diff --git a/.gitignore b/.gitignore index 2dad9f1..7d9dc53 100644 --- a/.gitignore +++ b/.gitignore @@ -481,3 +481,5 @@ TSWLatexianTemp* __*.data *.pdf +/python/richard_hops/data +ltximg diff --git a/.gitmodules b/.gitmodules new file mode 100644 index 0000000..23ca481 --- /dev/null +++ b/.gitmodules @@ -0,0 +1,3 @@ +[submodule "python/energy_flow_proper/hops"] + path = python/energy_flow_proper/hops + url = git@gitlab.hrz.tu-chemnitz.de:s4498638--tu-dresden.de/hops.git diff --git a/project.org b/project.org index da90eab..7f44710 100644 --- a/project.org +++ b/project.org @@ -61,7 +61,6 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] => 4:12 :END: - see [[file:python/experiments/stochproc/test_stoch.org][my stoch. proc experiments]] - ill use [[https://github.com/cimatosa/stocproc/tree/master/stocproc][richards]] package -** Find the Steady State ** Quantify Heat Transfer - not as easy as in the cite:Kato2015Aug paper - maybe heisenberg picture useful @@ -97,6 +96,7 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] => 4:12 *** TODO Analytic Verification - cummings - and pseudo-mode +**** TODO Valentin's QMB Gaussian states *** DONE figure out why means involving the stoch. process are so bad - maybe y is wrong -> no - then: not differentiable + too noisy @@ -104,9 +104,6 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] => 4:12 - my test with the gauss process was tupid -> no sum of exponentials - it works with proper smooth process: [[id:2872b2db-5d3d-470d-8c35-94aca6925f14][Energy Flow in the linear case with smooth correlation...]] -**** ASK -- why do i have to take the conjugate of the process? - *** DONE VORTRAG - https://www.youtube.com/watch?v=5bRii85RT8s&list=PLJfdTiUFX4cNiK44-ScthZC2SNNrtUGu1&index=33; - where do i find out more about \(C^\ast\) algebras? @@ -118,8 +115,10 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] => 4:12 - Initial time: \(E_{\text {int }}(0):=\operatorname{Tr}\left[\rho_{\mathrm{S}}(0) H_{\mathrm{S}}\right] \quad\left(H_{\mathrm{S}}^{\circledast}(0, \beta)=H_{\mathrm{S}}\right)\) *** TODO Compare with Rivas Method *** DONE Find Rivas Paper +*** TODO Make proper library +*** TODO Adapt New HOPS - [[id:64c775a3-860e-479d-8b08-904dc210991d][Strong coupling thermodynamics of open quantum systems]] -** Rivas Vortrag +** Find the Steady State ** Matrix Eigenvals - see cite:Pan1999May ** Relation between coerrelation time and hops depth diff --git a/python/richard_hops/energy_flow_nonlinear.org b/python/richard_hops/energy_flow_nonlinear.org index 94cc162..ceb2e4d 100644 --- a/python/richard_hops/energy_flow_nonlinear.org +++ b/python/richard_hops/energy_flow_nonlinear.org @@ -9,10 +9,6 @@ #+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 @@ -106,9 +102,9 @@ Basic parameters. #+RESULTS: :RESULTS: -| | -| | -| | +| | +| | +| | [[file:./.ob-jupyter/cc8a82c1bde6ea1912c1b977e822908ef92ed79a.png]] :END: @@ -298,1065 +294,13 @@ Run the integration. #+end_src #+RESULTS: -#+begin_example - samples :0.0% - integration :0.0% - samples :50.0% - integration :90.5% - samples :50.1% - integration :98.6% - samples :50.3% - integration :3.0% - samples :50.4% - integration :4.1% - samples :50.5% - integration :5.9% - samples :50.6% - integration :14.8% - samples :50.7% - integration :25.1% - samples :50.8% - integration :34.7% - samples :50.9% - integration :44.0% - samples :51.0% - integration :50.7% - samples :51.1% - integration :56.9% - samples :51.2% - integration :67.1% - samples :51.3% - integration :76.0% - samples :51.4% - integration :87.7% - samples :51.5% - integration :94.7% - samples :51.7% - integration :2.0% - samples :51.8% - integration :5.3% - 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samples :97.7% - integration :23.0% - samples :97.7% - integration :96.5% - samples :97.8% - integration :53.8% - samples :97.9% - integration :25.5% - samples :97.9% - integration :97.0% - samples :98.0% - integration :62.2% - samples :98.1% - integration :29.8% - samples :98.2% - integration :1.6% - samples :98.3% - integration :4.1% - samples :98.4% - integration :2.8% - samples :98.4% - integration :67.4% - samples :98.5% - integration :33.6% - samples :98.6% - integration :4.4% - samples :98.6% - integration :69.5% - samples :98.7% - integration :38.0% - samples :98.8% - integration :23.4% - samples :98.9% - integration :2.7% - samples :98.9% - integration :58.5% - samples :99.0% - integration :26.7% - samples :99.1% - integration :4.6% - samples :99.1% - integration :63.2% - samples :99.2% - integration :12.8% - samples :99.2% - integration :83.4% - samples :99.3% - integration :45.0% - samples :99.4% - integration :10.1% - samples :99.5% - integration :10.3% - samples :99.6% - integration :0.2% - samples :99.6% - integration :77.5% - samples :99.7% - integration :45.7% - samples :99.8% - integration :20.7% - samples :99.9% - integration :21.7% - samples : 100% - integration :0.0% -  -#+end_example +: samples :0.0% +: integration :0.0% +: samples :49.0% +: integration :0.0% +: samples : 100% +: integration :0.0% +:  Get the samples. @@ -1382,13 +326,14 @@ Get the samples. Calculate energy. #+begin_src jupyter-python %matplotlib inline + import qutip energy = np.array([np.trace(ρ @ H_s).real for ρ in rho_τ]) plt.plot(τ, energy) #+end_src #+RESULTS: :RESULTS: -| | +| | [[file:./.ob-jupyter/6f9ff44b906cf57c7c84d88a0a157cc66b911965.png]] :END: @@ -1399,7 +344,7 @@ Calculate energy. #+RESULTS: :RESULTS: -| | +| | [[file:./.ob-jupyter/f3f9c51e9054713cfd1c1c767658d98df3b5a747.png]] :END: @@ -1421,7 +366,7 @@ Let's look at the norm. #+RESULTS: :RESULTS: -| | +| | [[file:./.ob-jupyter/410aaf67c52a948f72fac9345da5fb6cedf4889d.png]] :END: diff --git a/python/richard_hops/energy_flow_thermal.org b/python/richard_hops/energy_flow_thermal.org index 63a464c..878b378 100644 --- a/python/richard_hops/energy_flow_thermal.org +++ b/python/richard_hops/energy_flow_thermal.org @@ -1,4 +1,4 @@ -#+PROPERTY: header-args :session /ssh:l:/home/hiro/.local/share/jupyter/runtime/kernel-db283c80-f40c-4ded-8b78-99c9efe3be3c.json :kernel python :pandoc t :async yes +#+PROPERTY: header-args :session /ssh:l:/home/hiro/.local/share/jupyter/runtime/kernel-b0451759-0699-4f14-8dd0-8e96ed3cfa21.json :kernel python :pandoc t :async yes * Setup ** Jupyter @@ -11,6 +11,8 @@ #+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 @@ -59,8 +61,8 @@ Basic parameters. class params: T = 2 - t_max = 15 - t_steps = int(t_max * 1/.05) + t_max = 2 + t_steps = int(t_max * 1/.001) k_max = 10 N = 4000 @@ -178,7 +180,7 @@ Let's look a the result. #+end_src #+RESULTS: -[[file:./.ob-jupyter/9f05a1fbf06920c271f0667db664ce2972415437.png]] +[[file:./.ob-jupyter/94716da4c1c533b5ae91de94ef8e00707e7da233.png]] Seems ok for now. ** Hops setup @@ -251,31 +253,24 @@ The quantum noise. #+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 - acc interp N 33 dt 1.25e-01 -> diff 4.49e-03 + stocproc.method_ft - INFO - acc interp N 65 dt 6.25e-02 -> diff 1.08e-03 + stocproc.method_ft - INFO - acc interp N 129 dt 3.12e-02 -> diff 2.69e-04 + stocproc.method_ft - INFO - requires dt < 3.125e-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-03 N 32 yields: interval [0.00e+00,9.12e+00] diff 3.11e-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 - J_w_min:1.00e-04 N 32 yields: interval [0.00e+00,1.17e+01] diff 5.62e-03 + stocproc.method_ft - INFO - J_w_min:1.00e-03 N 64 yields: interval [0.00e+00,9.12e+00] diff 7.23e-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.method_ft - INFO - requires dx < 1.425e-01 + stocproc.stocproc - INFO - Fourier Integral Boundaries: [0.000e+00, 2.422e+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 + stocproc.stocproc - INFO - yields dx : 1.183e-01 + stocproc.stocproc - INFO - yields dt : 2.594e-02 + stocproc.stocproc - INFO - yields t_max : 5.310e+01 #+end_example The sample trajectories are smooth. @@ -288,8 +283,8 @@ The sample trajectories are smooth. #+RESULTS: :RESULTS: -| | -[[file:./.ob-jupyter/10385a90753d7683d5740b88622cc4274de9c86a.png]] +| | +[[file:./.ob-jupyter/4e525ff2fa6e494fb3abab758809f3f335b7cf0e.png]] :END: And now the thermal noise. @@ -310,34 +305,27 @@ And now the thermal noise. #+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 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 - acc interp N 33 dt 1.25e-01 -> diff 8.75e-04 + stocproc.method_ft - INFO - requires dt < 1.250e-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 32 yields: interval [0.00e+00,4.10e+00] diff 9.15e-03 + stocproc.method_ft - INFO - J_w_min:1.00e-03 N 32 yields: interval [0.00e+00,5.82e+00] diff 4.69e-03 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 - J_w_min:1.00e-04 N 32 yields: interval [0.00e+00,7.50e+00] diff 9.58e-03 + stocproc.method_ft - INFO - J_w_min:1.00e-03 N 64 yields: interval [0.00e+00,5.82e+00] diff 1.59e-03 + 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 - 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+00,9.16e+00] diff 1.27e-02 + stocproc.method_ft - INFO - J_w_min:1.00e-04 N 64 yields: interval [0.00e+00,7.50e+00] diff 2.38e-03 + stocproc.method_ft - INFO - J_w_min:1.00e-03 N 128 yields: interval [0.00e+00,5.82e+00] diff 9.47e-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.method_ft - INFO - requires dx < 4.544e-02 + stocproc.stocproc - INFO - Fourier Integral Boundaries: [0.000e+00, 6.839e+01] + stocproc.stocproc - INFO - Number of Nodes : 2048 + stocproc.stocproc - INFO - yields dx : 3.340e-02 + stocproc.stocproc - INFO - yields dt : 9.187e-02 + stocproc.stocproc - INFO - yields t_max : 1.881e+02 #+end_example The sample trajectories are smooth too. @@ -350,8 +338,8 @@ The sample trajectories are smooth too. #+RESULTS: :RESULTS: -| | -[[file:./.ob-jupyter/6d082076097694cb45a42d4608ed411592bfcd3e.png]] +| | +[[file:./.ob-jupyter/7c2fb11537e9382b65fdbc4225025dce060892b9.png]] :END: * Actual Hops @@ -374,9 +362,9 @@ Initialize Hierarchy. #+end_src #+RESULTS: -: init Hi class, use 2002 equation : /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 @@ -384,13 +372,21 @@ Run the integration. #+end_src #+RESULTS: -: samples :[TET 5.48ms [0.0c/s] TTG -- 0.0% ETA -- ORT --] -: integration :[TET 5.28ms [0.0c/s] TTG -- 0.0% ETA -- ORT --] -: samples :[TET-2.01s---[866.5c/s]-TTG-3.00s-------------> 43.5% ETA 20211103_10:49:30 ORT 5.01s] -: integration :[TET 1.71ms [0.0c/s] TTG -- 0.0% ETA -- ORT --] -: samples :[TET-4.00s---[999.5c/s]-TTG-0.00ms------------------100%-------------------ETA-20211103_10:49:29-ORT-4.00s] -: integration :[TET 3.71ms [0.0c/s] TTG -- 0.0% ETA -- ORT --] -:  +#+begin_example + samples :[TET 5.52ms [0.0c/s] TTG -- 0.0% ETA -- ORT --] + integration :[TET 5.32ms [0.0c/s] TTG -- 0.0% ETA -- ORT --] + samples :[E-2.01s---[428.3c/s] G 8.00s 21.5% A 20211104_10:14:07 O 00:00:10] + integration :[TET 7.05ms [0.0c/s] TTG -- 0.0% ETA -- ORT --] + samples :[E-4.01s---[451.3c/s]-G-5.00s->45.2% A 20211104_10:14:06 O 9.01s] + integration :[TET 19.33ms [0.0c/s] TTG -- 0.0% ETA -- ORT --] + samples :[E-6.01s---[455.7c/s]-G-3.00s--68.5%---A-20211104_10:14:06 O 9.01s] + integration :[TET 27.20ms [0.0c/s] TTG -- 0.0% ETA -- ORT --] + samples :[E-8.02s---[456.6c/s]-G-1.00s--91.5%---A-20211104_10:14:06-O>9.02s] + integration :[TET 19.95ms [0.0c/s] TTG -- 0.0% ETA -- ORT --] + samples :[E-8.75s---[457.4c/s]-G-0.00ms--100%---A-20211104_10:14:06-O-8.75s] + integration :[TET 4.00ms [0.0c/s] TTG -- 0.0% ETA -- ORT --] +  +#+end_example Get the samples. #+BEGIN_SRC jupyter-python @@ -425,8 +421,8 @@ Calculate energy. #+RESULTS: :RESULTS: -| | -[[file:./.ob-jupyter/8e6031964f047808246e7cc787bff3a3133b953e.png]] +| | +[[file:./.ob-jupyter/b02f05ff976469eb5f86581f73e361ba4169d4ee.png]] :END: * Energy Flow @@ -438,7 +434,7 @@ Calculate energy. #+end_src #+RESULTS: -| 5120 | 300 | 8 | +| 5120 | 2000 | 8 | Let's look at the norm. #+begin_src jupyter-python @@ -447,17 +443,17 @@ Let's look at the norm. #+RESULTS: :RESULTS: -| | -[[file:./.ob-jupyter/46197d5b229e031e905aea1a0f5b517e977f711d.png]] +| | +[[file:./.ob-jupyter/89c2992c07948ad101e60c83c395c1767e351af7.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) + b = np.array(((params.L @ params.H_s - params.H_s @ 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) - + η_dot = scipy.misc.derivative(EtaTherm, int_result.τ, dx=1e-3, order=3) ψ_1 = (-w * g * params.bcf_scale)[None, :, None] * ψ_1.reshape( params.t_steps, params.num_exp_t, params.dim ) @@ -475,12 +471,30 @@ And try to calculate the energy flow. j_therm = -np.array( 2 ,* ( - (np.sum(a.conj() * ψ_0, axis=1)) * η_dot + (np.sum(a.conj() * ψ_0, axis=1)) * η_dot / np.sum(ψ_0.conj() * ψ_0, axis=1) + ).real + ).flatten() + + shift_energy = ( + 2 + ,* ( + EtaTherm(int_result.τ) + ,* np.sum(a.conj() * ψ_0, axis=1) / np.sum(ψ_0.conj() * ψ_0, axis=1) ).real ).flatten() - return j_0, j_therm + shift_energy_normal = ( + 2 + ,* (1j * + EtaTherm(int_result.τ) * + (np.sum(b.conj() * ψ_0, axis=1)) + / np.sum(ψ_0.conj() * ψ_0, axis=1) + ).real + ).flatten() + + j_therm_alt = np.gradient(shift_energy, int_result.τ, edge_order=2) + return j_0, j_therm, j_therm_alt + shift_energy_normal #+end_src #+RESULTS: @@ -490,15 +504,18 @@ Now we calculate the average over all trajectories. class Flow: j_0 = np.zeros_like(int_result.τ) j_therm = np.zeros_like(int_result.τ) + j_therm_alt = np.zeros_like(int_result.τ) for i in range(0, params.N): - dj, dj_therm = flow_for_traj( + dj, dj_therm, dj_therm_alt = 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_therm_alt += dj_therm_alt j_0 /= params.N j_therm /= params.N + j_therm_alt /= params.N j = j_0 + j_therm #+end_src @@ -510,14 +527,15 @@ And plot it :). %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_therm_alt, label=r"$j_\mathrm{therm}^\mathrm{alt}$") plt.plot(int_result.τ, Flow.j, label=r"$j$") plt.legend() #+end_src #+RESULTS: :RESULTS: -: -[[file:./.ob-jupyter/8ee454c5d5d79c6ebc664d4e6c9fa86ddd22d76b.png]] +: +[[file:./.ob-jupyter/a11b670c1a122ed76028d9bd56c9ff33d49f4521.png]] :END: Let's calculate the integrated energy. @@ -533,7 +551,7 @@ Let's calculate the integrated energy. #+end_src #+RESULTS: -: 0.2055296100424721 +: 0.1557882146641204 With this we can retrieve the energy of the interaction Hamiltonian. #+begin_src jupyter-python @@ -556,12 +574,12 @@ With this we can retrieve the energy of the interaction Hamiltonian. #+RESULTS: :RESULTS: -| | -| | -| | +| | +| | +| | : Text(0.5, 0, 'τ') -: -[[file:./.ob-jupyter/4667ed4d0c34454379b42baac0449563ea26df93.png]] +: +[[file:./.ob-jupyter/4019e2cde4e898f0a3174476803a78debd331d90.png]] :END: * System + Interaction Energy @@ -600,7 +618,7 @@ With this we can retrieve the energy of the interaction Hamiltonian. 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 + return (E_i + E_s * 0) / np.sum(ψ_0.conj() * ψ_0, axis=1).real #+end_src #+RESULTS: @@ -616,7 +634,7 @@ With this we can retrieve the energy of the interaction Hamiltonian. 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_si, label=r"direct") plt.plot(int_result.τ, E_I) plt.legend() #+end_src @@ -624,6 +642,6 @@ Doesn't work out. #+RESULTS: :RESULTS: -: -[[file:./.ob-jupyter/c8c68dc3ee919f1306e4df7b284c3de1d8d24e8e.png]] +: +[[file:./.ob-jupyter/7b84ba5527e25086a3b332b30c87a195c3e767c0.png]] :END: diff --git a/python/richard_hops/energy_flow_thermal_lin.org b/python/richard_hops/energy_flow_thermal_lin.org index 83d6c2e..3f3e438 100644 --- a/python/richard_hops/energy_flow_thermal_lin.org +++ b/python/richard_hops/energy_flow_thermal_lin.org @@ -9,8 +9,6 @@ #+end_src #+RESULTS: -: The autoreload extension is already loaded. To reload it, use: -: %reload_ext autoreload ** Matplotlib #+begin_src jupyter-python @@ -59,10 +57,10 @@ Basic parameters. class params: T = 2.09 - t_max = 4 + t_max = 1 t_steps = int(t_max * 1/.01) k_max = 3 - N = 4000 + N = 17 seed = 100 dim = 2 @@ -178,7 +176,7 @@ Let's look a the result. #+end_src #+RESULTS: -[[file:./.ob-jupyter/3abd0a6ad02389d5ec933b1d83115fb4fc204dbf.png]] +[[file:./.ob-jupyter/8aef9360013cb6fc910354f4a0876034bbc0f184.png]] Seems ok for now. ** Hops setup @@ -251,35 +249,33 @@ The quantum noise. #+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 2.50e-01 -> diff 2.04e-02 - stocproc.method_ft - INFO - acc interp N 65 dt 1.25e-01 -> diff 4.49e-03 - stocproc.method_ft - INFO - acc interp N 129 dt 6.25e-02 -> diff 1.08e-03 - stocproc.method_ft - INFO - acc interp N 257 dt 3.12e-02 -> diff 2.69e-04 - stocproc.method_ft - INFO - acc interp N 513 dt 1.56e-02 -> diff 6.71e-05 + stocproc.method_ft - INFO - acc interp N 33 dt 6.25e-02 -> diff 1.08e-03 + stocproc.method_ft - INFO - acc interp N 65 dt 3.12e-02 -> diff 2.69e-04 + stocproc.method_ft - INFO - acc interp N 129 dt 1.56e-02 -> diff 6.71e-05 stocproc.method_ft - INFO - requires dt < 1.562e-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 3.58e-03 + stocproc.method_ft - INFO - J_w_min:1.00e-03 N 32 yields: interval [0.00e+00,9.12e+00] diff 2.72e-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 6.45e-03 - stocproc.method_ft - INFO - J_w_min:1.00e-03 N 64 yields: interval [0.00e+00,9.12e+00] diff 8.35e-04 + stocproc.method_ft - INFO - J_w_min:1.00e-04 N 32 yields: interval [0.00e+00,1.17e+01] diff 5.41e-03 + stocproc.method_ft - INFO - J_w_min:1.00e-03 N 64 yields: interval [0.00e+00,9.12e+00] diff 5.54e-04 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 1.05e-02 - stocproc.method_ft - INFO - J_w_min:1.00e-04 N 64 yields: interval [0.00e+00,1.17e+01] diff 1.43e-03 + stocproc.method_ft - INFO - J_w_min:1.00e-05 N 32 yields: interval [0.00e+00,1.42e+01] diff 8.13e-03 + stocproc.method_ft - INFO - J_w_min:1.00e-04 N 64 yields: interval [0.00e+00,1.17e+01] diff 1.30e-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 - J_w_min:1.00e-02 N 256 yields: interval [0.00e+00,6.47e+00] diff 1.15e-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-06 N 32 yields: interval [0.00e+00,1.66e+01] diff 1.54e-02 - stocproc.method_ft - INFO - J_w_min:1.00e-05 N 64 yields: interval [0.00e+00,1.42e+01] diff 2.18e-03 - stocproc.method_ft - INFO - J_w_min:1.00e-04 N 128 yields: interval [0.00e+00,1.17e+01] diff 3.44e-04 + stocproc.method_ft - INFO - J_w_min:1.00e-06 N 32 yields: interval [0.00e+00,1.66e+01] diff 1.11e-02 + stocproc.method_ft - INFO - J_w_min:1.00e-05 N 64 yields: interval [0.00e+00,1.42e+01] diff 2.03e-03 + stocproc.method_ft - INFO - J_w_min:1.00e-04 N 128 yields: interval [0.00e+00,1.17e+01] diff 2.69e-04 stocproc.method_ft - INFO - J_w_min:1.00e-03 N 256 yields: interval [0.00e+00,9.12e+00] diff 1.06e-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-07 N 32 yields: interval [0.00e+00,1.91e+01] diff 2.33e-02 - stocproc.method_ft - INFO - J_w_min:1.00e-06 N 64 yields: interval [0.00e+00,1.66e+01] diff 3.04e-03 - stocproc.method_ft - INFO - J_w_min:1.00e-05 N 128 yields: interval [0.00e+00,1.42e+01] diff 5.18e-04 - stocproc.method_ft - INFO - J_w_min:1.00e-04 N 256 yields: interval [0.00e+00,1.17e+01] diff 8.45e-05 + stocproc.method_ft - INFO - J_w_min:1.00e-07 N 32 yields: interval [0.00e+00,1.91e+01] diff 1.48e-02 + stocproc.method_ft - INFO - J_w_min:1.00e-06 N 64 yields: interval [0.00e+00,1.66e+01] diff 2.80e-03 + stocproc.method_ft - INFO - J_w_min:1.00e-05 N 128 yields: interval [0.00e+00,1.42e+01] diff 5.04e-04 + stocproc.method_ft - INFO - J_w_min:1.00e-04 N 256 yields: interval [0.00e+00,1.17e+01] diff 4.76e-05 stocproc.method_ft - INFO - return, cause tol of 0.0001 was reached stocproc.method_ft - INFO - requires dx < 4.557e-02 stocproc.stocproc - INFO - Fourier Integral Boundaries: [0.000e+00, 5.480e+02] @@ -299,8 +295,8 @@ The sample trajectories are smooth. #+RESULTS: :RESULTS: -| | -[[file:./.ob-jupyter/a0e1c0f89b5156debf397da1b99611475940605e.png]] +| | +[[file:./.ob-jupyter/e263d6d8b8147ea9a2e498b427f567ba34a2b6a7.png]] :END: And now the thermal noise. @@ -321,26 +317,26 @@ And now the thermal noise. #+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 2.50e-01 -> diff 3.75e-03 - stocproc.method_ft - INFO - acc interp N 65 dt 1.25e-01 -> diff 8.94e-04 - stocproc.method_ft - INFO - requires dt < 1.250e-01 + stocproc.method_ft - INFO - acc interp N 33 dt 6.25e-02 -> diff 2.21e-04 + stocproc.method_ft - INFO - requires dt < 6.250e-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+00,4.18e+00] diff 9.38e-03 - stocproc.method_ft - INFO - J_w_min:1.00e-03 N 32 yields: interval [0.00e+00,5.92e+00] diff 1.01e-02 + stocproc.method_ft - INFO - J_w_min:1.00e-03 N 32 yields: interval [0.00e+00,5.92e+00] diff 4.42e-03 stocproc.method_ft - INFO - J_w_min:1.00e-02 N 64 yields: interval [0.00e+00,4.18e+00] diff 8.00e-03 - stocproc.method_ft - INFO - J_w_min:1.00e-04 N 32 yields: interval [0.00e+00,7.62e+00] diff 1.77e-02 - stocproc.method_ft - INFO - J_w_min:1.00e-03 N 64 yields: interval [0.00e+00,5.92e+00] diff 2.35e-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-04 N 32 yields: interval [0.00e+00,7.62e+00] diff 7.37e-03 + stocproc.method_ft - INFO - J_w_min:1.00e-03 N 64 yields: interval [0.00e+00,5.92e+00] diff 1.66e-03 stocproc.method_ft - INFO - J_w_min:1.00e-02 N 128 yields: interval [0.00e+00,4.18e+00] diff 7.66e-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-05 N 32 yields: interval [0.00e+00,9.30e+00] diff 2.71e-02 - stocproc.method_ft - INFO - J_w_min:1.00e-04 N 64 yields: interval [0.00e+00,7.62e+00] diff 4.35e-03 + stocproc.method_ft - INFO - J_w_min:1.00e-05 N 32 yields: interval [0.00e+00,9.30e+00] diff 1.04e-02 + stocproc.method_ft - INFO - J_w_min:1.00e-04 N 64 yields: interval [0.00e+00,7.62e+00] diff 1.87e-03 stocproc.method_ft - INFO - J_w_min:1.00e-03 N 128 yields: interval [0.00e+00,5.92e+00] diff 9.72e-04 stocproc.method_ft - INFO - return, cause tol of 0.001 was reached stocproc.method_ft - INFO - requires dx < 4.622e-02 - stocproc.stocproc - INFO - Fourier Integral Boundaries: [0.000e+00, 6.898e+01] - stocproc.stocproc - INFO - Number of Nodes : 2048 + stocproc.stocproc - INFO - Fourier Integral Boundaries: [0.000e+00, 1.380e+02] + stocproc.stocproc - INFO - Number of Nodes : 4096 stocproc.stocproc - INFO - yields dx : 3.368e-02 - stocproc.stocproc - INFO - yields dt : 9.109e-02 + stocproc.stocproc - INFO - yields dt : 4.555e-02 stocproc.stocproc - INFO - yields t_max : 1.865e+02 #+end_example @@ -354,8 +350,8 @@ The sample trajectories are smooth too. #+RESULTS: :RESULTS: -| | -[[file:./.ob-jupyter/8a11e7589322c005ad1b68c72035dc4c859e97b1.png]] +| | +[[file:./.ob-jupyter/fa5c945d8f37080bcad16c6fda2ebe4221da87ae.png]] :END: * Actual Hops @@ -388,139 +384,12 @@ Run the integration. #+end_src #+RESULTS: -#+begin_example - samples :0.0% - integration :0.0% - samples :4.0% - integration :3.5% - samples :5.7% - integration :60.5% - samples :7.4% - integration :31.0% - samples :9.1% - integration :78.8% - samples :10.8% - integration :99.5% - samples :12.4% - integration :61.8% - samples :14.1% - integration :7.2% - samples :15.8% - integration :45.5% - samples :17.5% - integration :31.0% - samples :19.1% - integration :0.5% - samples :20.8% - integration :59.8% - samples :22.5% - integration :26.8% - samples :24.1% - integration :22.5% - samples :25.7% - integration :99.8% - samples :27.1% - integration :16.5% - samples :28.0% - integration :99.8% - samples :29.0% - integration :72.8% - samples :30.6% - integration :99.8% - samples :31.5% - integration :32.8% - samples :32.1% - integration :0.0% - samples :33.4% - integration :99.8% - samples :34.2% - integration :99.8% - samples :35.5% - integration :0.0% - samples :37.1% - integration :99.8% - samples :38.8% - integration :58.5% - samples :40.5% - integration :0.8% - samples :42.2% - integration :10.2% - samples :43.9% - integration :70.5% - samples :45.1% - integration :99.8% - samples :46.8% - integration :25.5% - samples :48.5% - integration :73.0% - samples :49.9% - integration :65.2% - samples :51.5% - integration :0.0% - samples :52.9% - integration :99.8% - samples :54.4% - integration :11.2% - samples :56.1% - integration :41.5% - samples :57.8% - integration :22.2% - samples :59.5% - integration :17.8% - samples :61.1% - integration :1.2% - samples :62.7% - integration :45.5% - samples :64.3% - integration :18.2% - samples :65.8% - integration :40.2% - samples :67.3% - integration :99.8% - samples :68.9% - integration :5.5% - samples :70.3% - integration :93.8% - samples :71.9% - integration :63.0% - samples :73.5% - integration :22.5% - samples :75.1% - integration :3.2% - samples :76.6% - integration :52.5% - samples :78.3% - integration :26.0% - samples :80.0% - integration :0.0% - samples :81.5% - integration :84.0% - samples :83.2% - integration :47.2% - samples :84.9% - integration :37.8% - samples :86.6% - integration :52.8% - samples :88.3% - integration :1.0% - samples :89.9% - integration :69.5% - samples :91.6% - integration :99.8% - samples :93.3% - integration :99.8% - samples :95.0% - integration :0.0% - samples :96.6% - integration :0.2% - samples :98.2% - integration :0.0% - samples :99.8% - integration :53.5% - samples : 100% - integration :0.0% -  -#+end_example +: (10, 100, 56) +: samples :0.0% +: integration :0.0% +: samples : 100% +: integration :0.0% +:  Get the samples. #+BEGIN_SRC jupyter-python # to access the data the 'hi_key' is used to find the data in the hdf5 file @@ -542,7 +411,7 @@ Get the samples. #+end_src #+RESULTS: -: 4000 samples found in database +: 17 samples found in database Calculate energy. #+begin_src jupyter-python @@ -553,8 +422,8 @@ Calculate energy. #+RESULTS: :RESULTS: -| | -[[file:./.ob-jupyter/e8fe3d35c11c218d4443333cec849e3e5a0102c3.png]] +| | +[[file:./.ob-jupyter/f17cfebfc5e7c505b28a2ffe32c89e50dd078f1e.png]] :END: * Energy Flow