axes = clp.initialize(col=2,
row=1,
width=4.3,
height=4.3 * 0.618 * 2,
fontsize=12,
LaTeX=True,
labelthem=True,
labelthemPosition=[0.04, 0.96])
xs, ys = gather_data(Nlst)
clp.plotone([x / kFGR for x in xs],
ys,
axes[0],
labels=labels,
colors=["r--", "c", "b"],
xlabel="time ($t$)",
ylabel="Avg. excited state popu. $\\bar{\\rho}_{ee}(t)$",
lw=2,
alphaspacing=0.02)
# In the second subplot, we need to calculate the effective decay rate
Nlst = [7, 9, 11, 15, 19, 25, 35, 45]
xs, ys = gather_data(Nlst)
from scipy.optimize import curve_fit
def exponenial_func(x, k):
return np.exp(-k * x)
t_QM, p1_QM, p2_QM = get_popu_data(path+"traj_QM.txt")
t_MMST, p1_MMST, p2_MMST = get_popu_data(path+"traj_MultiEh.txt")
xs = [t_MMST /np.pi, t_QM / np.pi]
y1s = [p1_MMST, p1_QM]
y2s = [p2_MMST, p2_QM]
labels = ["MMST", "QM"]
colors1 = ["r--", "k--"]
colors2 = ["r", "k"]
ax = clp.initialize(col=1, row=1, width=4.3, fontsize=12, LaTeX=True)
clp.plotone(xs, y1s, ax, colors=colors1, alphaspacing=0.0, lw=2)
clp.plotone(xs, y2s, ax, labels=labels, colors=colors2, xlabel="time ($t$)",
ylabel="Electronic population", alphaspacing=0.0, lw=2)
# Plot x-axis as a function of PI
def format_func(value, tick_number):
# find number of multiples of pi/2
N = value
if N == 0:
return "0"
else:
return r"${0}\pi$".format(N)
ax.xaxis.set_major_formatter(FuncFormatter(format_func))
# output figure
width=4.3,
height=4.3 * 0.618 * 2,
fontsize=12,
LaTeX=True,
labelthem=True,
labelthemPosition=[0.04, 0.95])
# For the first plot, gather many trajs
xs, ys = get_N_trajs(path=path, Ntraj=5, Natoms=35)
x_avg, y_avg = gather_dpdt([35])
clp.plotone(xs,
ys,
axes[0],
labels=["No.%d MMST traj N=35" % (i + 1) for i in range(len(xs))],
xlabel="time ($t$)",
ylabel="$d\\bar{\\rho}_{ee}/dt$",
lw=1.5,
xlim=[-0.005, 0.2],
ylim=[-10, 105])
clp.plotone(x_avg,
y_avg,
axes[0],
colors=["b"],
labels=["MMST avg traj N=35"],
xlabel="time ($t$)",
ylabel="$d\\bar{\\rho}_{ee}/dt$",
lw=3,
xlim=[-0.005, 0.2],
ylim=[-10, 105])
return xnew, ynew
def calc_analytical(xs, ys, Nlst):
xnew, ynew = xs, []
for i in range(len(xs)):
x, y = xs[i], ys[i]
N = Nlst[i]
td = x[np.argmax(y)]
y_analytical = kFGR * N / 4.0 * np.cosh(kFGR*N / 2.0 * (x - td))**(-2)
ynew.append(y_analytical)
return xnew, ynew
Nlst = [7, 35]
labels = ["MMST N = %d" %N for N in Nlst]
ax = clp.initialize(col=1, row=1, width=4.3, height=4.3*0.618, fontsize=12, LaTeX=True)
xs, ys = gather_data(Nlst)
xnew, dydt = calculate_derivative(xs,ys)
clp.plotone(xnew, dydt, ax, labels=labels, colors=["c", "b"], xlabel="time ($t$)", ylabel="$d\\bar{\\rho}_{ee}/dt$", lw=2, xlim=[-0.005, 0.2])
xnew, dydt = calc_analytical(xnew,dydt, Nlst)
labels = ["mean-field N = %d" %N for N in Nlst]
clp.plotone(xnew, dydt, ax, labels=labels, colors=["k-.", "k--"], xlabel="time ($t$)", lw=2, xlim=[-0.005, 0.2], ylim=[-2, 30])
# output figure
clp.adjust(tight_layout=True, savefile="SE_Dicke_delay_time.pdf")
LaTeX=True)
N = 50 #average over 50 points
for i in range(n):
X = [data_EhR[:, 0], data_QM[:, 0]]
X = [x / np.pi for x in X]
Y = [data_EhR[:, i + 1], data_QM[:, i + 1]]
Y = [(y + spacing_y * i) / spacing_y for y in Y]
X_avg = [X[0][int(N / 2) - 1:-int(N / 2)]]
Y_avg = [running_mean(Y[0], N)]
X = X + X_avg
Y = Y + Y_avg
clp.plotone(
X,
Y,
ax,
colors=['r', "k--", "c-."],
labels=["MMST", "QM", "coarse-grained MMST"] if i == 0 else None,
alphaspacing=0.01,
ylim=[-0.2, 12])
ax.set_xlabel("Cavity position")
ax.set_ylabel("E-field Intensity (arbi. units)")
def format_func(value, tick_number):
# find number of multiples of pi/2
N = value
if N == 0:
return "0"
else:
return r"${0}\pi$".format(N)
]
colors1 = ["b--", "g--", "r--", 'k--']
colors2 = ["b--", "g-.", "r", 'k--']
ax = clp.initialize(col=1,
row=1,
width=4.6,
fontsize=12,
LaTeX=True,
sharex=True)
clp.plotone(xs,
y2s,
ax,
labels=labels,
colors=colors2,
xlabel="time (t)",
ylabel="Excited state population",
alphaspacing=0.0,
lw=2,
ylim=[-0.51, 2.0])
# Plot x-axis as a function of PI
def format_func(value, tick_number):
# find number of multiples of pi/2
N = value
if N == 0:
return "0"
else:
return r"${0}\pi$".format(N)
axes = clp.initialize(col=1,
row=3,
width=4.3 * 2,
height=4.3 * 0.618,
fontsize=12,
LaTeX=True,
sharey=True,
labelthem=True,
labelthemPosition=[0.13, 0.95])
xs, y2s = gather_data("SE_101TLS_FDTD_dx_25")
clp.plotone(xs,
y2s,
axes[0],
labels=labels,
colors=colors2,
xlabel="time ($t$)",
ylabel="Excited state population",
alphaspacing=0.1,
lw=2)
axes[0].set_title("101 TLSs, $a = \lambda/2$")
xs, y2s = gather_data("SE_101TLS_FDTD_dx_13")
clp.plotone(xs,
y2s,
axes[1],
labels=labels,
colors=colors2,
xlabel="time ($t$)",
alphaspacing=0.1,
lw=2,
showlegend=False)
spacing_y = np.max(np.max(data_QM[1:-1, :])) * 1.15
for i in range(n):
X = [data_EhR[:, 0], data_QM[:, 0]]
X = [x / np.pi for x in X]
Y = [data_EhR[:, i + 1], data_QM[:, i + 1]]
Y = [(y + spacing_y * i) / spacing_y for y in Y]
X_avg = [X[0][int(N / 2) - 1:-int(N / 2)]]
Y_avg = [running_mean(Y[0], N)]
X = X + X_avg
Y = Y + Y_avg
for k in range(2):
clp.plotone(X,
Y,
axes[k, j],
colors=['r', "k--", "c-."],
labels=["MMST", "QM", "coarse-grained MMST"] if
(i == 0 and j == 0) else None,
alphaspacing=0.01,
ylim=[-0.2, 12],
showlegend=True if (j == 0 and k == 0) else False,
xlim=None if k == 0 else [0.9622, 1.0378])
axes[0, j].set_title(methods[j])
axes[1, j].set_xlabel("Cavity position")
if j is 0:
for k in range(2):
axes[k, j].set_ylabel("E-field Intensity (arbi. units)")
axes[0, j].xaxis.set_major_formatter(FuncFormatter(format_func))
axes[1, j].xaxis.set_major_formatter(FuncFormatter(format_func))
# Add arrow
axes[0, -1].text(2.25, 5.0, 'time increment', rotation=90, color='b', size=12)
#axes[1, -1].text(2.25, 5.0, 'time increment', rotation=90, color='b', size=12)
t_MMST, p1_MMST, p2_MMST = get_popu_data(path+"traj_MultiEh.txt")
t_p, p1_p, p2_p = get_popu_data(path+"traj_PreBinSQC.txt")
t_sed, p1_sed, p2_sed = get_popu_data(path+"traj_StochasticED.txt")
xs = [t_p /np.pi, t_sed/np.pi, t_MMST / np.pi]
y1s = [p1_p, p1_sed, p1_MMST]
y2s = [p2_p, p2_sed, p2_MMST]
labels = ["Sampling electronic ZPE (self-interaction)", "Sampling photonic ZPE (vacuum fluctuations)", "Sampling both (MMST)"]
colors1 = ["b--", "g-.", "r"]
colors2 = ["b--", "g--", "r--"]
ax = clp.initialize(col=1, row=1, width=4.3, fontsize=10, LaTeX=True)
clp.plotone(xs, y2s, ax, labels=labels, colors=colors1, xlabel="time ($t$)",
ylabel="Excited state population", alphaspacing=0.0, lw=2, xlim=[0, 1.2], ylim=[-0.6, 1.0])
# Plot x-axis as a function of PI
def format_func(value, tick_number):
# find number of multiples of pi/2
N = int(value * 10)
if N == 0:
return "0"
else:
return r"${0}\pi$".format(N/10)
ax.xaxis.set_major_formatter(FuncFormatter(format_func))
# output figure
clp.adjust(tight_layout=True, savefile="ground_state_popu.pdf")
colors2 = ["r", "k--", "0.7"]
axes = clp.initialize(col=1,
row=2,
width=4.3 * 1.5,
height=4.3 * 0.618,
fontsize=12,
LaTeX=True,
sharey=True)
xs, y2s = gather_data("SE_1TLS_FDTD_near_mirror/dx_25")
clp.plotone(xs,
y2s,
axes[0],
labels=labels,
colors=colors2,
xlabel="time ($t$)",
ylabel="Excited state population",
alphaspacing=0.1,
lw=2,
xlim=[0, 1.0])
axes[0].set_title("1 TLS near mirror, $r = \lambda/2$")
xs, y2s = gather_data("SE_1TLS_FDTD_near_mirror/dx_13")
clp.plotone(xs,
y2s,
axes[1],
labels=labels,
colors=colors2,
xlabel="time ($t$)",
alphaspacing=0.1,
lw=2,
showlegend=False,
fontsize=12,
LaTeX=True,
labelthem=True,
labelthemPosition=[0.10, 0.95])
# Subplot 1: decay dynamics for different spacing with N = 35
Nlst = [1, 7, 35]
xs, ys = gather_data(Nlst, path="SE_Dicke_dx_13/")
labels = ["N=%d, $a = \lambda / 4$" % N for N in Nlst]
labels[0] = "N=1"
colors = ["r--", "c", "b"]
clp.plotone([x / kFGR for x in xs],
ys,
axes[0],
labels=labels,
colors=colors,
xlabel="time ($t$)",
ylabel="Avg. excited state popu. $\\bar{\\rho}_{ee}(t)$",
lw=2,
xlim=[-0.01, 1.5]) #, ylog=True, ylim= [6e-3, 2.0])
axes[0].xaxis.set_major_formatter(FuncFormatter(format_func))
# Subplot 2: effective decay rate as a function of spacing for N = 35
Nlst = [7, 9, 11, 15, 19, 25, 35, 45]
xs, ys = gather_data(Nlst, path="SE_Dicke_dx_13/")
from scipy.optimize import curve_fit
def biexponenial_func(x, ks, kf, A):
return A * np.exp(-ks * x) + (1.0 - A) * np.exp(-kf * x)