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small updates on the relaxation front

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valentin.boettcher@mailbox.tu-dresden.de 2023-02-13 12:13:45 -05:00
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commit 3a717743c5
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2 changed files with 92 additions and 17 deletions
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78
python/otto_motor/subprojects/relaxation/finding_relaxation_time.org
View file

@ -51,10 +51,11 @@ Therefore we need a way to keep the coupling switching speed constant.
#+end_src
Now we define the prototype. The numeric accuracy is jacked down, as
we don't need precision.
we don't need precision. We only use two cycles because of the long
cycle time.
#+begin_src jupyter-python
def make_cycle(θ):
(p_H, p_L) = timings(3 / θ, 3 / θ)
(p_H, p_L) = timings(3. / θ, 3. / θ)
return OttoEngine(
δ=[0.4, 0.4],
@ -69,7 +70,7 @@ we don't need precision.
T=[0.5, 4],
therm_methods=["tanhsinh", "tanhsinh"],
Δ=1,
num_cycles=3,
num_cycles=2,
Θ=θ,
dt=0.001,
timings_H=p_H,
@ -83,29 +84,78 @@ we don't need precision.
#+RESULTS:
#+begin_src jupyter-python :tangle no
ot.plot_cycle(make_cycle(50))
ot.plot_cycle(make_cycle(100))
#+end_src
#+RESULTS:
:RESULTS:
| <Figure | size | 1200x400 | with | 1 | Axes> | <AxesSubplot: | xlabel= | $\tau$ | ylabel= | Operator Norm | > |
[[file:./.ob-jupyter/18806741c1252bcffe79195955c565429406d683.svg]]
[[file:./.ob-jupyter/1f628c0de83132def7283aefd2884d611b0ea5e5.svg]]
:END:
* Cursory Scanning
We can now test the model to find wether it allows enough time for
complete thermalization. We'll start with a really long cycle.
We tried 100, now we try 60. 60 is a bit too short. So let's try 70
#+begin_src jupyter-python :results none
long_cycle = make_cycle(70)
#+end_src
#+begin_src jupyter-python
ot.integrate_online(make_cycle(60), 1000)
ot.integrate_online(long_cycle, 10000)
#+end_src
Now we look at the system energy.
#+begin_src jupyter-python
f, a, *_ = pu.plot_with_σ(long_cycle.t, long_cycle.system_energy())
a.set_xlim(0, long_cycle.Θ)
#+end_src
#+RESULTS:
: [INFO hops.core.integration 67753] Choosing the nonlinear integrator.
: [INFO root 67753] Starting analysis process.
: [INFO root 67753] Started analysis process with pid 69649.
: [INFO hops.core.hierarchy_data 67753] Creating the streaming fifo at: /home/hiro/Documents/Projects/UNI/master/eflow_paper/python/otto_motor/subprojects/relaxation/results_d2fc0c70ef3fa02e3f899c319307ee683ee264dddd838adc175f3209910580ea.fifo
: [INFO hops.core.integration 67753] Using 16 integrators.
: [INFO hops.core.integration 67753] Some 1000 trajectories have to be integrated.
: [INFO hops.core.integration 67753] Using 165 hierarchy states.
: 32% 320/1000 [16:58<36:03, 3.18s/it]
:RESULTS:
| 0.0 | 70.0 |
[[file:./.ob-jupyter/429c4411f7c721afd6ef116f635b8e45cec17dcf.svg]]
:END:
#+begin_src jupyter-python
ot.plot_energy(long_cycle)
#+end_src
#+RESULTS:
:RESULTS:
| <Figure | size | 1200x400 | with | 1 | Axes> | <AxesSubplot: | xlabel= | $\tau$ | ylabel= | Energy | > |
[[file:./.ob-jupyter/01a3e4d5c924de01d1bc25e3a858b00afbd06140.svg]]
:END:
We would like to know how far away from the thermal state the system is.
#+begin_src jupyter-python :results none
def thermal_state(Ω, T):
ρ = np.array([[np.exp(-Ω/T), 0], [0, 1]])
ρ /= np.sum(np.diag(ρ))
return ρ
#+end_src
#+begin_src jupyter-python
import hops.util.utilities
from hopsflow.util import EnsembleValue
with aux.get_data(long_cycle) as data:
trace_dist_c = hops.util.utilities.trace_distance(data, relative_to=thermal_state(long_cycle.T[0], long_cycle.energy_gaps[0]))
trace_dist_h = hops.util.utilities.trace_distance(data, relative_to=thermal_state(long_cycle.T[1], long_cycle.energy_gaps[1]))
f, a = plt.subplots()
pu.plot_with_σ(long_cycle.t, EnsembleValue(trace_dist_c), ax=a)
pu.plot_with_σ(long_cycle.t, EnsembleValue(trace_dist_h), ax=a)
a.plot(long_cycle.t, long_cycle.H(long_cycle.t)[:, 0, 0] - 1)
#a.set_xlim(155)
#+end_src
#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7f76af34bf10> |
[[file:./.ob-jupyter/c3ab5d34881edb6ba2e30ace5d0fae61870040f3.svg]]
:END:

31
python/otto_motor/subprojects/relaxation/tangle/otto_relax.py
View file

@ -31,7 +31,7 @@ def timings(τ_c, τ_i):
return timings_H, (timings_L_cold, timings_L_hot)
def make_cycle(θ):
(p_H, p_L) = timings(3 / θ, 3 / θ)
(p_H, p_L) = timings(3. / θ, 3. / θ)
return OttoEngine(
δ=[0.4, 0.4],
@ -46,7 +46,7 @@ def make_cycle(θ):
T=[0.5, 4],
therm_methods=["tanhsinh", "tanhsinh"],
Δ=1,
num_cycles=3,
num_cycles=2,
Θ=θ,
dt=0.001,
timings_H=p_H,
@ -56,4 +56,29 @@ def make_cycle(θ):
L_shift=(0, 0),
)
ot.integrate_online(make_cycle(60), 1000)
long_cycle = make_cycle(70)
ot.integrate_online(long_cycle, 10000)
f, a, *_ = pu.plot_with_σ(long_cycle.t, long_cycle.system_energy())
a.set_xlim(0, long_cycle.Θ)
ot.plot_energy(long_cycle)
def thermal_state(Ω, T):
ρ = np.array([[np.exp(-Ω/T), 0], [0, 1]])
ρ /= np.sum(np.diag(ρ))
return ρ
import hops.util.utilities
from hopsflow.util import EnsembleValue
with aux.get_data(long_cycle) as data:
trace_dist_c = hops.util.utilities.trace_distance(data, relative_to=thermal_state(long_cycle.T[0], long_cycle.energy_gaps[0]))
trace_dist_h = hops.util.utilities.trace_distance(data, relative_to=thermal_state(long_cycle.T[1], long_cycle.energy_gaps[1]))
f, a = plt.subplots()
pu.plot_with_σ(long_cycle.t, EnsembleValue(trace_dist_c), ax=a)
pu.plot_with_σ(long_cycle.t, EnsembleValue(trace_dist_h), ax=a)
a.plot(long_cycle.t, long_cycle.H(long_cycle.t)[:, 0, 0] - 1)
#a.set_xlim(155)