mirror of
https://github.com/vale981/master-thesis
synced 2025-03-08 19:31:40 -05:00
67 lines
1.7 KiB
Python
67 lines
1.7 KiB
Python
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%load_ext autoreload
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%autoreload 2
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%load_ext jupyter_spaces
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import hops
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import stocproc as sp
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import numpy as np
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import matplotlib.pyplot as plt
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import scipy
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plt.style.use('ggplot')
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from IPython.display import set_matplotlib_formats
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set_matplotlib_formats('pdf', 'svg')
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σ1 = np.matrix([[0,1],[1,0]])
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σ2 = np.matrix([[0,-1j],[1j,0]])
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σ3 = np.matrix([[1,0],[0,-1]])
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γ = 5 # coupling ratio
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ω_c = 1 # center of spect. dens
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δ = 2 # breadth BCF
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W = -ω_c * 1j - δ # exponent BCF
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τ_max = 40 # the maximal simulation time
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seed = 1 # seed for all pseudo random generators
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H_s = σ3
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L = 1/2 * (σ1 - 1j * σ2) * γ
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def α(τ):
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return np.exp(-1j * ω_c * τ - np.abs(τ) * δ)
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def I(ω):
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return 1 / (δ + (ω - ω_c) ** 2 / δ)
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%%space plot
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t = np.linspace(0, τ_max, 1000)
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ω = np.linspace(ω_c - 10, ω_c + 10, 1000)
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fig, axs = plt.subplots(2)
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axs[0].plot(t, np.real(α(t)))
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axs[0].plot(t, np.imag(α(t)))
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axs[1].plot(ω, I(ω))
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η = sp.StocProc_FFT(
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I, τ_max, α, negative_frequencies=True, seed=seed, intgr_tol=1e-2, intpl_tol=1e-2
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)
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%%space plot
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η.new_process(seed=seed)
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plt.plot(η.t, np.real(η(η.t)), label="Re")
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plt.plot(η.t, np.imag(η(η.t)), linestyle="--", label="Im")
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plt.ylabel("η")
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plt.xlabel("τ")
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plt.legend()
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step = hops.make_hops_step(η, H_s, L, W, 3)
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step(0, np.array([1, 1, 0, 0, 0, 0, 0, 0]))
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res = hops.integrate_hops_trajectory(η, H_s, L, W, 15, [1, 0], τ_max, seed, atol=1e-8, rtol=1e-8)
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%%space plot
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t = np.linspace(0, τ_max, 1000)
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plt.plot(t, np.abs(res.sol(t)[0]))
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ts, ρs = hops.integrate_hops_ensemble(η, H_s, L, W, 10, [1, 0], τ_max, 10)
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energy = [np.trace(ρ @ σ3 @ σ3)/np.trace(ρ)-(np.trace(ρ @ σ3)/np.trace(ρ))**2 for ρ in ρs]
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plt.plot(ts, energy)
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