samples :30.3% integration :53.3% samples :30.3% integration :85.7% samples :30.4% integration :67.7% samples :30.5% integration :84.0% samples :30.6% integration :99.0% samples :30.6% integration :27.7% samples :30.7% integration :38.0% samples :30.8% integration :13.0% samples :30.9% integration :25.0% samples :30.9% integration :51.0% samples :31.0% integration :54.0% samples :31.1% integration :74.0% samples :31.1% integration :97.3% samples :31.2% integration :29.3% samples :31.3% integration :99.7% samples :31.4% integration :22.7% samples :31.4% integration :32.0% samples :31.5% integration :24.7% samples :31.6% integration :42.7% samples :31.6% integration :99.7% samples :31.7% integration :91.3% samples :31.8% integration :17.7% samples :31.8% integration :99.7% samples :31.9% integration :80.0% samples :31.9% integration :99.7% samples :32.0% integration :99.7% samples :32.1% integration :98.7% samples :32.1% integration :68.3% samples :32.2% integration :93.3% samples :32.3% integration :99.7% samples :32.4% integration :40.0% samples :32.5% integration :67.3% samples :32.5% integration :31.3% samples :32.6% integration :56.3% samples :32.7% integration :72.0% samples :32.7% integration :95.7% samples :32.8% integration :23.0% samples :32.9% integration :99.7% samples :33.0% integration :6.7% samples :33.1% integration :40.0% samples :33.1% integration :99.7% samples :33.1% integration :62.3% samples :33.2% integration :99.7% samples :33.3% integration :30.0% samples :33.4% integration :48.3% samples :33.4% integration :99.0% samples :33.5% integration :35.3% samples :33.6% integration :99.7% samples :33.6% integration :55.3% samples :33.7% integration :72.3% samples :33.8% integration :81.3% samples :33.9% integration :0.0% samples :33.9% integration :37.0% samples :34.0% integration :81.3% samples :34.1% integration :0.7% samples :34.1% integration :30.3% samples :34.2% integration :45.0% samples :34.3% integration :50.0% samples :34.4% integration :74.0% samples :34.4% integration :94.7% samples :34.5% integration :11.7% samples :34.6% integration :37.3% samples :34.7% integration :59.3% samples :34.8% integration :79.0% samples :34.8% integration :5.7% samples :34.9% integration :89.7% samples :34.9% integration :60.7% samples :35.0% integration :93.0% samples :35.0% integration :99.7% samples :35.1% integration :88.7% samples :35.2% integration :99.7% samples :35.3% integration :68.0% samples :35.4% integration :85.0% samples :35.4% integration :99.7% samples :35.5% integration :3.3% samples :35.6% integration :30.0% samples :35.6% integration :27.3% samples :35.7% integration :47.3% samples :35.8% integration :23.0% samples :35.9% integration :49.3% samples :35.9% integration :74.3% samples :36.0% integration :75.0% samples :36.1% integration :97.3% samples :36.1% integration :1.0% samples :36.2% integration :14.3% samples :36.3% integration :42.0% samples :36.4% integration :39.0% samples :36.4% integration :66.0% samples :36.5% integration :93.7% samples :36.6% integration :83.0% samples :36.7% integration :0.0% samples :36.7% integration :99.7% samples :36.7% integration :69.3% samples :36.8% integration :79.3% samples :36.9% integration :80.0% samples :37.0% integration :99.0% samples :37.0% integration :57.0% samples :37.1% integration :68.0% samples :37.2% integration :85.3% samples :37.2% integration :19.0% samples :37.3% integration :37.0% samples :37.4% integration :99.7% samples :37.4% integration :75.0% samples :37.5% integration :93.7% samples :37.6% integration :4.0% samples :37.6% integration :32.7% samples :37.7% integration :99.7% samples :37.8% integration :60.7% samples :37.9% integration :78.3% samples :37.9% integration :48.0% samples :38.0% integration :82.3% samples :38.1% integration :99.7% samples :38.1% integration :68.7% samples :38.2% integration :99.7% samples :38.3% integration :96.3% samples :38.4% integration :24.7% samples :38.5% integration :50.3% samples :38.5% integration :15.7% samples :38.6% integration :42.7% samples :38.6% integration :80.0% samples :38.7% integration :92.0% samples :38.8% integration :99.7% samples :38.9% integration :20.7% samples :38.9% integration :43.3% samples :39.0% integration :13.7% samples :39.1% integration :40.0% samples :39.1% integration :55.7% samples :39.2% integration :78.0% samples :39.3% integration :97.0% samples :39.4% integration :99.7% samples :39.4% integration :29.7% samples :39.5% integration :63.7% samples :39.6% integration :39.3% samples :39.6% integration :64.0% samples :39.7% integration :97.0% samples :39.8% integration :71.7% samples :39.9% integration :0.0% samples :40.0% integration :86.7% samples :40.1% integration :5.7% samples :40.1% integration :99.7% samples :40.2% integration :50.7% samples :40.2% integration :69.7% samples :40.3% integration :99.7% samples :40.3% integration :29.0% samples :40.4% integration :49.0% samples :40.5% integration :30.3% samples :40.6% integration :60.3% samples :40.6% integration :92.0% samples :40.7% integration :11.7% samples :40.8% integration :49.3% samples :40.9% integration :71.3% samples :41.0% integration :4.3% samples :41.0% integration :39.3% samples :41.1% integration :66.0% samples :41.2% integration :90.3% samples :41.3% integration :40.3% samples :41.3% integration :67.7% samples :41.4% integration :88.3% samples :41.4% integration :68.7% samples :41.5% integration :96.3% samples :41.5% integration :99.7% samples :41.6% integration :72.0% samples :41.7% integration :91.0% samples :41.8% integration :56.0% samples :41.9% integration :86.3% samples :41.9% integration :49.3% samples :42.0% integration :88.7% samples :42.1% integration :26.3% samples :42.1% integration :90.3% samples :42.2% integration :28.3% samples :42.3% integration :22.3% samples :42.4% integration :56.0% samples :42.4% integration :87.0% samples :42.5% integration :23.7% samples :42.6% integration :50.3% samples :42.6% integration :99.7% samples :42.7% integration :27.3% samples :42.8% integration :55.0% samples :42.9% integration :17.3% samples :43.0% integration :43.7% samples :43.0% integration :99.7% samples :43.1% integration :77.7% samples :43.2% integration :2.0% samples :43.2% integration :79.3% samples :43.3% integration :0.0% samples :43.4% integration :13.3% samples :43.5% integration :66.0% samples :43.5% integration :74.3% samples :43.6% integration :57.3% samples :43.7% integration :79.3% samples :43.8% integration :6.7% samples :43.8% integration :76.3% samples :43.9% integration :9.7% samples :44.0% integration :18.3% samples :44.0% integration :31.7% samples :44.1% integration :60.3% samples :44.1% integration :99.7% samples :44.2% integration :54.0% samples :44.3% integration :7.0% samples :44.4% integration :38.7% samples :44.4% integration :55.0% samples :44.5% integration :17.3% samples :44.6% integration :50.0% samples :44.6% integration :99.7% samples :44.7% integration :75.3% samples :44.8% integration :98.0% samples :44.9% integration :76.7% samples :45.0% integration :14.0% samples :45.0% integration :99.7% samples :45.1% integration :23.7% samples :45.1% integration :52.3% samples :45.2% integration :84.7% samples :45.3% integration :16.3% samples :45.4% integration :32.7% samples :45.4% integration :84.7% samples :45.5% integration :9.3% samples :45.6% integration :13.0% samples :45.6% integration :47.0% samples :45.7% integration :64.3% samples :45.8% integration :97.3% samples :45.9% integration :16.7% samples :45.9% integration :99.7% samples :46.0% integration :97.3% samples :46.1% integration :27.7% samples :46.1% integration :99.7% samples :46.2% integration :18.7% samples :46.3% integration :99.7% samples :46.4% integration :85.0% samples :46.5% integration :2.0% samples :46.5% integration :73.7% samples :46.6% integration :99.3% samples :46.7% integration :99.7% samples :46.7% integration :31.7% samples :46.8% integration :67.3% samples :46.9% integration :34.3% samples :46.9% integration :46.7% samples :47.0% integration :70.0% samples :47.1% integration :81.3% samples :47.2% integration :13.0% samples :47.2% integration :11.3% samples :47.3% integration :38.3% samples :47.4% integration :62.7% samples :47.4% integration :35.7% samples :47.5% integration :59.7% samples :47.6% integration :99.7% samples :47.7% integration :11.0% samples :47.8% integration :26.0% samples :47.8% integration :76.0% samples :47.9% integration :87.7% samples :47.9% integration :99.7% samples :47.9% integration :99.7% samples :48.0% integration :30.3% samples :48.1% integration :15.0% samples :48.2% integration :47.3% samples :48.3% integration :69.0% samples :48.4% integration :1.0% samples :48.4% integration :15.3% samples :48.5% integration :41.3% samples :48.5% integration :61.0% samples :48.6% integration :82.3% samples :48.7% integration :83.0% samples :48.8% integration :95.3% samples :48.8% integration :4.0% samples :48.9% integration :24.3% samples :49.0% integration :42.3% samples :49.0% integration :99.7% samples :49.0% integration :77.0% samples :49.1% integration :99.7% samples :49.2% integration :8.0% samples :49.3% integration :36.0% samples :49.4% integration :0.7% samples :49.5% integration :20.3% samples :49.5% integration :99.7% samples :49.6% integration :60.7% samples :49.6% integration :81.0% samples :49.7% integration :65.3% samples :49.8% integration :91.7% samples :49.9% integration :99.7% samples :49.9% integration :63.3% samples :50.0% integration :97.0% samples :50.0% integration :56.3% samples :50.1% integration :86.7% samples :50.2% integration :12.7% samples :50.3% integration :21.0% samples :50.3% integration :40.3% samples :50.4% integration :0.3% samples :50.5% integration :33.7% samples :50.6% integration :81.3% samples :50.6% integration :31.3% samples :50.7% integration :50.7% samples :50.7% integration :99.7% samples :50.8% integration :5.3% samples :50.9% integration :6.3% samples :51.0% integration :18.7% samples :51.0% integration :49.3% samples :51.1% integration :83.3% samples :51.2% integration :40.0% samples :51.3% integration :60.7% samples :51.3% integration :70.3% samples :51.4% integration :97.0% samples :51.5% integration :36.0% samples :51.5% integration :71.0% samples :51.6% integration :98.0% samples :51.7% integration :99.7% samples :51.7% integration :97.7% samples :51.8% integration :15.0% samples :51.9% integration :8.7% samples :51.9% integration :43.7% samples :52.0% integration :99.7% samples :52.1% integration :23.3% samples :52.2% integration :56.3% samples :52.2% integration :28.0% samples :52.3% integration :63.7% samples :52.4% integration :93.0% samples :52.5% integration :83.0% samples :52.6% integration :23.3% samples :52.6% integration :88.0% samples :52.7% integration :16.0% samples :52.8% integration :99.7% samples :52.8% integration :59.7% samples :52.9% integration :80.0% samples :52.9% integration :83.0% samples :53.0% integration :99.7% samples :53.1% integration :36.7% samples :53.2% integration :5.0% samples :53.3% integration :31.3% samples :53.3% integration :18.7% samples :53.4% integration :40.3% samples :53.5% integration :76.3% samples :53.5% integration :90.3% samples :53.6% integration :15.3% samples :53.7% integration :99.7% samples :53.8% integration :6.3% samples :53.8% integration :34.0% samples :53.9% integration :33.3% samples :54.0% integration :54.0% samples :54.0% integration :83.7% samples :54.1% integration :42.7% samples :54.2% integration :74.7% samples :54.2% integration :17.7% samples :54.3% integration :40.3% samples :54.4% integration :63.7% samples :54.5% integration :37.7% samples :54.5% integration :57.3% samples :54.6% integration :69.0% samples :54.7% integration :99.7% samples :54.8% integration :24.0% samples :54.9% integration :0.0% samples :54.9% integration :28.3% samples :55.0% integration :21.7% samples :55.0% integration :62.7% samples :55.1% integration :90.3% samples :55.2% integration :65.7% samples :55.3% integration :92.0% samples :55.4% integration :99.7% samples :55.4% integration :45.0% samples :55.5% integration :69.7% samples :55.6% integration :40.0% samples :55.6% integration :64.7% samples :55.7% integration :85.7% samples :55.8% integration :75.0% samples :55.9% integration :3.7% samples :55.9% integration :99.7% samples :56.0% integration :48.0% samples :56.0% integration :82.7% samples :56.1% integration :87.0% samples :56.2% integration :17.7% samples :56.2% integration :57.7% samples :56.3% integration :86.3% samples :56.4% integration :99.7% samples :56.5% integration :81.0% samples :56.5% integration :12.0% samples :56.6% integration :38.0% samples :56.7% integration :61.7% samples :56.8% integration :94.0% samples :56.8% integration :53.7% samples :56.9% integration :80.0% samples :57.0% integration :99.7% samples :57.0% integration :29.3% samples :57.1% integration :60.0% samples :57.1% integration :41.0% samples :57.2% integration :64.7% samples :57.3% integration :87.0% samples :57.4% integration :57.0% samples :57.5% integration :83.3% samples :57.5% integration :8.3% samples :57.6% integration :42.0% samples :57.7% integration :72.0% samples :57.8% integration :28.7% samples :57.8% integration :51.0% samples :57.9% integration :55.0% samples :58.0% integration :81.0% samples :58.1% integration :13.3% samples :58.1% integration :58.0% samples :58.1% integration :74.3% samples :58.2% integration :31.3% samples :58.3% integration :45.3% samples :58.4% integration :47.0% samples :58.4% integration :62.0% samples :58.5% integration :79.3% samples :58.6% integration :99.7% samples :58.6% integration :94.7% samples :58.7% integration :23.3% samples :58.8% integration :25.3% samples :58.9% integration :55.7% samples :58.9% integration :88.3% samples :59.0% integration :85.7% samples :59.1% integration :16.0% samples :59.1% integration :99.0% samples :59.2% integration :41.0% samples :59.3% integration :59.7% samples :59.4% integration :18.3% samples :59.5% integration :45.3% samples :59.5% integration :53.7% samples :59.6% integration :89.7% samples :59.7% integration :22.3% samples :59.7% integration :86.0% samples :59.8% integration :17.3% samples :59.9% integration :19.3% samples :60.0% integration :57.3% samples :60.0% integration :91.3% samples :60.1% integration :99.7% samples :60.1% integration :98.3% samples :60.2% integration :99.7% samples :60.2% integration :58.7% samples :60.3% integration :79.7% samples :60.4% integration :99.7% samples :60.4% integration :94.0% samples :60.5% integration :99.7% samples :60.6% integration :0.0% samples :60.6% integration :33.3% samples :60.7% integration :59.7% samples :60.8% integration :81.3% samples :60.8% integration :99.7% samples :60.9% integration :62.7% samples :60.9% integration :68.0% samples :61.0% integration :99.7% samples :61.0% integration :60.7% samples :61.1% integration :89.3% samples :61.2% integration :13.0% samples :61.3% integration :42.0% samples :61.3% integration :99.7% samples :61.4% integration :87.3% samples :61.5% integration :17.3% samples :61.5% integration :99.7% samples :61.6% integration :70.7% samples :61.6% integration :99.7% samples :61.7% integration :14.3% samples :61.7% integration :45.7% samples :61.8% integration :78.3% samples :61.9% integration :3.7% samples :61.9% integration :99.7% samples :62.0% integration :35.3% samples :62.0% integration :70.0% samples :62.1% integration :99.7% samples :62.1% integration :84.3% samples :62.2% integration :99.7% samples :62.3% integration :42.7% samples :62.3% integration :71.7% samples :62.4% integration :99.7% samples :62.4% integration :1.7% samples :62.5% integration :41.7% samples :62.5% integration :99.7% samples :62.6% integration :4.0% samples :62.6% integration :99.7% samples :62.7% integration :18.3% samples :62.8% integration :51.7% samples :62.8% integration :56.0% samples :62.9% integration :81.0% samples :63.0% integration :99.7% samples :63.0% integration :53.7% samples :63.1% integration :79.0% samples :63.1% integration :99.7% samples :63.2% integration :36.7% samples :63.3% integration :60.0% samples :63.4% integration :37.7% samples :63.4% integration :60.7% samples :63.5% integration :99.7% samples :63.6% integration :26.3% samples :63.6% integration :44.3% samples :63.7% integration :10.7% samples :63.8% integration :10.7% samples :63.8% integration :99.7% samples :63.9% integration :33.0% samples :64.0% integration :68.3% samples :64.0% integration :92.0% samples :64.1% integration :12.3% samples :64.2% integration :99.7% samples :64.2% integration :96.0% samples :64.3% integration :19.3% samples :64.3% integration :32.7% samples :64.4% integration :62.3% samples :64.5% integration :99.7% samples :64.5% integration :46.0% samples :64.6% integration :73.7% samples :64.6% integration :99.7% samples :64.7% integration :6.3% samples :64.8% integration :99.7% samples :64.8% integration :69.3% samples :64.9% integration :93.3% samples :65.0% integration :62.0% samples :65.0% integration :80.3% samples :65.1% integration :97.0% samples :65.2% integration :18.0% samples :65.3% integration :48.7% samples :65.3% integration :26.0% samples :65.4% integration :47.7% samples :65.5% integration :69.3% samples :65.5% integration :90.0% samples :65.6% integration :18.3% samples :65.7% integration :99.7% samples :65.8% integration :10.7% samples :65.9% integration :32.7% samples :65.9% integration :99.7% samples :66.0% integration :29.3% samples :66.0% integration :99.7% samples :66.1% integration :36.7% samples :66.1% integration :59.7% samples :66.2% integration :99.7% samples :66.2% integration :24.3% samples :66.3% integration :99.7% samples :66.4% integration :77.7% samples :66.5% integration :96.0% samples :66.5% integration :99.7% samples :66.6% integration :81.3% samples :66.6% integration :99.7% samples :66.6% integration :99.7% samples :66.8% integration :0.0% samples :66.8% integration :99.7% samples :66.8% integration :11.7% samples :66.9% integration :36.7% samples :67.0% integration :37.7% samples :67.0% integration :58.3% samples :67.1% integration :99.7% samples :67.2% integration :76.7% samples :67.2% integration :98.0% samples :67.3% integration :99.7% samples :67.4% integration :12.7% samples :67.4% integration :99.7% samples :67.5% integration :17.3% samples :67.6% integration :42.0% samples :67.6% integration :99.7% samples :67.7% integration :48.3% samples :67.8% integration :67.7% samples :67.8% integration :25.3% samples :67.9% integration :46.0% samples :67.9% integration :99.7% samples :68.0% integration :46.0% samples :68.0% integration :65.0% samples :68.1% integration :24.0% samples :68.2% integration :55.0% samples :68.2% integration :99.7% samples :68.2% integration :73.0% samples :68.3% integration :92.7% samples :68.4% integration :20.0% samples :68.5% integration :38.0% samples :68.5% integration :99.7% samples :68.5% integration :86.7% samples :68.6% integration :16.3% samples :68.7% integration :53.7% samples :68.7% integration :73.7% samples :68.8% integration :85.3% samples :68.8% integration :33.7% samples :68.9% integration :57.0% samples :69.0% integration :81.0% samples :69.0% integration :99.7% samples :69.1% integration :99.7% samples :69.2% integration :65.7% samples :69.2% integration :99.3% samples :69.3% integration :99.7% samples :69.4% integration :74.3% samples :69.5% integration :91.0% samples :69.5% integration :99.7% samples :69.5% integration :17.7% samples :69.6% integration :99.7% samples :69.7% integration :7.3% samples :69.8% integration :24.7% samples :69.8% integration :51.0% samples :69.9% integration :83.7% samples :69.9% integration :99.7% samples :70.0% integration :75.7% samples :70.0% integration :0.3% samples :70.1% integration :5.3% samples :70.2% integration :7.0% samples :70.2% integration :99.7% samples :70.3% integration :98.7% samples :70.4% integration :28.7% samples :70.4% integration :99.7% samples :70.5% integration :46.3% samples :70.5% integration :68.7% samples :70.6% integration :94.3% samples :70.7% integration :13.3% samples :70.7% integration :99.7% samples :70.8% integration :43.3% samples :70.9% integration :82.3% samples :70.9% integration :15.0% samples :71.0% integration :52.0% samples :71.0% integration :99.7% samples :71.1% integration :21.3% samples :71.2% integration :58.7% samples :71.2% integration :31.3% samples :71.3% integration :50.3% samples :71.4% integration :99.7% samples :71.4% integration :87.7% samples :71.5% integration :14.7% samples :71.5% integration :58.0% samples :71.6% integration :83.7% samples :71.7% integration :99.7% samples :71.7% integration :41.0% samples :71.8% integration :53.3% samples :71.8% integration :99.7% samples :71.9% integration :33.3% samples :72.0% integration :50.0% samples :72.0% integration :20.3% samples :72.1% integration :52.7% samples :72.2% integration :99.7% samples :72.2% integration :82.3% samples :72.3% integration :99.7% samples :72.4% integration :88.7% samples :72.5% integration :12.7% samples :72.5% integration :99.7% samples :72.6% integration :15.0% samples :72.7% integration :42.0% samples :72.7% integration :26.0% samples :72.8% integration :61.7% samples :72.8% integration :99.7% samples :72.9% integration :28.3% samples :73.0% integration :55.7% samples :73.0% integration :73.7% samples :73.1% integration :99.0% samples :73.2% integration :99.7% samples :73.2% integration :60.0% samples :73.2% integration :90.7% samples :73.3% integration :99.7% samples :73.4% integration :15.3% samples :73.5% integration :43.0% samples :73.5% integration :78.3% samples :73.6% integration :99.0% samples :73.7% integration :99.7% samples :73.7% integration :76.3% samples :73.8% integration :9.7% samples :73.9% integration :93.3% samples :74.0% integration :2.7% samples :74.0% integration :28.3% samples :74.1% integration :48.3% samples :74.2% integration :76.7% samples :74.2% integration :99.7% samples :74.2% integration :56.7% samples :74.3% integration :99.7% samples :74.4% integration :59.7% samples :74.4% integration :75.3% samples :74.5% integration :90.7% samples :74.6% integration :15.7% samples :74.6% integration :99.7% samples :74.7% integration :92.0% samples :74.8% integration :11.0% samples :74.8% integration :99.7% samples :74.9% integration :64.0% samples :74.9% integration :94.7% samples :75.0% integration :6.0% samples :75.1% integration :33.0% samples :75.1% integration :99.7% samples :75.2% integration :4.7% samples :75.2% integration :28.7% samples :75.3% integration :53.3% samples :75.4% integration :75.0% samples :75.5% integration :4.7% samples :75.6% integration :22.7% samples :75.6% integration :48.7% samples :75.7% integration :66.3% samples :75.8% integration :96.7% samples :75.9% integration :99.7% samples :75.9% integration :58.0% samples :76.0% integration :74.0% samples :76.0% integration :64.3% samples :76.1% integration :90.3% samples :76.2% integration :99.7% samples :76.2% integration :22.3% samples :76.3% integration :44.3% samples :76.3% integration :99.7% samples :76.3% integration :93.3% samples :76.4% integration :99.7% samples :76.5% integration :39.7% samples :76.6% integration :72.0% samples :76.6% integration :99.7% samples :76.7% integration :22.3% samples :76.8% integration :58.0% samples :76.8% integration :91.7% samples :76.9% integration :9.7% samples :76.9% integration :99.7% samples :77.0% integration :97.0% samples :77.0% integration :99.0% samples :77.1% integration :0.0% samples :77.1% integration :47.3% samples :77.2% integration :99.7% samples :77.2% integration :79.0% samples :77.3% integration :8.0% samples :77.3% integration :99.7% samples :77.4% integration :61.3% samples :77.5% integration :85.3% samples :77.5% integration :68.7% samples :77.6% integration :0.0% samples :77.6% integration :99.7% samples :77.7% integration :97.7% samples :77.8% integration :32.7% samples :77.9% integration :0.7% samples :78.0% integration :33.0% samples :78.0% integration :99.7% samples :78.0% integration :54.7% samples :78.1% integration :86.7% samples :78.2% integration :2.3% samples :78.3% integration :21.3% samples :78.3% integration :99.7% samples :78.4% integration :90.3% samples :78.5% integration :13.3% samples :78.5% integration :99.7% samples :78.5% integration :67.0% samples :78.6% integration :99.7% samples :78.7% integration :66.0% samples :78.8% integration :87.0% samples :78.8% integration :4.0% samples :78.9% integration :34.7% samples :79.0% integration :62.3% samples :79.0% integration :10.0% samples :79.1% integration :44.3% samples :79.1% integration :99.7% samples :79.1% integration :89.7% samples :79.2% integration :99.7% samples :79.3% integration :70.0% samples :79.4% integration :95.7% samples :79.4% integration :99.7% samples :79.5% integration :11.3% samples :79.6% integration :41.3% samples :79.6% integration :99.7% samples :79.7% integration :77.0% samples :79.7% integration :99.7% samples :79.8% integration :82.3% samples :79.9% integration :9.7% samples :79.9% integration :99.7% samples :80.0% integration :22.0% samples :80.0% integration :99.7% samples :80.1% integration :49.7% samples :80.2% integration :79.3% samples :80.2% integration :90.3% samples :80.3% integration :16.0% samples :80.3% integration :99.7% samples :80.4% integration :81.7% samples :80.5% integration :8.3% samples :80.5% integration :99.7% samples :80.6% integration :80.7% samples :80.7% integration :99.7% samples :80.7% integration :61.7% samples :80.8% integration :86.0% samples :80.8% integration :99.7% samples :80.9% integration :0.3% samples :81.0% integration :29.7% samples :81.0% integration :50.3% samples :81.1% integration :83.0% samples :81.2% integration :99.7% samples :81.2% integration :91.3% samples :81.3% integration :20.7% samples :81.3% integration :4.7% samples :81.4% integration :26.3% samples :81.4% integration :99.7% samples :81.5% integration :99.0% samples :81.6% integration :12.7% samples :81.6% integration :99.7% samples :81.7% integration :18.0% samples :81.8% integration :48.0% samples :81.8% integration :33.0% samples :81.9% integration :60.0% samples :82.0% integration :14.7% samples :82.0% integration :43.0% samples :82.1% integration :85.3% samples :82.2% integration :95.0% samples :82.2% integration :25.7% samples :82.3% integration :19.7% samples :82.4% integration :43.7% samples :82.5% integration :71.7% samples :82.5% integration :99.7% samples :82.5% integration :29.3% samples :82.6% integration :4.7% samples :82.7% integration :32.0% samples :82.8% integration :60.0% samples :82.8% integration :99.7% samples :82.9% integration :25.0% samples :82.9% integration :99.7% samples :83.0% integration :1.7% samples :83.1% integration :28.3% samples :83.1% integration :99.7% samples :83.2% integration :41.7% samples :83.3% integration :74.3% samples :83.3% integration :36.7% samples :83.4% integration :63.3% samples :83.5% integration :34.0% samples :83.5% integration :55.7% samples :83.6% integration :74.7% samples :83.6% integration :99.7% samples :83.7% integration :0.0% samples :83.8% integration :0.3% samples :83.8% integration :38.0% samples :83.9% integration :71.0% samples :83.9% integration :99.7% samples :84.0% integration :7.7% samples :84.0% integration :99.7% samples :84.1% integration :31.3% samples :84.2% integration :42.3% samples :84.2% integration :1.7% samples :84.3% integration :44.3% samples :84.4% integration :99.7% samples :84.4% integration :74.3% samples :84.5% integration :91.7% samples :84.5% integration :99.7% samples :84.6% integration :36.3% samples :84.7% integration :57.3% samples :84.7% integration :23.7% samples :84.8% integration :43.0% samples :84.8% integration :99.7% samples :84.9% integration :62.0% samples :85.0% integration :69.0% samples :85.0% integration :3.3% samples :85.1% integration :19.0% samples :85.2% integration :42.7% samples :85.2% integration :70.7% samples :85.3% integration :96.0% samples :85.4% integration :24.7% samples :85.5% integration :57.0% samples :85.5% integration :86.0% samples :85.7% integration :10.0% samples :85.7% integration :41.7% samples :85.8% integration :74.0% samples :85.9% integration :0.0% samples :86.0% integration :99.7% samples :86.0% integration :99.7% samples :86.0% integration :91.0% samples :86.1% integration :15.7% samples :86.1% integration :49.3% samples :86.2% integration :62.0% samples :86.2% integration :87.0% samples :86.4% integration :3.7% samples :86.4% integration :99.7% samples :86.5% integration :59.7% samples :86.5% integration :80.7% samples :86.6% integration :18.3% samples :86.6% integration :25.0% samples :86.7% integration :99.7% samples :86.7% integration :67.7% samples :86.8% integration :88.3% samples :86.9% integration :34.3% samples :87.0% integration :33.7% samples :87.0% integration :99.7% samples :87.1% integration :29.7% samples :87.1% integration :44.7% samples :87.2% integration :99.7% samples :87.2% integration :85.0% samples :87.3% integration :72.3% samples :87.4% integration :20.7% samples :87.5% integration :56.0% samples :87.5% integration :99.7% samples :87.6% integration :15.0% samples :87.6% integration :17.3% samples :87.6% integration :99.7% samples :87.8% integration :16.0% samples :87.8% integration :99.7% samples :87.8% integration :31.0% samples :87.9% integration :60.3% samples :87.9% integration :55.7% samples :88.0% integration :73.3% samples :88.1% integration :99.7% samples :88.1% integration :79.7% samples :88.2% integration :10.7% samples :88.3% integration :23.0% samples :88.3% integration :64.7% samples :88.4% integration :99.7% samples :88.4% integration :35.0% samples :88.5% integration :54.0% samples :88.6% integration :40.7% samples :88.6% integration :64.7% samples :88.7% integration :59.3% samples :88.8% integration :99.0% samples :88.8% integration :32.0% samples :88.9% integration :0.0% samples :89.0% integration :26.3% samples :89.0% integration :36.0% samples :89.1% integration :73.7% samples :89.1% integration :95.7% samples :89.2% integration :99.7% samples :89.2% integration :99.3% samples :89.3% integration :36.7% samples :89.4% integration :41.0% samples :89.5% integration :53.7% samples :89.5% integration :99.7% samples :89.5% integration :73.3% samples :89.6% integration :90.3% samples :89.6% integration :99.7% samples :89.7% integration :52.0% samples :89.8% integration :99.7% samples :89.8% integration :51.7% samples :89.9% integration :71.7% samples :90.0% integration :24.3% samples :90.0% integration :50.7% samples :90.1% integration :65.7% samples :90.1% integration :15.3% samples :90.2% integration :51.0% samples :90.3% integration :55.7% samples :90.3% integration :90.0% samples :90.4% integration :99.7% samples :90.5% integration :10.3% samples :90.5% integration :36.3% samples :90.6% integration :2.3% samples :90.6% integration :25.7% samples :90.7% integration :50.7% samples :90.7% integration :99.7% samples :90.8% integration :3.7% samples :90.8% integration :99.7% samples :90.9% integration :49.7% samples :91.0% integration :66.0% samples :91.0% integration :99.7% samples :91.1% integration :14.0% samples :91.2% integration :99.7% samples :91.2% integration :41.7% samples :91.3% integration :63.0% samples :91.4% integration :62.0% samples :91.5% integration :94.7% samples :91.5% integration :99.7% samples :91.6% integration :54.0% samples :91.6% integration :85.0% samples :91.7% integration :99.7% samples :91.8% integration :45.3% samples :91.8% integration :80.0% samples :91.9% integration :13.3% samples :92.0% integration :27.3% samples :92.0% integration :99.7% samples :92.1% integration :20.3% samples :92.2% integration :48.3% samples :92.2% integration :7.0% samples :92.2% integration :33.0% samples :92.3% integration :18.3% samples :92.4% integration :43.3% samples :92.5% integration :64.7% samples :92.5% integration :15.7% samples :92.6% integration :41.3% samples :92.7% integration :99.7% samples :92.7% integration :51.7% samples :92.8% integration :69.7% samples :92.8% integration :99.7% samples :92.9% integration :38.0% samples :92.9% integration :99.7% samples :93.0% integration :53.7% samples :93.1% integration :57.0% samples :93.1% integration :68.0% samples :93.2% integration :97.7% samples :93.3% integration :22.3% samples :93.3% integration :79.3% samples :93.4% integration :99.7% samples :93.5% integration :32.7% samples :93.5% integration :65.3% samples :93.6% integration :85.3% samples :93.7% integration :99.7% samples :93.8% integration :16.0% samples :93.8% integration :99.7% samples :93.8% integration :49.3% samples :93.9% integration :72.7% samples :94.0% integration :34.0% samples :94.0% integration :56.3% samples :94.1% integration :99.7% samples :94.2% integration :53.0% samples :94.2% integration :76.0% samples :94.3% integration :73.3% samples :94.4% integration :96.3% samples :94.5% integration :99.7% samples :94.5% integration :4.7% samples :94.6% integration :28.7% samples :94.7% integration :64.3% samples :94.7% integration :94.0% samples :94.8% integration :25.0% samples :94.8% integration :99.7% samples :94.9% integration :83.0% samples :95.0% integration :99.7% samples :95.0% integration :21.3% samples :95.1% integration :35.0% samples :95.2% integration :60.0% samples :95.2% integration :77.3% samples :95.3% integration :99.7% samples :95.3% integration :65.0% samples :95.4% integration :88.3% samples :95.4% integration :99.7% samples :95.5% integration :28.7% samples :95.5% integration :99.7% samples :95.5% integration :99.7% samples :95.6% integration :10.7% samples :95.6% integration :99.7% samples :95.7% integration :37.0% samples :95.8% integration :49.0% samples :95.8% integration :10.0% samples :95.9% integration :42.3% samples :95.9% integration :99.7% samples :95.9% integration :63.3% samples :96.0% integration :86.3% samples :96.0% integration :99.7% samples :96.1% integration :5.7% samples :96.1% integration :99.7% samples :96.2% integration :42.7% samples :96.2% integration :65.0% samples :96.2% integration :99.7% samples :96.3% integration :72.0% samples :96.4% integration :99.7% samples :96.4% integration :91.7% samples :96.5% integration :23.7% samples :96.5% integration :99.7% samples :96.6% integration :43.7% samples :96.6% integration :99.7% samples :96.7% integration :59.0% samples :96.7% integration :81.3% samples :96.8% integration :99.7% samples :96.8% integration :86.7% samples :96.9% integration :99.7% samples :96.9% integration :13.0% samples :97.0% integration :43.7% samples :97.0% integration :99.7% samples :97.0% integration :62.0% samples :97.1% integration :75.3% samples :97.1% integration :99.7% samples :97.2% integration :5.0% samples :97.2% integration :99.7% samples :97.3% integration :19.0% samples :97.4% integration :48.7% samples :97.4% integration :99.7% samples :97.5% integration :80.7% samples :97.5% integration :99.7% samples :97.5% integration :94.0% samples :97.6% integration :0.7% samples :97.6% integration :99.7% samples :97.7% integration :41.3% samples :97.8% integration :99.7% samples :97.8% integration :44.3% samples :97.9% integration :67.7% samples :97.9% integration :99.7% samples :97.9% integration :99.0% samples :98.0% integration :99.7% samples :98.0% integration :11.0% samples :98.1% integration :26.0% samples :98.1% integration :99.7% samples :98.2% integration :65.7% samples :98.2% integration :94.0% samples :98.2% integration :99.7% samples :98.3% integration :48.7% samples :98.4% integration :77.7% samples :98.5% integration :5.3% samples :98.5% integration :26.7% samples :98.6% integration :50.7% samples :98.7% integration :74.0% samples :98.8% integration :96.7% samples :98.9% integration :22.0% samples :98.9% integration :48.7% samples :99.0% integration :99.7% samples :99.0% integration :19.3% samples :99.1% integration :90.3% samples :99.1% integration :30.7% samples :99.2% integration :59.3% samples :99.2% integration :68.7% samples :99.3% integration :94.7% samples :99.4% integration :36.7% samples :99.4% integration :99.7% samples :99.5% integration :23.0% samples :99.6% integration :99.7% samples :99.6% integration :39.7% samples :99.7% integration :68.7% samples :99.8% integration :51.3% samples :99.8% integration :76.7% samples :99.9% integration :99.7% samples :99.9% integration :98.0% samples : 100% integration :0.0%  #+end_example Get the samples. #+BEGIN_SRC jupyter-python # to access the data the 'hi_key' is used to find the data in the hdf5 file class int_result: with hierarchyData.HIMetaData( hid_name="energy_flow_therm_new_again_less.data", hid_path="data" ) as metaData: with metaData.get_HIData(hi_key, read_only=True) as data: smp = data.get_samples() print("{} samples found in database".format(smp)) τ = data.get_time() rho_τ = data.get_rho_t() #s_proc = np.array(data.stoc_proc) #states = np.array(data.aux_states).copy() ψ_1 = np.array(data.aux_states[:, :, 0 : params.num_exp_t * params.dim]) ψ_0 = np.array(data.stoc_traj) y = np.array(data.y) #η = np.array(data.stoc_proc) temp_y = np.array(data.temp_y) #+end_src #+RESULTS: : 4000 samples found in database Calculate energy. #+begin_src jupyter-python %matplotlib inline energy = np.einsum("ijk,kj", int_result.rho_τ,params.H_s).real plt.plot(int_result.τ, energy) #+end_src #+RESULTS: :RESULTS: | | [[file:./.ob-jupyter/8e6031964f047808246e7cc787bff3a3133b953e.png]] :END: * Energy Flow :PROPERTIES: :ID: 9ce93da8-d323-40ec-96a2-42ba184dc963 :END: #+begin_src jupyter-python int_result.ψ_1.shape #+end_src #+RESULTS: | 5120 | 300 | 8 | Let's look at the norm. #+begin_src jupyter-python plt.plot(int_result.τ, (int_result.ψ_0[0].conj() * int_result.ψ_0[0]).sum(axis=1).real) #+end_src #+RESULTS: :RESULTS: | | [[file:./.ob-jupyter/46197d5b229e031e905aea1a0f5b517e977f711d.png]] :END: And try to calculate the energy flow. #+begin_src jupyter-python def flow_for_traj(ψ_0, ψ_1, temp_y): a = np.array((params.L @ ψ_0.T).T) EtaTherm.new_process(temp_y) η_dot = scipy.misc.derivative(EtaTherm, int_result.τ, dx=1e-3, order=5) ψ_1 = (-w * g * params.bcf_scale)[None, :, None] * ψ_1.reshape( params.t_steps, params.num_exp_t, params.dim ) # return np.array(np.sum(ψ_0.conj() * ψ_0, axis=1)).flatten().real j_0 = np.array( 2 ,* ( 1j ,* (np.sum(a.conj()[:, None, :] * ψ_1, axis=(1, 2))) / np.sum(ψ_0.conj() * ψ_0, axis=1) ).real ).flatten() j_therm = np.array( 2 ,* ( 1j ,* (np.sum(a.conj() * ψ_0, axis=1)) * η_dot / np.sum(ψ_0.conj() * ψ_0, axis=1) ).real ).flatten() return j_0, j_therm #+end_src #+RESULTS: Now we calculate the average over all trajectories. #+begin_src jupyter-python class Flow: j_0 = np.zeros_like(int_result.τ) j_therm = np.zeros_like(int_result.τ) for i in range(0, params.N): dj, dj_therm = flow_for_traj( int_result.ψ_0[i], int_result.ψ_1[i], int_result.temp_y[i] ) j_0 += dj j_therm += dj_therm j_0 /= params.N j_therm /= params.N j = j_0 + j_therm #+end_src #+RESULTS: And plot it :). #+begin_src jupyter-python %matplotlib inline plt.plot(int_result.τ, Flow.j_0, label=r"$j_0$") plt.plot(int_result.τ, Flow.j_therm, label=r"$j_\mathrm{therm}$") plt.plot(int_result.τ, Flow.j, label=r"$j$") plt.legend() #+end_src #+RESULTS: :RESULTS: : [[file:./.ob-jupyter/5a475f8087beb6abe79b48efe888fe5c4e4e182d.png]] :END: Let's calculate the integrated energy. #+begin_src jupyter-python E_t = np.array( [0] + [ scipy.integrate.simpson(Flow.j[0:n], int_result.τ[0:n]) for n in range(1, len(int_result.τ)) ] ) E_t[-1] #+end_src #+RESULTS: : 0.18349268980598232 With this we can retrieve the energy of the interaction Hamiltonian. #+begin_src jupyter-python E_I = - energy - E_t #+end_src #+RESULTS: #+begin_src jupyter-python %%space plot #plt.plot(τ, j, label="$J$", linestyle='--') plt.plot(int_result.τ, E_t, label=r"$\langle H_{\mathrm{B}}\rangle$") plt.plot(int_result.τ, E_I, label=r"$\langle H_{\mathrm{I}}\rangle$") plt.plot(int_result.τ, energy, label=r"$\langle H_{\mathrm{S}}\rangle$") plt.xlabel("τ") plt.legend() plt.show() #+end_src #+RESULTS: :RESULTS: | | | | | | : Text(0.5, 0, 'τ') : [[file:./.ob-jupyter/070f131d17f8426b384f26f16434edde81064452.png]] :END: * System + Interaction Energy #+begin_src jupyter-python def h_si_for_traj(ψ_0, ψ_1, temp_y): a = np.array((params.L @ ψ_0.T).T) b = np.array((params.H_s @ ψ_0.T).T) ψ_1 = (g*params.bcf_scale)[None, :, None] * ψ_1.reshape( params.t_steps, params.num_exp_t, params.dim ) EtaTherm.new_process(temp_y) E_i = np.array( 2 ,* ( -1j ,* np.sum( a.conj()[:, None, :] ,* ψ_1, axis=(1, 2), ) ).real ).flatten() E_i += np.array( 2 ,* ( EtaTherm(int_result.τ) ,* np.sum( a.conj() ,* ψ_0, axis=1, ) ).real ).flatten() E_s = np.array(np.sum(b.conj() * ψ_0, axis=1)).flatten().real return (E_i + E_s) / np.sum(ψ_0.conj() * ψ_0, axis=1).real #+end_src #+RESULTS: #+begin_src jupyter-python e_si = np.zeros_like(int_result.τ) for i in range(0, params.N): e_si += h_si_for_traj(int_result.ψ_0[i], int_result.ψ_1[i], int_result.temp_y[i]) e_si /= params.N #+end_src #+RESULTS: Doesn't work out. #+begin_src jupyter-python plt.plot(int_result.τ, e_si -energy, label=r"direct") plt.plot(int_result.τ, E_I) plt.legend() #+end_src #+RESULTS: :RESULTS: : [[file:./.ob-jupyter/5d121c7f9496bd6f69931ad6252f2ae57660bd48.png]] :END: