mirror of
https://github.com/vale981/master-thesis
synced 2025-03-05 10:01:43 -05:00
add cycle of coupling and system
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1 changed files with 380 additions and 0 deletions
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#+PROPERTY: header-args :session 08_coup_sys_cycle :kernel python :pandoc no :async yes :tangle no
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Now let's try to actually extract energy.
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* Boilerplate
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#+begin_src jupyter-python :results none
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import figsaver as fs
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from hiro_models.one_qubit_model import QubitModel, StocProcTolerances
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import hiro_models.model_auxiliary as aux
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import numpy as np
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import qutip as qt
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#+end_src
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Init ray and silence stocproc.
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#+begin_src jupyter-python
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import ray
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ray.shutdown()
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#ray.init(address='auto')
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ray.init()
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#+end_src
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#+RESULTS:
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: RayContext(dashboard_url='', python_version='3.9.10', ray_version='1.12.0', ray_commit='f18fc31c7562990955556899090f8e8656b48d2d', address_info={'node_ip_address': '141.30.17.221', 'raylet_ip_address': '141.30.17.221', 'redis_address': None, 'object_store_address': '/tmp/ray/session_2022-04-28_16-22-15_573871_76439/sockets/plasma_store', 'raylet_socket_name': '/tmp/ray/session_2022-04-28_16-22-15_573871_76439/sockets/raylet', 'webui_url': '', 'session_dir': '/tmp/ray/session_2022-04-28_16-22-15_573871_76439', 'metrics_export_port': 64264, 'gcs_address': '141.30.17.221:57854', 'address': '141.30.17.221:57854', 'node_id': '3d8ae351108358a0a4635b495c616f4e81a6fc9404e1d11c82389af6'})
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#+begin_src jupyter-python :results none
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from hops.util.logging_setup import logging_setup
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import logging
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logging_setup(logging.INFO)
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#+end_src
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* Cycle
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#+begin_src jupyter-python :results none
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from hops.util.dynamic_matrix import SmoothStep, Periodic, ConstantMatrix, ScaleTime, Shift, Harmonic
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#+end_src
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Now let's design an asymetric cycle.
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#+begin_src jupyter-python :results none
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L_op = (1/2 * qt.sigmam() + 0 * qt.sigmax()).full()
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L_pos = SmoothStep(L_op, 0, .4, 3) - SmoothStep(L_op, .6, .8, 3)
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L = ScaleTime(Periodic(L_pos, 1), 1)
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#+end_src
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Let's plot such a nice smooth-step.
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#+begin_src jupyter-python
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ts = np.linspace(0, 5, 10000)
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plt.plot(ts, L.operator_norm(ts))
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#+end_src
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#+RESULTS:
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:RESULTS:
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| <matplotlib.lines.Line2D | at | 0x7fbd0788afa0> |
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[[file:./.ob-jupyter/caedb7196fc09f0ed309141321acb49502ee3df5.svg]]
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:END:
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Now we turn the system around after each fill-cycle.
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#+begin_src jupyter-python :results none
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H_op = 1 * (1/2 * (qt.sigmaz() + qt.identity(2))).full()
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H = ScaleTime((ConstantMatrix(H_op) - .5 * Harmonic(qt.sigmay().full(), 1, 0)), np.pi)
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#+end_src
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#+begin_src jupyter-python
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plt.plot(ts, L(ts)[:,1,0].real)
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plt.plot(ts, H.operator_norm(ts))
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#+end_src
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#+RESULTS:
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:RESULTS:
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| <matplotlib.lines.Line2D | at | 0x7fbd0775fc10> |
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[[file:./.ob-jupyter/3760d5d9641934a8fdf7a9c97bac3d154e935f47.svg]]
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:END:
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* Model: Very Non-Markovian
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#+begin_src jupyter-python
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model = QubitModel(
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δ=.5,
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ω_c=.1,
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t=np.linspace(0, 20, 1_000),
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ψ_0=qt.basis([2], [1]),
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description=f"Testing the time dependent coupling with smooth step.",
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k_max=7,
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bcf_terms=6,
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truncation_scheme="simplex",
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driving_process_tolerance=StocProcTolerances(1e-3, 1e-3),
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thermal_process_tolerance=StocProcTolerances(1e-3, 1e-3),
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T = 4,
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L = L,
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H = H,
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)
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#+end_src
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#+RESULTS:
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#+begin_src jupyter-python
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plt.plot(model.t, model.spectral_density(model.t))
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plt.axvline(model.ω_c)
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# plt.axhline(1/(np.exp(model.ω_c / model.T) - 1) * model.ω_c)
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# plt.axhline(1/(np.exp(1e-3 / model.T) - 1) * 1e-3)
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#plt.axhline(model.T ** 2 * np.pi **2 /6 * model.ω_c)
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#+end_src
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#+RESULTS:
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:RESULTS:
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: <matplotlib.lines.Line2D at 0x7fbc32d0b2b0>
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[[file:./.ob-jupyter/93c7bcaec0d9c6529fbf419915378372b7fb7f31.svg]]
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:END:
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#+begin_src jupyter-python
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aux.integrate(model, 10000)
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#+end_src
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#+RESULTS:
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#+begin_example
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/home/hiro/src/hops/hops/util/bcf.py:280: UserWarning: this implementation uses mpmath to evaluate the zeta_function! for a better performance consider the 'OhmEnv' package
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warnings.warn(
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n:32 d:0.00014166421319021928 tol:0.001
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done!
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[INFO hops.core.integration 76439] Choosing the nonlinear integrator.
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[INFO hops.core.integration 76439] Using 4 integrators.
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[INFO hops.core.integration 76439] Some 0 trajectories have to be integrated.
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[INFO hops.core.integration 76439] Using 1716 hierarchy states.
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0it [00:00, ?it/s]
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#+end_example
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#+begin_src jupyter-python
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import scipy
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with aux.get_data(model) as data:
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fs.plot_with_σ(model.t, model.system_energy(data))
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plt.plot(
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model.t, [-np.trace(ρ @ scipy.linalg.logm(ρ)) for ρ in data.rho_t_accum.mean]
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)
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plt.plot(model.t, model.H(model.t)[:, 0, 0].real)
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plt.plot(model.t, model.L(model.t)[:, 0, 1].real)
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#+end_src
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#+RESULTS:
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:RESULTS:
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: /nix/store/6md8j2v3a9xhxllmyha3gn1qwrfllm3n-python3-3.9.10-env/lib/python3.9/site-packages/scipy/linalg/_matfuncs_inv_ssq.py:827: LogmExactlySingularWarning: The logm input matrix is exactly singular.
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: warnings.warn(exact_singularity_msg, LogmExactlySingularWarning)
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: /nix/store/6md8j2v3a9xhxllmyha3gn1qwrfllm3n-python3-3.9.10-env/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part
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: return np.asarray(x, float)
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[[file:./.ob-jupyter/8142cb1061478cc43e470575d8d7382628cbca4b.svg]]
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:END:
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#+begin_src jupyter-python
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fig, ax = fs.plot_energy_overview(model)
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plt.plot(model.t, model.H.operator_norm(model.t), label="$H(t)$")
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plt.plot(model.t, model.L.operator_norm(model.t), label="$L(t)$")
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with aux.get_data(model) as data:
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plt.plot(
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model.t, [-np.trace(ρ @ scipy.linalg.logm(ρ)) for ρ in data.rho_t_accum.mean],
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label="$S[ρ_{s}]$"
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)
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ax.legend()
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#+end_src
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#+RESULTS:
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:RESULTS:
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#+begin_example
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/home/hiro/src/hops/hops/util/bcf.py:280: UserWarning: this implementation uses mpmath to evaluate the zeta_function! for a better performance consider the 'OhmEnv' package
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warnings.warn(
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n:32 d:0.00014166421319021928 tol:0.001
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done!
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n:32 d:0.00014166421319021928 tol:0.001
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done!
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n:32 d:0.00014166421319021928 tol:0.001
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done!
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/nix/store/6md8j2v3a9xhxllmyha3gn1qwrfllm3n-python3-3.9.10-env/lib/python3.9/site-packages/scipy/linalg/_matfuncs_inv_ssq.py:827: LogmExactlySingularWarning: The logm input matrix is exactly singular.
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warnings.warn(exact_singularity_msg, LogmExactlySingularWarning)
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/nix/store/6md8j2v3a9xhxllmyha3gn1qwrfllm3n-python3-3.9.10-env/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part
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return np.asarray(x, float)
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#+end_example
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: <matplotlib.legend.Legend at 0x7fbc4c27bf70>
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[[file:./.ob-jupyter/dec6c0d24496e2029b219adca1c4496a70fcbacc.svg]]
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:END:
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#+begin_src jupyter-python :results none
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with aux.get_data(model) as data:
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ρ = data.rho_t_accum.mean[:]
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σ_ρ = data.rho_t_accum.ensemble_std[:]
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xs = np.einsum("tij,ji->t", ρ, qt.sigmax().full())
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ys = np.einsum("tij,ji->t", ρ, qt.sigmay().full())
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zs = np.einsum("tij,ji->t", ρ, qt.sigmaz().full())
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#+end_src
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#+begin_src jupyter-python
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b = qt.Bloch()
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b.add_points([xs, ys, zs])
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b.view = [20, 20]
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b.point_size = [0.1]
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b.sphere_alpha = 0.1
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b.size = [20, 20]
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b.render()
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b.fig
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#+end_src
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#+RESULTS:
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[[file:./.ob-jupyter/ee1a474570fad49dfefa176ff8b1b3262354d107.svg]]
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#+begin_src jupyter-python
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#plt.plot(model.t, zs)
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#plt.plot(model.t, xs)
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plt.plot(model.t, np.abs(ρ[:, 0,1]))
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plt.plot(model.t, σ_ρ[:, 0,1])
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#+end_src
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#+RESULTS:
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:RESULTS:
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| <matplotlib.lines.Line2D | at | 0x7fbc330abcd0> |
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[[file:./.ob-jupyter/155688dabfd7fbccbdab22a83c9cd9f1aa34f5d1.svg]]
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:END:
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* Model: Maximum Flow
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#+begin_src jupyter-python
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model = QubitModel(
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δ=.5,
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ω_c=2,
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t=np.linspace(0, 5, 1_000),
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ψ_0=qt.basis([2], [1]),
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description=f"Testing the time dependent coupling with smooth step.",
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k_max=7,
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bcf_terms=6,
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truncation_scheme="simplex",
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driving_process_tolerance=StocProcTolerances(1e-3, 1e-3),
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thermal_process_tolerance=StocProcTolerances(1e-3, 1e-3),
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T = 4,
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L = L,
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H = ConstantMatrix(H_op),
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)
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#+end_src
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#+RESULTS:
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#+begin_src jupyter-python
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aux.integrate(model, 100)
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#+end_src
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#+RESULTS:
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#+begin_example
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/home/hiro/src/hops/hops/util/bcf.py:280: UserWarning: this implementation uses mpmath to evaluate the zeta_function! for a better performance consider the 'OhmEnv' package
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warnings.warn(
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n:32 d:0.33446500514383937 tol:0.001
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n:64 d:0.02262163635902933 tol:0.001
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n:128 d:2.2746881114193725e-05 tol:0.001
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done!
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[INFO hops.core.integration 76439] Choosing the nonlinear integrator.
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[INFO hops.core.integration 76439] Using 4 integrators.
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[INFO hops.core.integration 76439] Some 100 trajectories have to be integrated.
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[INFO hops.core.integration 76439] Using 1716 hierarchy states.
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100% 100/100 [01:21<00:00, 1.23it/s]
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#+end_example
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#+begin_src jupyter-python
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import scipy
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with aux.get_data(model) as data:
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fs.plot_with_σ(model.t, model.system_energy(data))
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plt.plot(
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model.t, [-np.trace(ρ @ scipy.linalg.logm(ρ)) for ρ in data.rho_t_accum.mean]
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)
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plt.plot(model.t, model.H(model.t)[:, 0, 0].real)
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plt.plot(model.t, model.L(model.t)[:, 0, 1].real)
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#+end_src
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#+RESULTS:
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:RESULTS:
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: Loading: 100% 5/5 [00:00<00:00, 82.94it/s]
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: Processing: 100% 5/5 [00:00<00:00, 761.02it/s]
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: [INFO root 76439] Writing cache to: results/3694939998333a5d25b932d5b63ea70f47cb547297a909f142e8b51d8a096d9b_573fc383266c5ec57f5ac393c4145a64be86ba7915c0cd8da8bfc887bdb3cbc0_op_exp_task_100_None_1ff6d34b7de893995dfd0ae8efe2ed770a6773ef52b6e717b4b4ee9b9e5d285d.npy
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: /nix/store/6md8j2v3a9xhxllmyha3gn1qwrfllm3n-python3-3.9.10-env/lib/python3.9/site-packages/scipy/linalg/_matfuncs_inv_ssq.py:827: LogmExactlySingularWarning: The logm input matrix is exactly singular.
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: warnings.warn(exact_singularity_msg, LogmExactlySingularWarning)
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: /nix/store/6md8j2v3a9xhxllmyha3gn1qwrfllm3n-python3-3.9.10-env/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part
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: return np.asarray(x, float)
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[[file:./.ob-jupyter/84f50c19b292b6f8968709211eb9f1e8e8b83a91.svg]]
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:END:
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#+begin_src jupyter-python
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fig, ax = fs.plot_energy_overview(model)
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plt.plot(model.t, model.H.operator_norm(model.t), label="$H(t)$")
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plt.plot(model.t, model.L.operator_norm(model.t), label="$L(t)$")
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with aux.get_data(model) as data:
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plt.plot(
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model.t, [-np.trace(ρ @ scipy.linalg.logm(ρ)) for ρ in data.rho_t_accum.mean],
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label="$S[ρ_{s}]$"
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)
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ax.legend()
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#+end_src
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#+RESULTS:
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:RESULTS:
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#+begin_example
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/home/hiro/src/hops/hops/util/bcf.py:280: UserWarning: this implementation uses mpmath to evaluate the zeta_function! for a better performance consider the 'OhmEnv' package
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warnings.warn(
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n:32 d:0.33446500514383937 tol:0.001
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n:64 d:0.02262163635902933 tol:0.001
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n:128 d:2.2746881114193725e-05 tol:0.001
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done!
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Loading: 100% 5/5 [00:00<00:00, 19.33it/s]
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Processing: 100% 5/5 [00:00<00:00, 22.99it/s]
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[INFO root 76439] Writing cache to: results/flow_573fc383266c5ec57f5ac393c4145a64be86ba7915c0cd8da8bfc887bdb3cbc0_flow_worker_100_None_0c0cafd9366880235df0a72a856be2f076e35acf3353bfe08d1d3ec198a02f32.npy
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n:32 d:0.33446500514383937 tol:0.001
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n:64 d:0.02262163635902933 tol:0.001
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n:128 d:2.2746881114193725e-05 tol:0.001
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done!
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Loading: 100% 5/5 [00:00<00:00, 30.33it/s]
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Processing: 100% 5/5 [00:00<00:00, 19.61it/s]
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[INFO root 76439] Writing cache to: results/interaction_573fc383266c5ec57f5ac393c4145a64be86ba7915c0cd8da8bfc887bdb3cbc0_interaction_energy_task_100_None_a1ebae168ba6027d405a66e94ca963c84f8aedb16621da5954b5631bcd1636c4.npy
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n:32 d:0.33446500514383937 tol:0.001
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n:64 d:0.02262163635902933 tol:0.001
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n:128 d:2.2746881114193725e-05 tol:0.001
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done!
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/nix/store/6md8j2v3a9xhxllmyha3gn1qwrfllm3n-python3-3.9.10-env/lib/python3.9/site-packages/scipy/linalg/_matfuncs_inv_ssq.py:827: LogmExactlySingularWarning: The logm input matrix is exactly singular.
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warnings.warn(exact_singularity_msg, LogmExactlySingularWarning)
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/nix/store/6md8j2v3a9xhxllmyha3gn1qwrfllm3n-python3-3.9.10-env/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part
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return np.asarray(x, float)
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#+end_example
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: <matplotlib.legend.Legend at 0x7fbcc82836a0>
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[[file:./.ob-jupyter/494a441d03c95f40fbd6b286f580057e33d5f49c.svg]]
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:END:
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#+begin_src jupyter-python :results none
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with aux.get_data(model) as data:
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ρ = data.rho_t_accum.mean[:]
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σ_ρ = data.rho_t_accum.ensemble_std[:]
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xs = np.einsum("tij,ji->t", ρ, qt.sigmax().full())
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ys = np.einsum("tij,ji->t", ρ, qt.sigmay().full())
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zs = np.einsum("tij,ji->t", ρ, qt.sigmaz().full())
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#+end_src
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||||
|
||||
|
||||
#+begin_src jupyter-python
|
||||
b = qt.Bloch()
|
||||
b.add_points([xs, ys, zs])
|
||||
b.view = [20, 20]
|
||||
b.point_size = [0.1]
|
||||
b.sphere_alpha = 0.1
|
||||
b.size = [20, 20]
|
||||
b.render()
|
||||
b.fig
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
[[file:./.ob-jupyter/3f303eb2cb2fe0ca8714be20de2b8856aa6e6951.svg]]
|
||||
|
||||
|
||||
#+begin_src jupyter-python
|
||||
#plt.plot(model.t, zs)
|
||||
#plt.plot(model.t, xs)
|
||||
plt.plot(model.t, np.abs(ρ[:, 0,1]))
|
||||
plt.plot(model.t, σ_ρ[:, 0,1])
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
:RESULTS:
|
||||
| <matplotlib.lines.Line2D | at | 0x7fbc330b2100> |
|
||||
[[file:./.ob-jupyter/00b87c2e8644894417234a73c220d39a811a5aa5.svg]]
|
||||
:END:
|
||||
|
||||
|
||||
* Findings
|
||||
- flipping H does not work -> Thermalization does not create inversion
|
||||
- one can't extract energy from the single bath because it is in a
|
||||
passive state -> WRONG
|
||||
- Choosing $T>2*\omega_c$ and $\omega_c\approx ||H||$ and $L=\sigma_{+}$ yields the deal
|
||||
- after certain time span -> non-passivity exausted -> when system is "full"
|
||||
- adding some $\sigma_x$ reduces the total intial energy loss and hampers energy transfer
|
||||
- turn-around comes later because energy transfer is slower
|
||||
- maybe zero mean entropy production helps?
|
||||
- maybe the "forgetful" nature of the bath helps
|
||||
Loading…
Add table
Reference in a new issue