QuTiPv5 Paper Notebook: new Solver class and various applications of mesolve, brsolve and heom #111
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- added simple sesolver - added mesolver for local dissipation - added mesolver for global version - added comparison to brsolver - everything supported by text from the paper
- collapse list is now created by a function and for specific hamiltonians - fixed variable names to fit 80 char width - fixed typos
Langhaarzombie
changed the title
- fixed many typos and errors - rewrote much in own words - added reference section
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Thanks @Langhaarzombie this looks great. Left a few comments and suggestions.
| ## Testing | ||
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| ```python | ||
| # test sesolve gives the same result as SESolver |
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i guess checking long-time limit of global ME is close to ground state, and that global and brmesolve produce similar results in that example, is enough?
| ```python | ||
| t = 0 | ||
| dt = 40 / 100 | ||
| se_solver2 = SESolver(H) | ||
| se_solver2.start(psi0, t) | ||
| while t < 40: | ||
| t = t + dt | ||
| psi = se_solver2.step(t) | ||
| # process the result psi and calculate next time step | ||
| ``` |
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This example is a bit meh to be honest (it is from me 🙂), and it doesn't really show the args stuff that the text above it discusses... Not sure what to do about it
| ```python | ||
| plt.plot(tlist_fine, me_local_res.expect[0], label="i=1") | ||
| plt.plot(tlist_fine, me_local_res.expect[1], label="i=2") | ||
| plt.xlabel("Time") | ||
| plt.ylabel(r"$\langle \sigma_z^{(i)} \rangle$") | ||
| plt.legend() | ||
| plt.show() | ||
| ``` |
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Should this plot something with manual_res?
| ```python | ||
| plt.plot(tlist, adi_me_res.expect[0], "-", label="mesolve") | ||
| plt.plot(tlist, np.real(results_corr_fit.expect[0]), '--', label=r'heomsolve') | ||
| plt.plot(tlist, brme_result.expect[0], ":", linewidth=6, | ||
| label="brmesolve non-flat") | ||
| plt.plot(tlist, brme_result2.expect[0], ":", linewidth=6, label="brmesolve") | ||
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| plt.xlabel(r"$t\, /\, \Delta^{-1}$", fontsize=18) | ||
| plt.ylabel(r"$\langle \sigma_z \rangle$", fontsize=18) | ||
| plt.legend() | ||
| plt.show() | ||
| ``` |
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Since it is maybe not obvious how to do that, I have added the HEOM part using the new environment module. However, I am confused that the plot looks a bit different from the one in the paper... I must have missed some parameter, but couldn't immediately find what I am missing
| ``` | ||
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| ```python | ||
| # HEOM |
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Since the parameter gamma is slightly changed we need to refit the heom bath here, i.e., have again:
max_depth = 4 # number of hierarchy levels
wsamp = 2 * np.pi
w0 = 5 * 2 * np.pi
gamma_heom = 1.9 * w0
lambd = np.sqrt(
0.5 * gamma / (gamma_heom * wsamp)
* ((w0**2 - wsamp**2) ** 2 + (gamma_heom**2) * ((wsamp) ** 2))
)
# Create Environment
bath = UnderDampedEnvironment(lam=lambd, w0=w0, gamma=gamma_heom, T=1e-10)
fit_times = np.linspace(0, 5, 1000) # range for correlation function fit
# Fit correlation function with exponentials
exp_bath, fit_info = bath.approx_by_cf_fit(fit_times, Ni_max=1, Nr_max=2, target_rsme=None)
print(fit_info["summary"])
- adjusted formatting acc. to repo specs - added Paul as author - streamlined equation formatting
This notebook includes the examples in the qutip v5 paper that are found in section 3.2 up until (and including) 3.3.4.
The PR remains as a draft for now as much of the code needed to generate the last few plots that are connected to the HEOM environment. See PR #2534 in the main qutip repo.
Therefore the things left to do are: