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clean up cycle_shift and generate ipython notebook

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valentin.boettcher@mailbox.tu-dresden.de 2023-05-11 12:53:11 -04:00
parent df2d87a26c
commit 3f25d296c2
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51 changed files with 40365 additions and 117569 deletions
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6
python/otto_motor/otto_utilities.py
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@ -9,7 +9,7 @@ import qutip as qt
import itertools
def plot_power_eff_convergence(models, steady_idx=1):
def plot_power_eff_convergence(models, steady_idx=2):
f, (a_power, a_efficiency) = plt.subplots(ncols=2)
a_efficiency.set_yscale("log")
@ -26,7 +26,7 @@ def plot_power_eff_convergence(models, steady_idx=1):
@pu.wrap_plot
def plot_powers_and_efficiencies(x, models, steady_idx=1, ax=None, xlabel=""):
def plot_powers_and_efficiencies(x, models, steady_idx=2, ax=None, xlabel=""):
powers = [-model.power(steady_idx=steady_idx).value for model in models]
powers_σ = [model.power(steady_idx=steady_idx).σ for model in models]
@ -112,7 +112,7 @@ def plot_powers_and_efficiencies(x, models, steady_idx=1, ax=None, xlabel=""):
def plot_multi_powers_and_efficiencies(
x, multi_models, titles, steady_idx=1, xlabel=""
x, multi_models, titles, steady_idx=2, xlabel=""
):
fig, axs = plt.subplots(nrows=2, ncols=2)
(efficiency, power, system_power, interaction_power) = axs.flatten()

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python/otto_motor/subprojects/cycle_shift/.ipynb_checkpoints/cycle_shift-checkpoint.ipynb Normal file
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View file

@ -31,10 +31,13 @@ find if there is an improvement.
logging_setup(logging.INFO)
#+end_src
* Cycles
As we found in [[id:66cb884e-8724-488d-88da-21b929ffc2bb][finding_relaxation_time.org]], we use a larger coupling
strength to demonstrate strong coupling effects and to limit the cycle time.
* Baseline Model and Shifts
In here, we define the baseline model and shift the cycle.
Later we will experiment with some modifications to this baseline
cycle.
** Model Definition
**Note: Don't run this in Jupyter**
#+begin_src jupyter-python :tangle tangle/original.py :results none
<<boilerplate>>
#+end_src
@ -57,21 +60,6 @@ We shift so that we just overlap with coupling/decoupling and one above.
baseline = models[3]
#+end_src
#+RESULTS:
#+begin_example
3.5999999999999996
3.5999999999999996
3.5999999999999996
3.5999999999999996
3.5999999999999996
3.5999999999999996
3.5999999999999996
3.5999999999999996
3.5999999999999996
3.5999999999999996
3.5999999999999996
#+end_example
#+begin_src jupyter-python
ot.plot_cycle(baseline)
@ -106,6 +94,10 @@ We shift so that we just overlap with coupling/decoupling and one above.
[[file:./.ob-jupyter/2eaccf65458d4ed821c07abbb83664ee16b423f9.svg]]
** Integrate
Here we integrate/simulate the models. This should be run on the
cluster.
Running it locally won't do any harm though.
#+begin_src jupyter-python :tangle tangle/original.py
ot.integrate_online_multi(models, 80_000, increment=10_000, analyze_kwargs=dict(every=10_000))
#+end_src
@ -113,26 +105,8 @@ We shift so that we just overlap with coupling/decoupling and one above.
#+RESULTS:
** Analysis
#+begin_src jupyter-python
for model in models:
print(model.power(steady_idx=1).value / baseline.power(steady_idx=1).value, model.efficiency(steady_idx=1).value)
#+end_src
#+RESULTS:
#+begin_example
-2.7704455654085876 -2.5219916727767804
-2.034015641972767 -1.6675487518853185
0.571544457513159 0.19650010500179352
1.0 0.30209537308799783
1.1652434363371367 0.3239348992880912
1.6254413169874071 0.3309674632505577
1.6802797038561466 0.3190991034856301
1.6058539780552505 0.2979616403269744
1.413212538480568 0.26307105710019735
0.7332591894799324 0.1434372231954891
-1.2500012707944386 -0.29523872560546577
#+end_example
*** Baseline
This plots the full energy overview for the baseline model.
#+begin_src jupyter-python
ot.plot_energy(baseline)
print(
@ -145,9 +119,10 @@ We shift so that we just overlap with coupling/decoupling and one above.
#+RESULTS:
:RESULTS:
: \(N=80000\)
[[file:./.ob-jupyter/f365b8ee0b20cdf41f305aaaf802be5b634b2953.svg]]
[[file:./.ob-jupyter/9f290df44db1418e0b27a61a97d2591f6845fa65.svg]]
:END:
We would like to know how close all of this comes to the thermal states.
#+begin_src jupyter-python
def thermal_state(T, Ω):
ρ = np.array([[np.exp(-Ω/T), 0], [0, 1]])
@ -189,38 +164,65 @@ We shift so that we just overlap with coupling/decoupling and one above.
[0. 0.88079708]]
[[0.37754067 0. ]
[0. 0.62245933]]
/nix/store/08ccd1bg10pbkpv71fwccyxabr1cycim-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1369: ComplexWarning: Casting complex values to real discards the imaginary part
/nix/store/x2w7bp64b3isjcw3ps8xsadrhxsnbpwh-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1369: ComplexWarning: Casting complex values to real discards the imaginary part
return np.asarray(x, float)
/nix/store/08ccd1bg10pbkpv71fwccyxabr1cycim-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/axes/_axes.py:5340: ComplexWarning: Casting complex values to real discards the imaginary part
/nix/store/x2w7bp64b3isjcw3ps8xsadrhxsnbpwh-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/axes/_axes.py:5340: ComplexWarning: Casting complex values to real discards the imaginary part
pts[0] = start
/nix/store/08ccd1bg10pbkpv71fwccyxabr1cycim-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/axes/_axes.py:5341: ComplexWarning: Casting complex values to real discards the imaginary part
/nix/store/x2w7bp64b3isjcw3ps8xsadrhxsnbpwh-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/axes/_axes.py:5341: ComplexWarning: Casting complex values to real discards the imaginary part
pts[N + 1] = end
/nix/store/08ccd1bg10pbkpv71fwccyxabr1cycim-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/axes/_axes.py:5344: ComplexWarning: Casting complex values to real discards the imaginary part
/nix/store/x2w7bp64b3isjcw3ps8xsadrhxsnbpwh-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/axes/_axes.py:5344: ComplexWarning: Casting complex values to real discards the imaginary part
pts[1:N+1, 1] = dep1slice
/nix/store/08ccd1bg10pbkpv71fwccyxabr1cycim-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/axes/_axes.py:5346: ComplexWarning: Casting complex values to real discards the imaginary part
/nix/store/x2w7bp64b3isjcw3ps8xsadrhxsnbpwh-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/axes/_axes.py:5346: ComplexWarning: Casting complex values to real discards the imaginary part
pts[N+2:, 1] = dep2slice[::-1]
#+end_example
[[file:./.ob-jupyter/de007b03b6f53431f27dcfefdd5740a92e27b785.svg]]
[[file:./.ob-jupyter/412ae179270758c9b9892f2e1a93b5583ede630b.svg]]
:END:
Plotting the pauli matrix expectation values, we can see that the
dynamics only take place on the z-axis. This is addressed in [[id:9d7a11f2-f479-4e95-8775-31050bcc4fb7][Off-Axis Hamiltonian]]
#+begin_src jupyter-python
ot.plot_bloch_components(baseline)
fs.export_fig("state_evolution", y_scaling=.7)
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/1a1f8810d9deff000ef064ac9ff34c328f5e846b.svg]]
[[file:./.ob-jupyter/ce6428315398ce5b39b5c39aae9d2b1cbdfd20f8.svg]]
Let us plot an overview of the work done by system and interaction
modulation over a cycle for the baseline model.
#+begin_src jupyter-python
ot.plot_steady_energy_changes([baseline], 2, label_fn=lambda _: "")
fs.export_fig("prototype_energy_change", y_scaling=.7)
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/962ffa455699bc4ceabd74a04f849593a57a8e96.svg]]
[[file:./.ob-jupyter/e11fc10ff666262bc6ab9abedc2cb0de38262905.svg]]
*** Shifted Models
Let us print the power output (relative to the baseline = unshifted model) and efficiency.
#+begin_src jupyter-python
for model in models:
print(model.power(steady_idx=2).value / baseline.power(steady_idx=2).value, model.efficiency(steady_idx=2).value)
#+end_src
#+RESULTS:
#+begin_example
-2.7704455654085876 -2.5219916727767804
-2.034015641972767 -1.6675487518853185
0.571544457513159 0.19650010500179352
1.0 0.30209537308799783
1.1652434363371367 0.3239348992880912
1.6254413169874071 0.3309674632505577
1.6802797038561466 0.3190991034856301
1.6058539780552505 0.2979616403269744
1.413212538480568 0.26307105710019735
0.7332591894799324 0.1434372231954891
-1.2500012707944386 -0.29523872560546577
#+end_example
This plots the power output and efficiency as a function of sample
size to check convergence.
#+begin_src jupyter-python
ot.plot_power_eff_convergence(models)
fs.export_fig("cycle_shift_convergence", x_scaling=2, y_scaling=.7)
@ -231,44 +233,39 @@ We shift so that we just overlap with coupling/decoupling and one above.
We see that we get a pretty good picture after about 30k-40k samples.
This is an overview over powers and the efficiency.
#+begin_src jupyter-python
ot.plot_powers_and_efficiencies(np.array(shifts) * 100, models, xlabel="Cycle Shift")
fs.export_fig("cycle_shift_power_efficiency", y_scaling=.7, x_scaling=1)
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/c4573aef927c867b1f7b60cb1176771fdaa66f5d.svg]]
[[file:./.ob-jupyter/50e0848230990f02d9ad40c7e049bcf8c6dcebc7.svg]]
The best shift:
#+begin_src jupyter-python
fig, ax =ot.plot_steady_energy_changes([baseline, models[3+2]], 2, label_fn=lambda m: ("baseline" if m.hexhash == baseline.hexhash else "shifted"))
best_shift = shifts[np.argmax([-model.power(steady_idx=2).value for model in models])]
best_shift_model = sc.make_model(best_shift, best_shift)
best_shift
#+end_src
#+RESULTS:
: 0.18
This contrasts the system/interaction power output for the baseline
and the best shift model.
#+begin_src jupyter-python
fig, ax =ot.plot_steady_energy_changes([baseline, best_shift_model], 2, label_fn=lambda m: ("baseline" if m.hexhash == baseline.hexhash else "shifted"))
ax.legend(loc="lower left")
fs.export_fig("shift_energy_change", y_scaling=.7)
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/e8e0f0c962520ab4b163a0756b2a22e2ebd7435f.svg]]
The best shift:
#+begin_src jupyter-python
best_shift = shifts[3+2]#[np.argmax([-model.power(steady_idx=2).value for model in models])]
best_shift_model = sc.make_model(best_shift, best_shift)
#+end_src
#+RESULTS:
: 3.5999999999999996
#+begin_src jupyter-python
ot.plot_bloch_components(best_shift_model)
#+end_src
#+RESULTS:
:RESULTS:
| <Figure | size | 340x320 | with | 1 | Axes> | <AxesSubplot: | xlabel= | $\tau$ | > |
[[file:./.ob-jupyter/39c87ed71bd7a32a2e9f1e4a360a9c8ae4827e5e.svg]]
:END:
[[file:./.ob-jupyter/60efd5889fe957f7b8cfe8d446f9953a95c516c9.svg]]
Let us plot the interaction power in the steady state for baseline and
best-shift. We have to shift the time to make them overlap correctly.
#+begin_src jupyter-python
t_shift_begin = (2 - best_shift) * baseline.Θ
t_begin = 2 * baseline.Θ
@ -318,23 +315,10 @@ The best shift:
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/0aaae8f600192b07ca01041789f5cbeaf0d48ee2.svg]]
#+begin_src jupyter-python
ot.plot_energy(baseline)
f, a = ot.plot_energy(best_shift_model)
a.plot(best_shift_model.t, best_shift_model.H(best_shift_model.t)[:, 0,0])
#+end_src
#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7fe9b1d26c40> |
[[file:./.ob-jupyter/a2139b7a51fb5e3f03188d349b787fb2e3030961.svg]]
[[file:./.ob-jupyter/737556be87761f7451bcfd437fd96170f7637ec9.svg]]
:END:
[[file:./.ob-jupyter/479a2efc17d04e372b0a09cfe1a97f48da88fa19.svg]]
Let us zoom in on the cold bath decoupling process to understnad this better.
#+begin_src jupyter-python
f, a = plt.subplots()
a.axhline(best_shift_model.system_energy().value[np.argmin(abs(best_shift_model.t - model.Θ * 2))], color="gray", linestyle="--")
@ -362,7 +346,7 @@ The best shift:
label="system modulation"
)
# a.plot(best_shift_model.t, best_shift_model.coupling_operators[1].operator_norm(best_shift_model.t) / 5)
a.set_xlim((model.Θ * 2, model.Θ * 2 + 7))
a.set_xlim((model.Θ * 2, model.Θ * 2 + 11))
a.set_ylim((-.21, .45))
a.set_xlabel(r"$\tau$")
@ -371,264 +355,26 @@ The best shift:
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/af9b31c1231b61d27855a73c8e6dc2f2db604233.svg]]
[[file:./.ob-jupyter/fa8d96bb86b08eaed1c7d3fe969e9a82c38a03c7.svg]]
* Explore Coupling Length Dimension for The best performing state
#+begin_src jupyter-python
def overlap(shift_model, N, step, switch_t=3.):
switch_time = switch_t / T
(p_H, p_L) = ot.timings(switch_time, switch_time)
next_model = shift_model.copy()
* Slower switching
Let us explore what happens when modulate the coupling a bit slower
switch slower.
** Model Construction
#+begin_src jupyter-python :tangle tangle/long.py
<<boilerplate>>
#+end_src
#next_model.timings_H=p_H
next_model.timings_L=p_L
(a, b, c, d) = next_model.timings_L[0]
(e, f, g, h) = next_model.timings_L[1]
next_step = step * N
(s1, s2) = next_model.L_shift
next_model.L_shift = (s1 + next_step, s2 - next_step)
next_model.timings_L = (
(a - 2 * next_step, b - 2 * next_step, c, d),
(e, f, g + 2 * next_step, h + 2 * next_step),
)
return next_model
def overlap_cold(shift_model, N, step):
next_model = shift_model.copy()
(a, b, c, d) = next_model.timings_L[0]
(e, f, g, h) = next_model.timings_L[1]
next_step = step * N
(s1, s2) = next_model.L_shift
next_model.L_shift = (s1 + next_step, s2 - next_step)
next_model.timings_L = (
(a - 2 * next_step, b - 2 * next_step, c - next_step, d - next_step),
(e + next_step, f + next_step, g + 2 * next_step, h + 2 * next_step),
)
return next_model
Ns = list(range(1, 4))[:1]
overlap_models = [overlap(best_shift_model, N, step) for N in Ns]
overlap_models = [overlap_cold(best_shift_model, N, step) for N in Ns]
new_step_size = 6
mini_step = (new_step_size / (N-N_over) / T)
print(mini_step)
overlap_models = [overlap(best_shift_model, N, mini_step, new_step_size) for N in Ns]
#+end_src
#+RESULTS:
:RESULTS:
# [goto error]
#+begin_example
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In[91], line 38
 34 return next_model
 37 Ns = list(range(1, 4))[:1]
---> 38 overlap_models = [overlap(best_shift_model, N, step) for N in Ns]
 39 overlap_models = [overlap_cold(best_shift_model, N, step) for N in Ns]
 40 new_step_size = 6
Cell In[91], line 38, in <listcomp>(.0)
 34 return next_model
 37 Ns = list(range(1, 4))[:1]
---> 38 overlap_models = [overlap(best_shift_model, N, step) for N in Ns]
 39 overlap_models = [overlap_cold(best_shift_model, N, step) for N in Ns]
 40 new_step_size = 6
NameError: name 'step' is not defined
#+end_example
:END:
#+begin_src jupyter-python :tangle no
ot.plot_cycles([overlap_models[0]], legend=True)
#+end_src
#+RESULTS:
:RESULTS:
# [goto error]
: ---------------------------------------------------------------------------
: NameError Traceback (most recent call last)
: Cell In[90], line 1
: ----> 1 ot.plot_cycles([overlap_models[0]], legend=True)
:
: NameError: name 'overlap_models' is not defined
:END:
** Integrate
#+begin_src jupyter-julia
all_overlap_models = [best_shift_model, *overlap_models]
#+end_src
#+begin_src jupyter-python
ot.integrate_online_multi(overlap_models, 80_000, increment=10_000, analyze_kwargs=dict(every=10_000))
#+end_src
** Analysis
#+begin_src jupyter-python :tangle no
fig, ax = plt.subplots()
t = np.linspace(0, all_overlap_models[0].Θ, 1000)
ax.plot(t, all_overlap_models[0].coupling_operators[0].operator_norm(t), color="C1", linewidth=1, label="Shifted")
ax.plot(t, all_overlap_models[0].coupling_operators[1].operator_norm(t), color="C1", linestyle="--", linewidth=1)
ax.plot(t, all_overlap_models[1].coupling_operators[0].operator_norm(t), color="C2", linewidth=1, label="Shifted with Overlap")
ax.plot(t, all_overlap_models[1].coupling_operators[1].operator_norm(t), color="C2", linestyle="--", linewidth=1)
ax.set_xlabel(r"$\tau$")
ax.set_ylabel(r"$||L_{h/c}||$")
ax.legend()
fs.export_fig("cycle_shift_shift_vs_overlap", y_scaling=.6)
#ot.plot_cycles(all_overlap_models[0:2], legend=True)
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/87df1592c89180bd0acbf7aa75af7506769e85ed.svg]]
#+begin_src jupyter-python
ot.plot_power_eff_convergence(all_overlap_models, 2)
#+end_src
#+RESULTS:
:RESULTS:
| <Figure | size | 340x320 | with | 2 | Axes> | (<AxesSubplot: xlabel= $N$ ylabel= $P$ > <AxesSubplot: xlabel= $N$ ylabel= $\eta$ >) |
[[file:./.ob-jupyter/e01f809855125e962fb4f56975fb4833b122dd1a.svg]]
:END:
#+begin_src jupyter-python
f, a= ot.plot_energy(all_overlap_models[-1])
a.plot(model.t, model.coupling_operators[0].operator_norm(model.t))
a.plot(model.t, model.coupling_operators[1].operator_norm(model.t))
a.plot(model.t, model.system.operator_norm(model.t))
#+end_src
#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7ff2b6947400> |
[[file:./.ob-jupyter/6f6fb7a34b89a008d51117d01b0dba6e6341fd8c.svg]]
:END:
#+begin_src jupyter-julia
[model.power(steady_idx=2).value / best_shift_model.power(steady_idx=2).value for model in all_overlap_models]
#+end_src
#+RESULTS:
| 1.0 | 1.3236593973330115 |
#+begin_src jupyter-julia
[model.efficiency(steady_idx=2).value / best_shift_model.efficiency(steady_idx=2).value for model in all_overlap_models]
#+end_src
#+RESULTS:
| 1.0 | 1.1230706203655971 |
#+begin_src jupyter-julia
[model.power(steady_idx=2).N for model in all_overlap_models]
#+end_src
#+RESULTS:
| 80000 | 80000 |
#+begin_src jupyter-python
ot.plot_powers_and_efficiencies([0] + Ns, all_overlap_models)
#+end_src
#+RESULTS:
:RESULTS:
| <Figure | size | 340x320 | with | 2 | Axes> | <AxesSubplot: | ylabel= | $-\bar{P}$ | > |
[[file:./.ob-jupyter/0b9adf725182e7385744287f98375c8b39c3471b.svg]]
:END:
#+begin_src jupyter-python
f, a = plt.subplots()
a.axhline(0, color="lightgrey")
for model, label in zip(all_overlap_models[:2], ["Shifted", "Shifted with Overlap"]):
_, _, lines = pu.plot_with_σ(model.t, model.interaction_power().sum_baths().integrate(model.t), ax=a, label=fr"$W_\mathrm{{int}}$ {label}")
pu.plot_with_σ(model.t, model.system_power().integrate(model.t), ax=a, color=lines[0][0].get_color(), linestyle="--", label=fr"$W_\mathrm{{sys}}$ {label}")
a.set_ylabel(r"$W_{\mathrm{int/sys}}$")
a.set_xlabel(r"$\tau$")
a.legend()
fs.export_fig("cycle_shift_shift_vs_overlap_power", x_scaling=2, y_scaling=.6)
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/a4e92f194bddc790d251d8118f1bf7592fb58bb7.svg]]
We see that the power boost is solely due to the interaction
modulation.
#+begin_src jupyter-python
fig, ax =ot.plot_steady_energy_changes(all_overlap_models, 2, label_fn=(lambda m: ["without overlap", "with overlap"][all_overlap_models.index(m)]))
ax.legend(loc="lower left")
fs.export_fig("overlap_energy_change", y_scaling=.9)
fig, ax =ot.plot_steady_work_baths(all_overlap_models, 2, label_fn=(lambda m: ["without overlap", "with overlap"][all_overlap_models.index(m)]))
ax.legend(loc="lower left")
fs.export_fig("overlap_energy_change_hot_cold", y_scaling=.9)
#+end_src
#+RESULTS:
:RESULTS:
# [goto error]
: ---------------------------------------------------------------------------
: NameError Traceback (most recent call last)
: Cell In[206], line 1
: ----> 1 fig, ax =ot.plot_steady_energy_changes(all_overlap_models, 2, label_fn=(lambda m: ["without overlap", "with overlap"][all_overlap_models.index(m)]))
:  2 ax.legend(loc="lower left")
:  4 fs.export_fig("overlap_energy_change", y_scaling=.9)
:
: NameError: name 'all_overlap_models' is not defined
:END:
#+begin_src jupyter-python
r = pu.plot_with_σ(all_overlap_models[-1].t, all_overlap_models[-1].interaction_energy().for_bath(0))
# a.plot(all_overlap_models[-1].t, all_overlap_models[-1].H(all_overlap_models[-1].t)[:, 0,0])
r[1].plot(all_overlap_models[-1].t, all_overlap_models[-1].coupling_operators[0].operator_norm(all_overlap_models[-1].t) / 5)
r[1].plot(all_overlap_models[-1].t, all_overlap_models[-1].coupling_operators[1].operator_norm(all_overlap_models[-1].t) / 5)
r[1].set_xlim((model.Θ*2, model.Θ*2+15))
#+end_src
#+RESULTS:
:RESULTS:
| 120.0 | 135.0 |
[[file:./.ob-jupyter/05702081169b9057efd24c51303402f7e774030e.svg]]
:END:
** Slower switching
#+begin_src jupyter-python :tangle tangle/long.py
#<<boilerplate>>
shifts = sc.make_shifts(extra_r=4)
#long_models = [sc.make_model(shift, shift, switch_t=6., switch_t_sys=3) for shift in shifts]
long_models = [sc.make_model(shift, shift, switch_t=6.) for shift in shifts]
long_baseline = sc.make_model(0., 0., switch_t=6.)
#+end_src
#+RESULTS:
#+begin_example
7.199999999999999
7.199999999999999
7.199999999999999
7.199999999999999
7.199999999999999
7.199999999999999
7.199999999999999
7.199999999999999
7.199999999999999
7.199999999999999
7.199999999999999
7.199999999999999
#+end_example
#+begin_src jupyter-python :tangle no
fig, ax = plt.subplots()
@ -647,43 +393,20 @@ modulation.
#+RESULTS:
:RESULTS:
: <matplotlib.legend.Legend at 0x7fe235bfd1f0>
[[file:./.ob-jupyter/b97b3645c10c9324bb66e178bdf8b63ec4a5a628.svg]]
: <matplotlib.legend.Legend at 0x7f6ce04d5d60>
[[file:./.ob-jupyter/4cc96e897c1648694dbc559354d2868d6bee8dd0.svg]]
:END:
*** Analysis
#+begin_src jupyter-python
from itertools import cycle
lines = ["--","-.",":", "-"]
linecycler = cycle(lines)
fig, ax = plt.subplots()
t = np.linspace(0, long_models[0].Θ, 1000)
l, = ax.plot(t, long_models[0].H.operator_norm(t)/2-.5, linewidth=3, color="lightgrey")
legend_1 = ax.legend([l], [r"$(||H||-1)/2$"], loc="center left", title="Reference")
from cycler import cycler
for model in [best_shift_model, long_models[5]]:
ax.plot(t, model.coupling_operators[1].operator_norm(t), label=fr"${model.L_shift[0] * 100:.0f}\%$", linestyle=(next(linecycler)))
#ax.plot(t, model.coupling_operators[0].operator_norm(t), label=fr"${model.L_shift[0] * 100:.0f}\%$", linestyle=(next(linecycler)))
ax.legend(title=r"Shift of $L_h$", fontsize="x-small", ncols=2)
ax.set_xlabel(r"$\tau$")
ax.set_ylabel(r"Operator Norm")
ax.add_artist(legend_1)
ax.set_xlim((0, long_models[0].Θ))
fs.export_fig("cycle_shift_long_shifts", x_scaling=2, y_scaling=.5)
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/ac824b547713cd79da184599c7f503e85b44bc40.svg]]
** Integration
#+begin_src jupyter-python :tangle tangle/long.py
ot.integrate_online_multi(long_models, 80_000, increment=10_000, analyze_kwargs=dict(every=10_000))
#+end_src
#+RESULTS:
** Anaylysis
Let us look at power and efficiency.
#+begin_src jupyter-python
for shift, model in zip(shifts, long_models):
print(
@ -710,7 +433,7 @@ modulation.
0.42 0.12 80000 -1.4846084056353754 -118.88415735590576 (-0.7558354513701987, 0.4330061221888589)
#+end_example
Here, we contrast the slow/fast coupling modulation protocols.
#+begin_src jupyter-python
fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2)
_, ax1_right = ot.plot_powers_and_efficiencies(np.array(shifts) * 100, models, xlabel="Cycle Shift", ax=ax1)[2]
@ -725,76 +448,32 @@ modulation.
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/04d76de3e6d507097b891765428934a25429abaf.svg]]
[[file:./.ob-jupyter/dfee46d2b1411c9ca3f0619ae9460a2435bd0825.svg]]
Aho! The trick is just to slow down the coupling switching.
I know, horrible code. I just wan't to finish this...
#+begin_src jupyter-python
fig, ax =ot.plot_steady_energy_changes([long_models[3+2], models[3+2]], 2, label_fn=lambda m: ("long" if m.hexhash == long_models[3+2].hexhash else "short"))
best_long_idx = np.argmax([-model.power(steady_idx=2).value for model in long_models])
best_long_shift = shifts[best_long_idx]
best_long_shift_model = long_models[best_long_idx]
best_long_shift
#+end_src
#+RESULTS:
: 0.18
Let's contrast the energy change dynamics in slow vs fast modulation
#+begin_src jupyter-python
fig, ax =ot.plot_steady_energy_changes([best_long_shift_model, best_shift_model], 2, label_fn=lambda m: ("long" if m.hexhash == best_long_shift_model.hexhash else "short"))
ax.legend(loc="lower left")
#fs.export_fig("shift_energy_change", y_scaling=.7)
fs.export_fig("long_short_energy_change", y_scaling=.7)
#+end_src
#+RESULTS:
:RESULTS:
: <matplotlib.legend.Legend at 0x7f0ef3d3d940>
[[file:./.ob-jupyter/bbb9d138d6915d98c086c7f49d76baf55e5f8e0c.svg]]
:END:
#+begin_src jupyter-python
powers_long = [-model.power(steady_idx=2).value for model in long_models]
powers_short = [-model.power(steady_idx=2).value for model in models]
power_overlap = -overlap_models[0].power(steady_idx=2).value
plt.plot(shifts, powers_short)
plt.plot(shifts, powers_long)
plt.axhline(power_overlap)
#+end_src
#+RESULTS:
:RESULTS:
# [goto error]
: ---------------------------------------------------------------------------
: NameError Traceback (most recent call last)
: Cell In[53], line 3
:  1 powers_long = [-model.power(steady_idx=2).value for model in long_models]
:  2 powers_short = [-model.power(steady_idx=2).value for model in models]
: ----> 3 power_overlap = -overlap_models[0].power(steady_idx=2).value
:  4 plt.plot(shifts, powers_short)
:  5 plt.plot(shifts, powers_long)
:
: NameError: name 'overlap_models' is not defined
:END:
The overlap model still has slightly, but negligible power advantage.
#+begin_src jupyter-python
efficiencys_long = [model.efficiency(steady_idx=2).value for model in long_models]
efficiencys_short = [model.efficiency(steady_idx=2).value for model in models]
efficiency_overlap = overlap_models[0].efficiency(steady_idx=2).value
plt.plot(shifts, efficiencys_short)
plt.plot(shifts, efficiencys_long)
plt.axhline(efficiency_overlap)
#+end_src
#+RESULTS:
:RESULTS:
# [goto error]
: ---------------------------------------------------------------------------
: NameError Traceback (most recent call last)
: Cell In[28], line 3
:  1 efficiencys_long = [model.efficiency(steady_idx=2).value for model in long_models]
:  2 efficiencys_short = [model.efficiency(steady_idx=2).value for model in models]
: ----> 3 efficiency_overlap = overlap_models[0].efficiency(steady_idx=2).value
:  4 plt.plot(shifts, efficiencys_short)
:  5 plt.plot(shifts, efficiencys_long)
:
: NameError: name 'overlap_models' is not defined
:END:
Ok, we find that there's nothing special about the overlap model.
[[file:./.ob-jupyter/739b3f82650ec9b841aadeb72d8ff4bb04ecb999.svg]]
Now let's try to find out why the efficiency improved.
@ -811,7 +490,7 @@ Now let's try to find out why the efficiency improved.
plt.plot(best_shift_model.t, flow_long.value, label="slow coupling")
plt.plot(best_shift_model.t, power_short.value, linestyle="--", color="C0")
plt.plot(best_shift_model.t, power_long.value, linestyle="--", color="C1")
plt.xlim((2*best_long_model.Θ-5, 2*best_long_model.Θ+10))
plt.xlim((2*best_long_model.Θ-5, 2*best_long_model.Θ+12))
plt.ylim((-.015,.06))
plt.legend()
plt.xlabel(r"$\tau$")
@ -819,9 +498,8 @@ Now let's try to find out why the efficiency improved.
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/8cb5b5062c2f5c2b8d1cb21f999a299098958e0d.svg]]
[[file:./.ob-jupyter/562aa3c2c2a3c3c1a83020137bdbd45bbe0f550d.svg]]
Way less energy is dumped into the cold bath.
#+begin_src jupyter-python
t, rel_short_cold = ot.val_relative_to_steady(
best_shift_model,
@ -878,31 +556,18 @@ Way less energy is dumped into the cold bath.
: + (left_i[1] / (right_i[1]) ** 2 * right_i[2]) ** 2
: /home/hiro/src/hopsflow/hopsflow/util.py:334: RuntimeWarning: invalid value encountered in divide
: + (left_i[1] / (right_i[1]) ** 2 * right_i[2]) ** 2
[[file:./.ob-jupyter/73f0fb2a97297159d4517b28ae328108d70c260c.svg]]
[[file:./.ob-jupyter/e773c9a5072cc7643a93d1f05180f5083f93a823.svg]]
:END:
#+begin_src jupyter-python
plt.plot(best_shift_model.t, (best_shift_model.bath_energy().for_bath(0) / best_shift_model.bath_energy().for_bath(1)).value)
plt.ylim((-1, 1))
#+end_src
* Slower switching + Only Cold Bath Coupling Shifted
Let's see what happens if we only shift the coupling to the cold bath.
The last section gave me the hunch, that only this shift matters.
#+RESULTS:
:RESULTS:
: /home/hiro/src/hopsflow/hopsflow/util.py:334: RuntimeWarning: invalid value encountered in divide
: (left_i[2] / right_i[1]) ** 2
| -1.0 | 1.0 |
[[file:./.ob-jupyter/e370756ca7053f6e2cd87fb4928a509100b6900d.svg]]
:END:
** Slower switching + Only Cold Bath Coupling Shifted
*** Model def and intergration
#+begin_src jupyter-python :tangle tangle/only_cold.py
#+begin_src jupyter-python :tangle tangle/only_cold.py :results none
<<boilerplate>>
#+end_src
#+RESULTS:
#+begin_src jupyter-python :results none :tangle tangle/only_cold.py
shifts = sc.make_shifts(extra_r=4)
@ -913,41 +578,10 @@ Way less energy is dumped into the cold bath.
ot.integrate_online_multi(cold_models, 1, increment=1, analyze_kwargs=dict(every=10_000))
#+end_src
#+RESULTS:
#+begin_example
[INFO hops.core.integration 7496] Choosing the nonlinear integrator.
[INFO root 7496] Starting analysis process.
[INFO root 7496] Started analysis process with pid 16271.
/home/hiro/src/hops/hops/core/hierarchy_data.py:570: UserWarning: Moving .data/5d118bc5b64eb105ed45c825742f9241f81efa681dc7f6095b7d27ab6b96c284/_6/5d118bc5b64eb105ed45c825742f9241f81efa681dc7f6095b7d27ab6b96c284_6c882ba21738f240daf65b5a8bfeab4b_1.h5 to .data/5d118bc5b64eb105ed45c825742f9241f81efa681dc7f6095b7d27ab6b96c284/_6/5d118bc5b64eb105ed45c825742f9241f81efa681dc7f6095b7d27ab6b96c284_6c882ba21738f240daf65b5a8bfeab4b_1.h5backup_1683647050.4820192 and starting fresh.
warnings.warn(
[INFO hops.core.hierarchy_data 7496] Creating the streaming fifo at: /home/hiro/Documents/Projects/UNI/master/eflow_paper/python/otto_motor/subprojects/cycle_shift/results_5d118bc5b64eb105ed45c825742f9241f81efa681dc7f6095b7d27ab6b96c284.fifo
[INFO hops.core.integration 7496] Using 13 integrators.
[INFO hops.core.integration 7496] Some 1 trajectories have to be integrated.
[INFO hops.core.integration 7496] Using 1001 hierarchy states.
100% 1/1 [00:09<00:00, 9.14s/it]
[INFO hops.core.integration 7496] Choosing the nonlinear integrator.
[INFO root 7496] Starting analysis process.
[INFO root 7496] Started analysis process with pid 16288.
[INFO hops.core.hierarchy_data 7496] Creating the streaming fifo at: /home/hiro/Documents/Projects/UNI/master/eflow_paper/python/otto_motor/subprojects/cycle_shift/results_a86b8a23ecd962904a2008808f85b00b9c337e36dc6bebe3b806343510f0ec7f.fifo
[INFO hops.core.integration 7496] Using 13 integrators.
[INFO hops.core.integration 7496] Some 1 trajectories have to be integrated.
[INFO hops.core.integration 7496] Using 1001 hierarchy states.
100% 1/1 [00:08<00:00, 8.61s/it]
[INFO hops.core.integration 7496] Choosing the nonlinear integrator.
[INFO root 7496] Starting analysis process.
[INFO root 7496] Started analysis process with pid 16320.
[INFO hops.core.hierarchy_data 7496] Creating the streaming fifo at: /home/hiro/Documents/Projects/UNI/master/eflow_paper/python/otto_motor/subprojects/cycle_shift/results_ca94f36cbacd1b29d6e4f3cf384624ef0f4930ef3b0f12b09179efb17e327454.fifo
[INFO hops.core.integration 7496] Using 13 integrators.
[INFO hops.core.integration 7496] Some 1 trajectories have to be integrated.
[INFO hops.core.integration 7496] Using 1001 hierarchy states.
100% 1/1 [00:09<00:00, 9.09s/it]
#+end_example
#+begin_src jupyter-julia
aux.import_results(other_data_path="taurus/.data", other_results_path="taurus/results", models_to_import=cold_models)
#+end_src
*** Cycle showcase
#+begin_src jupyter-python :tangle no
fig, ax = plt.subplots()
@ -966,7 +600,7 @@ Way less energy is dumped into the cold bath.
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/36b87a9b430be49e32f70cb561affccf8b682b0f.svg]]
[[file:./.ob-jupyter/90dc100de7e68a738757c7ceec88d138523edd24.svg]]
#+begin_src jupyter-python
@ -991,9 +625,11 @@ Way less energy is dumped into the cold bath.
#+RESULTS:
:RESULTS:
| 0.0 | 60.0 |
[[file:./.ob-jupyter/91f5f58abe88d312dda69ea17845661d235cbb7b.svg]]
[[file:./.ob-jupyter/3a99f0725ec23cdfff1c58405c0167881a0648d8.svg]]
:END:
*** Anaysis
Let's contrast all three protocols.
#+begin_src jupyter-python
fig, (ax2, ax1, ax3) = plt.subplots(nrows=1, ncols=3)
_, ax1_right = ot.plot_powers_and_efficiencies(np.array(shifts) * 100, cold_models, xlabel="Cycle Shift", ax=ax1)[2]
@ -1014,6 +650,7 @@ Way less energy is dumped into the cold bath.
#+RESULTS:
[[file:./.ob-jupyter/c3ba93c44254765a56fc0ba9f0d578fa5ebfa682.svg]]
And do it again, but in a more convenient format.
#+begin_src jupyter-python
ot.plot_multi_powers_and_efficiencies(shifts, [models, long_models, cold_models], ["shifted", "shifted + slower modulation", "slower + only cold shifted"], xlabel=r"Shift $\delta$")
fs.export_fig("shift_comparison", y_scaling=1, x_scaling=2)
@ -1022,38 +659,24 @@ Way less energy is dumped into the cold bath.
#+RESULTS:
[[file:./.ob-jupyter/25b9c2b69b9e6bea35b3b7765c35ac370ddb6e24.svg]]
** Findings
* Findings
- coupling overlap doesn't help much
- with these parameters the earlier obeservation does not recur
- more scan needed
- maybe slower coupling/decoupling will help
* Off-Axis Hamiltonian
:PROPERTIES:
:ID: 9d7a11f2-f479-4e95-8775-31050bcc4fb7
:END:
Let us brieofly demonstrate the effects of rotating the system
hamiltonian.
** Construction
#+begin_src jupyter-python :tangle tangle/off_axis.py :results none
<<boilerplate>>
#+end_src
#+begin_src jupyter-python
aux.import_results(other_data_path="taurus/.data_oa", other_results_path="taurus/results")
#+end_src
#+RESULTS:
#+begin_example
[INFO root 465451] Not importing 3a88241b44e111869567acbf6ae02285aed02d52bb726b72ac72f9ab31dd3519.
[WARNING root 465451] Importing taurus/.data_oa/1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a/_b/1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a_b840f965f993ebd32f9155891c0b1cb4_1.h5 to .data/1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a/_b/1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a_b840f965f993ebd32f9155891c0b1cb4_1.h5.
[WARNING root 465451] The model description is 'Classic Cycle'.
[WARNING root 465451] Importing taurus/results/flow_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz to results/flow_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a_10000.npz.
[WARNING root 465451] Importing taurus/results/flow_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz to results/flow_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz.
[WARNING root 465451] Importing taurus/results/interaction_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz to results/interaction_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a_10000.npz.
[WARNING root 465451] Importing taurus/results/interaction_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz to results/interaction_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz.
[WARNING root 465451] Importing taurus/results/interaction_power_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz to results/interaction_power_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a_10000.npz.
[WARNING root 465451] Importing taurus/results/interaction_power_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz to results/interaction_power_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz.
[WARNING root 465451] Importing taurus/results/system_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz to results/system_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz.
[WARNING root 465451] Importing taurus/results/system_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz to results/system_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a_10000.npz.
[WARNING root 465451] Importing taurus/results/system_power_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz to results/system_power_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a_10000.npz.
[WARNING root 465451] Importing taurus/results/system_power_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz to results/system_power_1ebe2f33ba38ab70dc6af5f72cd5e4163422489db2447d034dcd8d405a0fc79a.npz.
#+end_example
#+begin_src jupyter-python :tangle tangle/off_axis.py
off_ax_models = []
weights = [.3, .6]
@ -1069,16 +692,18 @@ Way less energy is dumped into the cold bath.
#+end_src
#+RESULTS:
: 3.5999999999999996
: 3.5999999999999996
: 7.199999999999999
: 7.199999999999999
** Integration
#+begin_src jupyter-python :tangle tangle/off_axis.py
ot.integrate_online_multi(off_ax_models, 10, increment=10, analyze_kwargs=dict(every=10_000))
#+end_src
#+begin_src jupyter-python
aux.import_results(other_data_path="taurus/.data_oa", other_results_path="taurus/results")
#+end_src
** Analysis
Let's plot the pauli expectation values.
#+begin_src jupyter-python
for (i, model), weight in zip(enumerate(off_ax_models), weights):
f, a = ot.plot_bloch_components(model)
@ -1090,8 +715,8 @@ Way less energy is dumped into the cold bath.
#+RESULTS:
:RESULTS:
[[file:./.ob-jupyter/9728f3b41ba1c00b9b3b8cdef827909ece227deb.svg]]
[[file:./.ob-jupyter/66410d6f93476857e9f7f681a59a0091ebc27231.svg]]
[[file:./.ob-jupyter/e0388abacb7b8d8791b4a243661de3e7cf92321e.svg]]
[[file:./.ob-jupyter/bf8f086e5b8211108f5481f511133342ddfb5c33.svg]]
:END:
#+begin_src jupyter-python
@ -1105,14 +730,14 @@ Way less energy is dumped into the cold bath.
#+begin_src jupyter-python
baselines = [baseline] * 2 + [long_baseline] * 2
for model, ref in zip(off_ax_models, baselines):
print(model.power(steady_idx=1).value / ref.power(steady_idx=1).value, model.efficiency(steady_idx=1).value / ref.efficiency(steady_idx=1).value)
print(model.power(steady_idx=2).value / ref.power(steady_idx=2).value, model.efficiency(steady_idx=2).value / ref.efficiency(steady_idx=2).value)
#+end_src
#+RESULTS:
: 1.0574121708551179 1.016329556714788
: 1.1608389370275625 0.9458062530964767
: 1.039411606725501 0.9835515009556695
: 1.117040153314062 0.9663817206527843
: 1.0868612980640593 1.0437773131214951
: 1.1468800706147944 0.9438835472008851
: 1.070328051487702 0.9917819857660193
: 1.1178966202334308 0.958371868191535
Interestingly, even with the too-fast switching we have greater power, and greater efficiency.
@ -1125,6 +750,6 @@ Interestingly, even with the too-fast switching we have greater power, and great
#+RESULTS:
:RESULTS:
[[file:./.ob-jupyter/b0afa48c75085e2a541587c350698ad79958b170.svg]]
[[file:./.ob-jupyter/cb9eaeab19b96ffab30ddb3adde4ba165801064d.svg]]
[[file:./.ob-jupyter/5639272b64cefcf447899df6ecf4d49baf35988d.svg]]
[[file:./.ob-jupyter/e0adfb01a3b456c2a8a22ecf281cbb7e914939a6.svg]]
:END:

229
python/otto_motor/subprojects/cycle_shift/cycle_shift.org_archive Normal file
View file

@ -0,0 +1,229 @@
# -*- mode: org -*-
Archived entries from file /home/hiro/Documents/master/eflow_paper/python/otto_motor/subprojects/cycle_shift/cycle_shift.org
* Overlapping the Phases
:PROPERTIES:
:ARCHIVE_TIME: 2023-05-11 Thu 12:33
:ARCHIVE_FILE: ~/Documents/master/eflow_paper/python/otto_motor/subprojects/cycle_shift/cycle_shift.org
:ARCHIVE_CATEGORY: cycle_shift
:END:
What happedn
#+begin_src jupyter-python
T = 50
def overlap(shift_model, N, step, switch_t=3.):
switch_time = switch_t / T
(p_H, p_L) = ot.timings(switch_time, switch_time)
next_model = shift_model.copy()
#next_model.timings_H=p_H
next_model.timings_L=p_L
(a, b, c, d) = next_model.timings_L[0]
(e, f, g, h) = next_model.timings_L[1]
next_step = step * N
(s1, s2) = next_model.L_shift
next_model.L_shift = (s1 + next_step, s2 - next_step)
next_model.timings_L = (
(a - 2 * next_step, b - 2 * next_step, c, d),
(e, f, g + 2 * next_step, h + 2 * next_step),
)
return next_model
def overlap_cold(shift_model, N, step):
next_model = shift_model.copy()
(a, b, c, d) = next_model.timings_L[0]
(e, f, g, h) = next_model.timings_L[1]
next_step = step * N
(s1, s2) = next_model.L_shift
next_model.L_shift = (s1 + next_step, s2 - next_step)
next_model.timings_L = (
(a - 2 * next_step, b - 2 * next_step, c - next_step, d - next_step),
(e + next_step, f + next_step, g + 2 * next_step, h + 2 * next_step),
)
return next_model
Ns = list(range(1, 4))[:1]
overlap_models = [overlap(best_shift_model, N, sc.make_step()) for N in Ns]
overlap_models = [overlap_cold(best_shift_model, N, sc.make_step()) for N in Ns]
new_step_size = 6
mini_step = (new_step_size / 10)
print(mini_step)
overlap_models = [overlap(best_shift_model, N, mini_step, new_step_size) for N in Ns]
#+end_src
#+RESULTS:
: 0.6
#+begin_src jupyter-python :tangle no
ot.plot_cycles([overlap_models[0]], legend=True)
#+end_src
#+RESULTS:
:RESULTS:
| <Figure | size | 340x320 | with | 1 | Axes> | <AxesSubplot: | xlabel= | $\tau$ | ylabel= | Operator Norm | > |
[[file:./.ob-jupyter/380373af099bbf5309b03dbaff5557e05ac11ed8.svg]]
:END:
** Integrate
#+begin_src jupyter-julia
all_overlap_models = [best_shift_model, *overlap_models]
#+end_src
#+begin_src jupyter-python
ot.integrate_online_multi(overlap_models, 80_000, increment=10_000, analyze_kwargs=dict(every=10_000))
#+end_src
** Analysis
#+begin_src jupyter-python :tangle no
fig, ax = plt.subplots()
t = np.linspace(0, all_overlap_models[0].Θ, 1000)
ax.plot(t, all_overlap_models[0].coupling_operators[0].operator_norm(t), color="C1", linewidth=1, label="Shifted")
ax.plot(t, all_overlap_models[0].coupling_operators[1].operator_norm(t), color="C1", linestyle="--", linewidth=1)
ax.plot(t, all_overlap_models[1].coupling_operators[0].operator_norm(t), color="C2", linewidth=1, label="Shifted with Overlap")
ax.plot(t, all_overlap_models[1].coupling_operators[1].operator_norm(t), color="C2", linestyle="--", linewidth=1)
ax.set_xlabel(r"$\tau$")
ax.set_ylabel(r"$||L_{h/c}||$")
ax.legend()
fs.export_fig("cycle_shift_shift_vs_overlap", y_scaling=.6)
#ot.plot_cycles(all_overlap_models[0:2], legend=True)
#+end_src
#+RESULTS:
:RESULTS:
# [goto error]
: ---------------------------------------------------------------------------
: NameError Traceback (most recent call last)
: Cell In[58], line 2
:  1 fig, ax = plt.subplots()
: ----> 2 t = np.linspace(0, all_overlap_models[0].Θ, 1000)
:  3 ax.plot(t, all_overlap_models[0].coupling_operators[0].operator_norm(t), color="C1", linewidth=1, label="Shifted")
:  4 ax.plot(t, all_overlap_models[0].coupling_operators[1].operator_norm(t), color="C1", linestyle="--", linewidth=1)
:
: NameError: name 'all_overlap_models' is not defined
[[file:./.ob-jupyter/7347018a6eb9899c10d9726fcc5d9b94fae25a6d.svg]]
:END:
#+begin_src jupyter-python
ot.plot_power_eff_convergence(all_overlap_models, 2)
#+end_src
#+RESULTS:
:RESULTS:
| <Figure | size | 340x320 | with | 2 | Axes> | (<AxesSubplot: xlabel= $N$ ylabel= $P$ > <AxesSubplot: xlabel= $N$ ylabel= $\eta$ >) |
[[file:./.ob-jupyter/e01f809855125e962fb4f56975fb4833b122dd1a.svg]]
:END:
#+begin_src jupyter-python
f, a= ot.plot_energy(all_overlap_models[-1])
a.plot(model.t, model.coupling_operators[0].operator_norm(model.t))
a.plot(model.t, model.coupling_operators[1].operator_norm(model.t))
a.plot(model.t, model.system.operator_norm(model.t))
#+end_src
#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7ff2b6947400> |
[[file:./.ob-jupyter/6f6fb7a34b89a008d51117d01b0dba6e6341fd8c.svg]]
:END:
#+begin_src jupyter-julia
[model.power(steady_idx=2).value / best_shift_model.power(steady_idx=2).value for model in all_overlap_models]
#+end_src
#+RESULTS:
| 1.0 | 1.3236593973330115 |
#+begin_src jupyter-julia
[model.efficiency(steady_idx=2).value / best_shift_model.efficiency(steady_idx=2).value for model in all_overlap_models]
#+end_src
#+RESULTS:
| 1.0 | 1.1230706203655971 |
#+begin_src jupyter-julia
[model.power(steady_idx=2).N for model in all_overlap_models]
#+end_src
#+RESULTS:
| 80000 | 80000 |
#+begin_src jupyter-python
ot.plot_powers_and_efficiencies([0] + Ns, all_overlap_models)
#+end_src
#+RESULTS:
:RESULTS:
| <Figure | size | 340x320 | with | 2 | Axes> | <AxesSubplot: | ylabel= | $-\bar{P}$ | > |
[[file:./.ob-jupyter/0b9adf725182e7385744287f98375c8b39c3471b.svg]]
:END:
#+begin_src jupyter-python
f, a = plt.subplots()
a.axhline(0, color="lightgrey")
for model, label in zip(all_overlap_models[:2], ["Shifted", "Shifted with Overlap"]):
_, _, lines = pu.plot_with_σ(model.t, model.interaction_power().sum_baths().integrate(model.t), ax=a, label=fr"$W_\mathrm{{int}}$ {label}")
pu.plot_with_σ(model.t, model.system_power().integrate(model.t), ax=a, color=lines[0][0].get_color(), linestyle="--", label=fr"$W_\mathrm{{sys}}$ {label}")
a.set_ylabel(r"$W_{\mathrm{int/sys}}$")
a.set_xlabel(r"$\tau$")
a.legend()
fs.export_fig("cycle_shift_shift_vs_overlap_power", x_scaling=2, y_scaling=.6)
#+end_src
#+RESULTS:
[[file:./.ob-jupyter/a4e92f194bddc790d251d8118f1bf7592fb58bb7.svg]]
We see that the power boost is solely due to the interaction
modulation.
#+begin_src jupyter-python
fig, ax =ot.plot_steady_energy_changes(all_overlap_models, 2, label_fn=(lambda m: ["without overlap", "with overlap"][all_overlap_models.index(m)]))
ax.legend(loc="lower left")
fs.export_fig("overlap_energy_change", y_scaling=.9)
fig, ax =ot.plot_steady_work_baths(all_overlap_models, 2, label_fn=(lambda m: ["without overlap", "with overlap"][all_overlap_models.index(m)]))
ax.legend(loc="lower left")
fs.export_fig("overlap_energy_change_hot_cold", y_scaling=.9)
#+end_src
#+RESULTS:
:RESULTS:
# [goto error]
: ---------------------------------------------------------------------------
: NameError Traceback (most recent call last)
: Cell In[206], line 1
: ----> 1 fig, ax =ot.plot_steady_energy_changes(all_overlap_models, 2, label_fn=(lambda m: ["without overlap", "with overlap"][all_overlap_models.index(m)]))
:  2 ax.legend(loc="lower left")
:  4 fs.export_fig("overlap_energy_change", y_scaling=.9)
:
: NameError: name 'all_overlap_models' is not defined
:END:
#+begin_src jupyter-python
r = pu.plot_with_σ(all_overlap_models[-1].t, all_overlap_models[-1].interaction_energy().for_bath(0))
# a.plot(all_overlap_models[-1].t, all_overlap_models[-1].H(all_overlap_models[-1].t)[:, 0,0])
r[1].plot(all_overlap_models[-1].t, all_overlap_models[-1].coupling_operators[0].operator_norm(all_overlap_models[-1].t) / 5)
r[1].plot(all_overlap_models[-1].t, all_overlap_models[-1].coupling_operators[1].operator_norm(all_overlap_models[-1].t) / 5)
r[1].set_xlim((model.Θ*2, model.Θ*2+15))
#+end_src
#+RESULTS:
:RESULTS:
| 120.0 | 135.0 |
[[file:./.ob-jupyter/05702081169b9057efd24c51303402f7e774030e.svg]]
:END:

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@ -10,7 +10,7 @@ T = 50
def make_model(shift_c, shift_h, switch_t=3.0, switch_t_sys=None, only_cold=False):
switch_time = switch_t / T
switch_time_sys = (switch_t_sys if switch_t_sys else switch_t) / T
print(switch_time * 60)
(p_H, p_L) = ot.timings(switch_time_sys, switch_time)
return OttoEngine(
δ=[0.7, 0.7],
@ -36,6 +36,10 @@ def make_model(shift_c, shift_h, switch_t=3.0, switch_t_sys=None, only_cold=Fals
)
def make_step(N=3, N_over=2):
return 3.0 / (T * (N - N_over))
def make_shifts(N=3, N_over=2, extra_r=2):
step = 3.0 / (T * (N - N_over))
shifts = [round(shift * step, 3) for shift in range(-N, N + 1 + extra_r)]

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python/otto_motor/subprojects/cycle_shift/tangle/cycle_shift.py
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@ -22,9 +22,6 @@ logging_setup(logging.INFO)
ot.plot_cycle(baseline)
fs.export_fig("cycle_prototype", y_scaling=.7)
for model in models:
print(model.power(steady_idx=1).value / baseline.power(steady_idx=1).value, model.efficiency(steady_idx=1).value)
ot.plot_energy(baseline)
print(
fs.tex_value(baseline.system_energy().N, prefix="N="),
@ -70,21 +67,23 @@ fs.export_fig("state_evolution", y_scaling=.7)
ot.plot_steady_energy_changes([baseline], 2, label_fn=lambda _: "")
fs.export_fig("prototype_energy_change", y_scaling=.7)
for model in models:
print(model.power(steady_idx=2).value / baseline.power(steady_idx=2).value, model.efficiency(steady_idx=2).value)
ot.plot_power_eff_convergence(models)
fs.export_fig("cycle_shift_convergence", x_scaling=2, y_scaling=.7)
ot.plot_powers_and_efficiencies(np.array(shifts) * 100, models, xlabel="Cycle Shift")
fs.export_fig("cycle_shift_power_efficiency", y_scaling=.7, x_scaling=1)
fig, ax =ot.plot_steady_energy_changes([baseline, models[3+2]], 2, label_fn=lambda m: ("baseline" if m.hexhash == baseline.hexhash else "shifted"))
best_shift = shifts[np.argmax([-model.power(steady_idx=2).value for model in models])]
best_shift_model = sc.make_model(best_shift, best_shift)
best_shift
fig, ax =ot.plot_steady_energy_changes([baseline, best_shift_model], 2, label_fn=lambda m: ("baseline" if m.hexhash == baseline.hexhash else "shifted"))
ax.legend(loc="lower left")
fs.export_fig("shift_energy_change", y_scaling=.7)
best_shift = shifts[3+2]#[np.argmax([-model.power(steady_idx=2).value for model in models])]
best_shift_model = sc.make_model(best_shift, best_shift)
ot.plot_bloch_components(best_shift_model)
t_shift_begin = (2 - best_shift) * baseline.Θ
t_begin = 2 * baseline.Θ
t_shift_end = (3 - best_shift) * baseline.Θ
@ -131,10 +130,6 @@ ax.set_xlabel(r"$\tau$")
ax.set_ylabel(r"$P_{\mathrm{int}}$")
fs.export_fig("shift_power", y_scaling=0.7)
ot.plot_energy(baseline)
f, a = ot.plot_energy(best_shift_model)
a.plot(best_shift_model.t, best_shift_model.H(best_shift_model.t)[:, 0,0])
f, a = plt.subplots()
a.axhline(best_shift_model.system_energy().value[np.argmin(abs(best_shift_model.t - model.Θ * 2))], color="gray", linestyle="--")
r = pu.plot_with_σ(
@ -161,121 +156,13 @@ a.plot(
label="system modulation"
)
# a.plot(best_shift_model.t, best_shift_model.coupling_operators[1].operator_norm(best_shift_model.t) / 5)
a.set_xlim((model.Θ * 2, model.Θ * 2 + 7))
a.set_xlim((model.Θ * 2, model.Θ * 2 + 11))
a.set_ylim((-.21, .45))
a.set_xlabel(r"$\tau$")
a.legend(loc="upper right", fontsize="x-small")
fs.export_fig("cold_bath_decoupling", y_scaling=.6)
def overlap(shift_model, N, step, switch_t=3.):
switch_time = switch_t / T
(p_H, p_L) = ot.timings(switch_time, switch_time)
next_model = shift_model.copy()
#next_model.timings_H=p_H
next_model.timings_L=p_L
(a, b, c, d) = next_model.timings_L[0]
(e, f, g, h) = next_model.timings_L[1]
next_step = step * N
(s1, s2) = next_model.L_shift
next_model.L_shift = (s1 + next_step, s2 - next_step)
next_model.timings_L = (
(a - 2 * next_step, b - 2 * next_step, c, d),
(e, f, g + 2 * next_step, h + 2 * next_step),
)
return next_model
def overlap_cold(shift_model, N, step):
next_model = shift_model.copy()
(a, b, c, d) = next_model.timings_L[0]
(e, f, g, h) = next_model.timings_L[1]
next_step = step * N
(s1, s2) = next_model.L_shift
next_model.L_shift = (s1 + next_step, s2 - next_step)
next_model.timings_L = (
(a - 2 * next_step, b - 2 * next_step, c - next_step, d - next_step),
(e + next_step, f + next_step, g + 2 * next_step, h + 2 * next_step),
)
return next_model
Ns = list(range(1, 4))[:1]
overlap_models = [overlap(best_shift_model, N, step) for N in Ns]
overlap_models = [overlap_cold(best_shift_model, N, step) for N in Ns]
new_step_size = 6
mini_step = (new_step_size / (N-N_over) / T)
print(mini_step)
overlap_models = [overlap(best_shift_model, N, mini_step, new_step_size) for N in Ns]
all_overlap_models = [best_shift_model, *overlap_models]
ot.integrate_online_multi(overlap_models, 80_000, increment=10_000, analyze_kwargs=dict(every=10_000))
ot.plot_power_eff_convergence(all_overlap_models, 2)
f, a= ot.plot_energy(all_overlap_models[-1])
a.plot(model.t, model.coupling_operators[0].operator_norm(model.t))
a.plot(model.t, model.coupling_operators[1].operator_norm(model.t))
a.plot(model.t, model.system.operator_norm(model.t))
[model.power(steady_idx=2).value / best_shift_model.power(steady_idx=2).value for model in all_overlap_models]
[model.efficiency(steady_idx=2).value / best_shift_model.efficiency(steady_idx=2).value for model in all_overlap_models]
[model.power(steady_idx=2).N for model in all_overlap_models]
ot.plot_powers_and_efficiencies([0] + Ns, all_overlap_models)
f, a = plt.subplots()
a.axhline(0, color="lightgrey")
for model, label in zip(all_overlap_models[:2], ["Shifted", "Shifted with Overlap"]):
_, _, lines = pu.plot_with_σ(model.t, model.interaction_power().sum_baths().integrate(model.t), ax=a, label=fr"$W_\mathrm{{int}}$ {label}")
pu.plot_with_σ(model.t, model.system_power().integrate(model.t), ax=a, color=lines[0][0].get_color(), linestyle="--", label=fr"$W_\mathrm{{sys}}$ {label}")
a.set_ylabel(r"$W_{\mathrm{int/sys}}$")
a.set_xlabel(r"$\tau$")
a.legend()
fs.export_fig("cycle_shift_shift_vs_overlap_power", x_scaling=2, y_scaling=.6)
fig, ax =ot.plot_steady_energy_changes(all_overlap_models, 2, label_fn=(lambda m: ["without overlap", "with overlap"][all_overlap_models.index(m)]))
ax.legend(loc="lower left")
fs.export_fig("overlap_energy_change", y_scaling=.9)
fig, ax =ot.plot_steady_work_baths(all_overlap_models, 2, label_fn=(lambda m: ["without overlap", "with overlap"][all_overlap_models.index(m)]))
ax.legend(loc="lower left")
fs.export_fig("overlap_energy_change_hot_cold", y_scaling=.9)
r = pu.plot_with_σ(all_overlap_models[-1].t, all_overlap_models[-1].interaction_energy().for_bath(0))
# a.plot(all_overlap_models[-1].t, all_overlap_models[-1].H(all_overlap_models[-1].t)[:, 0,0])
r[1].plot(all_overlap_models[-1].t, all_overlap_models[-1].coupling_operators[0].operator_norm(all_overlap_models[-1].t) / 5)
r[1].plot(all_overlap_models[-1].t, all_overlap_models[-1].coupling_operators[1].operator_norm(all_overlap_models[-1].t) / 5)
r[1].set_xlim((model.Θ*2, model.Θ*2+15))
from itertools import cycle
lines = ["--","-.",":", "-"]
linecycler = cycle(lines)
fig, ax = plt.subplots()
t = np.linspace(0, long_models[0].Θ, 1000)
l, = ax.plot(t, long_models[0].H.operator_norm(t)/2-.5, linewidth=3, color="lightgrey")
legend_1 = ax.legend([l], [r"$(||H||-1)/2$"], loc="center left", title="Reference")
from cycler import cycler
for model in [best_shift_model, long_models[5]]:
ax.plot(t, model.coupling_operators[1].operator_norm(t), label=fr"${model.L_shift[0] * 100:.0f}\%$", linestyle=(next(linecycler)))
#ax.plot(t, model.coupling_operators[0].operator_norm(t), label=fr"${model.L_shift[0] * 100:.0f}\%$", linestyle=(next(linecycler)))
ax.legend(title=r"Shift of $L_h$", fontsize="x-small", ncols=2)
ax.set_xlabel(r"$\tau$")
ax.set_ylabel(r"Operator Norm")
ax.add_artist(legend_1)
ax.set_xlim((0, long_models[0].Θ))
fs.export_fig("cycle_shift_long_shifts", x_scaling=2, y_scaling=.5)
for shift, model in zip(shifts, long_models):
print(
shift, best_shift,
@ -296,24 +183,15 @@ ax1.set_title("Fast Coupling")
ax2.set_title("Slow Coupling")
fs.export_fig("cycle_shift_power_efficiency_with_slower", y_scaling=.7, x_scaling=2)
fig, ax =ot.plot_steady_energy_changes([long_models[3+2], models[3+2]], 2, label_fn=lambda m: ("long" if m.hexhash == long_models[3+2].hexhash else "short"))
best_long_idx = np.argmax([-model.power(steady_idx=2).value for model in long_models])
best_long_shift = shifts[best_long_idx]
best_long_shift_model = long_models[best_long_idx]
best_long_shift
fig, ax =ot.plot_steady_energy_changes([best_long_shift_model, best_shift_model], 2, label_fn=lambda m: ("long" if m.hexhash == best_long_shift_model.hexhash else "short"))
ax.legend(loc="lower left")
#fs.export_fig("shift_energy_change", y_scaling=.7)
powers_long = [-model.power(steady_idx=2).value for model in long_models]
powers_short = [-model.power(steady_idx=2).value for model in models]
power_overlap = -overlap_models[0].power(steady_idx=2).value
plt.plot(shifts, powers_short)
plt.plot(shifts, powers_long)
plt.axhline(power_overlap)
efficiencys_long = [model.efficiency(steady_idx=2).value for model in long_models]
efficiencys_short = [model.efficiency(steady_idx=2).value for model in models]
efficiency_overlap = overlap_models[0].efficiency(steady_idx=2).value
plt.plot(shifts, efficiencys_short)
plt.plot(shifts, efficiencys_long)
plt.axhline(efficiency_overlap)
fs.export_fig("long_short_energy_change", y_scaling=.7)
best_long_model = long_models[5]
@ -327,7 +205,7 @@ plt.plot(best_shift_model.t, flow_short.value, label="fast coupling")
plt.plot(best_shift_model.t, flow_long.value, label="slow coupling")
plt.plot(best_shift_model.t, power_short.value, linestyle="--", color="C0")
plt.plot(best_shift_model.t, power_long.value, linestyle="--", color="C1")
plt.xlim((2*best_long_model.Θ-5, 2*best_long_model.Θ+10))
plt.xlim((2*best_long_model.Θ-5, 2*best_long_model.Θ+12))
plt.ylim((-.015,.06))
plt.legend()
plt.xlabel(r"$\tau$")
@ -375,9 +253,6 @@ plt.xlabel(r"$\tau$")
plt.ylabel(r"$-\Delta \langle{H_{\mathrm{B},c}}\rangle/\Delta \langle{H_{\mathrm{B},h}}\rangle$")
fs.export_fig("hot_vs_cold_bath", y_scaling=.7)
plt.plot(best_shift_model.t, (best_shift_model.bath_energy().for_bath(0) / best_shift_model.bath_energy().for_bath(1)).value)
plt.ylim((-1, 1))
aux.import_results(other_data_path="taurus/.data", other_results_path="taurus/results", models_to_import=cold_models)
from itertools import cycle
@ -428,7 +303,7 @@ np.array(weights) / np.sqrt(1 + np.array(weights) ** 2)
baselines = [baseline] * 2 + [long_baseline] * 2
for model, ref in zip(off_ax_models, baselines):
print(model.power(steady_idx=1).value / ref.power(steady_idx=1).value, model.efficiency(steady_idx=1).value / ref.efficiency(steady_idx=1).value)
print(model.power(steady_idx=2).value / ref.power(steady_idx=2).value, model.efficiency(steady_idx=2).value / ref.efficiency(steady_idx=2).value)
for (i, model), weight in zip(enumerate(off_ax_models), weights):
f, a = ot.plot_energy(model)

42
python/otto_motor/subprojects/cycle_shift/tangle/long.py
View file

@ -1,26 +1,26 @@
#import plot_utils as pu
#from hiro_models.one_qubit_model import StocProcTolerances
#from hiro_models.otto_cycle import OttoEngine
#import hiro_models.model_auxiliary as aux
#import numpy as np
#import qutip as qt
#import utilities as ut
#import stocproc
#import matplotlib.pyplot as plt
#import otto_utilities as ot
#import shift_cycle as sc
#import ray
#import figsaver as fs
#ray.shutdown()
#
##ray.init(address='auto')
#ray.init()
#from hops.util.logging_setup import logging_setup
#import logging
#logging_setup(logging.INFO)
import plot_utils as pu
from hiro_models.one_qubit_model import StocProcTolerances
from hiro_models.otto_cycle import OttoEngine
import hiro_models.model_auxiliary as aux
import numpy as np
import qutip as qt
import utilities as ut
import stocproc
import matplotlib.pyplot as plt
import otto_utilities as ot
import shift_cycle as sc
import ray
import figsaver as fs
ray.shutdown()
#ray.init(address='auto')
ray.init()
from hops.util.logging_setup import logging_setup
import logging
logging_setup(logging.INFO)
shifts = sc.make_shifts(extra_r=4)
#long_models = [sc.make_model(shift, shift, switch_t=6., switch_t_sys=3) for shift in shifts]
long_models = [sc.make_model(shift, shift, switch_t=6.) for shift in shifts]
long_baseline = sc.make_model(0., 0., switch_t=6.)