def get_optima(length,
V_0,
V_T,
phi,
method,
soc_field_variance={},
optima_TAT={}):
N = length**lattice_dim
if phi == None: phi = phi_opt.at[V_0, str(V_T)]
try:
soc_field_variance[V_0, phi]
except:
soc_field_variance[V_0, phi] = h_std(V_0, phi)**2
chi = soc_field_variance[V_0, phi] / ((N - 1) * U_int.at[V_0, str(V_T)])
if method[4:] == "dec":
dec_rates = (0, dec_rate / chi, dec_rate / chi)
else:
dec_rates = (0, 0, 0)
# return optimum squeezing value and time for OAT or TAT appropriately
if method[:3] == "OAT":
def sqz_OAT_val(chi_t):
return squeezing_OAT(N, chi_t, dec_rates)
optimum_OAT = optimize.minimize_scalar(sqz_OAT_val,
method="bounded",
bounds=(0, max_time(N)))
sqz_opt, t_opt = optimum_OAT.fun, optimum_OAT.x
if method[:3] == "TAT":
if optima_TAT.get(N) is None:
S_op_vec, SS_op_mat = spin_op_vec_mat_dicke(N)
S_op_vec = [X[::2, ::2] for X in S_op_vec]
SS_op_mat = [[X[::2, ::2] for X in XS] for XS in SS_op_mat]
H_TAT = 1 / 3 * (SS_op_mat[2][2] - SS_op_mat[1][1]).real
state_nZ = np.zeros(N // 2 + 1)
state_nZ[0] = 1
if N < N_crossover:
get_optima = get_optima_diagonalization
else:
get_optima = get_optima_simulation
optima_TAT[N] = get_optima(N, H_TAT, S_op_vec, SS_op_mat, state_nZ,
max_time(N))
sqz_opt, t_opt = optima_TAT[N]
return sqz_opt, t_opt / chi
plt.rcParams.update(params)
figsize = (1, 1)
fig_dir = "../figures/"
fig_dpi = 600
grid_size = 1000
N = 40
max_tau = 2
time_steps = 1000
ivp_tolerance = 1e-5
max_time = max_tau * N**(-2 / 3)
times = np.linspace(0, max_time, time_steps)
S_op_vec, SS_op_mat = spin_op_vec_mat_dicke(N)
S_z = S_op_vec[0]
H_OAT = S_z @ S_z
class Arrow3D(FancyArrowPatch):
def __init__(self, xs, ys, zs, *args, **kwargs):
FancyArrowPatch.__init__(self, (0, 0), (0, 0), *args, **kwargs)
self._verts3d = xs, ys, zs
def draw(self, renderer):
xs3d, ys3d, zs3d = self._verts3d
xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
FancyArrowPatch.draw(self, renderer)