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Valentin Boettcher 2021-11-30 17:42:03 +01:00
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After

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44
python/energy_flow_proper/03_gaussian/comparison_with_hops.org
View file

@ -267,18 +267,20 @@ Now we can load the data.
#+end_src
We calculate the sytem energy just for fun.
#+begin_src jupyter-python :results none
e_sys, var = util.operator_expectation_ensemble(
#+begin_src jupyter-python
_, e_sys, σ_e_sys = util.operator_expectation_ensemble(
iter(result.ψ),
system_params.H_sys.todense(),
result.N,
stg.__HI_nonlinear,
calculate_variance=True,
)
# for energy, var, n in zip(*e_sys):
# plt.plot(result.τ, energy.real, label=f"n={n}", alpha=n / e_sys[2][-1])
#+end_src
#+RESULTS:
: 100%|██████████| 999/999 [00:17<00:00, 58.45it/s]
#+begin_src jupyter-python
plt.errorbar(result.τ, e_sys.real, yerr=var.real, ecolor="yellow")
@ -287,7 +289,7 @@ We calculate the sytem energy just for fun.
#+RESULTS:
:RESULTS:
: <ErrorbarContainer object of 3 artists>
[[file:./.ob-jupyter/553154d037d94b170c4e1d571adb17144951238e.svg]]
[[file:./.ob-jupyter/04d99c440ddac4b7d5dee9cfd5b02818d98908a5.svg]]
:END:
** Heat Flow
@ -299,21 +301,26 @@ First we set up some parameter objects for the alogrithm.
#+end_src
And then we calculate the flow.
#+begin_src jupyter-python :results none
full_flow, full_flow_vars, full_flow_Ns = hopsflow.heat_flow_ensemble(
iter(result.ψ), iter(result.ψ_1), hf_system, result.N, every=500, calculate_variance=True
#+begin_src jupyter-python
full_flow = hopsflow.heat_flow_ensemble(
iter(result.ψ), iter(result.ψ_1), hf_system, result.N, every=int(result.N / 6)
)
#+end_src
#+RESULTS:
: 100%|██████████| 999/999 [01:17<00:00, 12.95it/s]
#+begin_src jupyter-python
plt.errorbar(result.τ, -full_flow[-1], yerr=full_flow_vars[-1], ecolor="yellow")
for n, flow, flow_std in full_flow[:-1]:
plt.plot(result.τ, -flow, label=f"n={n}", alpha=n / full_flow[-1][0], linestyle="--")
plt.errorbar(result.τ, -full_flow[-1][1], yerr=full_flow[-1][2], ecolor="yellow", label="final")
plt.legend()
#+end_src
#+RESULTS:
:RESULTS:
: <ErrorbarContainer object of 3 artists>
[[file:./.ob-jupyter/249a8cd0cb90aa30951adc579833e8c672784eeb.svg]]
: <matplotlib.legend.Legend at 0x7fcd8d8c4ee0>
[[file:./.ob-jupyter/13f71cca5af1453aa8ecf21ee62bdab8b0f6358c.svg]]
:END:
** Analytic
@ -352,25 +359,28 @@ Now we can define the flow:
And plot it against the numerically obtained flow.
#+begin_src jupyter-python
%matplotlib inline
plt.errorbar(result.τ, -full_flow[-1], yerr=full_flow_vars[-1]*2, ecolor="yellow", label="HOPS")
plt.errorbar(result.τ, -full_flow[-1][1], yerr=full_flow[-1][2]*2, ecolor="yellow", label="HOPS")
plt.plot(result.τ, flow_τ, label="analytic")
plt.legend()
#+end_src
#+RESULTS:
:RESULTS:
: <matplotlib.legend.Legend at 0x7fc06c26ba60>
[[file:./.ob-jupyter/575143018b151bbf636846d21fb9cd26e819b694.svg]]
: <matplotlib.legend.Legend at 0x7fcda31ac4f0>
[[file:./.ob-jupyter/077b084ddff22883354cf360214b35f32715f6dc.svg]]
:END:
#+begin_src jupyter-python
plt.plot(result.τ, np.abs(flow_τ + full_flow[-1]), label=f"n={full_flow_Ns[-1]}")
plt.plot(result.τ, full_flow_vars[-1] * 2, label=r"tolerance $2\sigma$")
for n, flow, flow_std in full_flow[:-1]:
plt.plot(result.τ, np.abs(flow_τ + flow), label=f"n={n}", alpha=n / full_flow[-1][0])
plt.plot(result.τ, np.abs(flow_τ + full_flow[-1][1]), label=f"n={full_flow[-1][0]}")
plt.plot(result.τ, full_flow[-1][2] * 2, label=r"tolerance $2\sigma$")
plt.legend()
#+end_src
#+RESULTS:
:RESULTS:
: <matplotlib.legend.Legend at 0x7fc05dc48dc0>
[[file:./.ob-jupyter/4a2ce280133f82d010b5d2803073b8cec982e140.svg]]
: <matplotlib.legend.Legend at 0x7fcd8d9961f0>
[[file:./.ob-jupyter/82d719707cd893d93e38fb048ba82df39433e05c.svg]]
:END: