def update_boundary(eps, delta):
L = abs(2*np.pi/(kr + delta))
# choose discretization such that r_nx < len(x_range)
r_nx_L = (L*(N*pphw + 1)).astype(int)
x_range = np.linspace(0, L, r_nx_L)
# no Delta-phase necessary if looking at loop_type constant!
WG = Dirichlet(loop_type='Constant', N=N, L=L, W=W, eta=eta)
xi_lower, xi_upper = WG.get_boundary(x=x_range, eps=eps, delta=delta)
print "lower.boundary.shape", xi_lower.shape
np.savetxt("lower.boundary", zip(x_range, xi_lower))
np.savetxt("upper.boundary", zip(x_range, xi_upper))
N_file_boundary = len(x_range)
replacements = {'NAME': CALC_NAME,
'LENGTH': str(L),
'WIDTH': str(W),
'MODES': str(N),
'PPHW': str(pphw),
'GAMMA0': str(eta),
'NEUMANN': "0",
'N_FILE_BOUNDARY': str(N_file_boundary),
'BOUNDARY_UPPER': 'upper.boundary',
'BOUNDARY_LOWER': 'lower.boundary'}
replace_in_file(xml_template, xml, **replacements)
def circle_EP(filename=None, write_profile=False, **kwargs):
"""Calculate trajectories around the EP."""
f = FileOperations(filename)
WG = Dirichlet(**kwargs)
##
# plot amplitudes b0(x), b1(x)
##
ax0 = plt.subplot2grid((3, 3), (0, 0), colspan=2)
ax0.set_label("x [a.u.]")
ax0.set_xlabel(r"x [a.u.]")
ax0.set_ylabel(r"Amplitudes $|b_n(x)|$")
set_scientific_axes(ax0)
x, b0, b1 = WG.solve_ODE()
# get adiabatic predictions
b0_ad, b1_ad = (WG.Psi_adiabatic[:, 0], WG.Psi_adiabatic[:, 1])
# account for initial population of states a and b
b0_ad *= abs(b0[0])
b1_ad *= abs(b1[0])
ax0.semilogy(x, abs(b0), "r-", label=r"$|b_0|$")
ax0.semilogy(x, abs(b1), "g-", label=r"$|b_1|$")
ax0.semilogy(x, abs(b0_ad), "b--", label=r"$|b_0^{\mathrm{ad}}|$")
ax0.semilogy(x, abs(b1_ad), "k--", label=r"$|b_1^{\mathrm{ad}}|$")
f.write("")
f.write("Diodicity D = {}".format(abs(b0[-1]) / abs(b1[-1])))
f.write("Diodicity D^-1 = {}".format(abs(b1[-1]) / abs(b0[-1])))
plt.rcParams.update({"font.size": 8})
plt.legend(
bbox_to_anchor=(0.0, 1.02, 1.0, 0.102),
loc=3,
ncol=4,
mode="expand",
borderaxespad=0.0,
labelspacing=0.2,
columnspacing=0.5,
handlelength=3,
handletextpad=0.2,
)
##
# plot real/imag(E1(t)), imag(E2(t))
##
ax1 = plt.subplot2grid((3, 3), (1, 0), colspan=2)
ax2 = ax1.twinx()
set_scientific_axes(ax1, axis="y")
set_scientific_axes(ax2, axis="y")
Ea, Eb = WG.eVals[:, 0], WG.eVals[:, 1]
ax1.set_xlabel("x [a.u.]")
ax1.set_ylabel("Energy")
ax1.yaxis.set_label_position("left")
ax1.plot(x, Ea.imag, "r-", label=r"$\mathrm{Im}(E_0)$")
ax1.plot(x, Eb.imag, "g-", label=r"$\mathrm{Im}(E_1)$")
ax2.plot(x, Ea.real, "r--", label=r"$\mathrm{Re}(E_0)$")
ax2.plot(x, Eb.real, "g--", label=r"$\mathrm{Re}(E_1)$")
t_imag = map_trajectory(b0, b1, Ea.imag, Eb.imag)
t_real = map_trajectory(b0, b1, Ea.real, Eb.real)
ax1.plot(x, t_imag, "k-")
ax2.plot(x, t_real, "k--")
lines1, labels1 = ax1.get_legend_handles_labels()
lines2, labels2 = ax2.get_legend_handles_labels()
ax2.legend(
lines1 + lines2,
labels1 + labels2,
bbox_to_anchor=(0.0, 1.02, 1.0, 0.102),
loc=3,
ncol=4,
mode="expand",
borderaxespad=0.0,
labelspacing=0.2,
columnspacing=0.5,
handlelength=2.5,
handletextpad=0.2,
)
##
# plot wavefunction
##
x0, y0 = WG.get_cycle_parameters(0.0)
x1, y1 = WG.get_cycle_parameters(WG.t)
####
####ax3 = subplot2grid((3,3), (2,0), colspan=2)
####WG.draw_wavefunction()
####WG.draw_dissipation_coefficient()
####WG.draw_boundary()
####tick_params(labelleft='off', left='off', right='off')
####ax3.set_xlabel("x [a.u.]")
####ax3.set_frame_on(False)
# ax3.xaxis.set_ticklabels([])
# ax3.get_xaxis().tick_bottom()
##
# plot path around EP
##
ax4 = plt.subplot2grid((3, 3), (2, 0))
set_scientific_axes(ax4, axis="both")
ax4.xaxis.set_label_position("top")
ax4.yaxis.set_label_position("right")
plt.xticks(rotation=30)
ax4.set_xlabel(r"$\epsilon$", fontsize=10)
ax4.set_ylabel(r"$\delta$", fontsize=10)
dx = dy = 0.5e-2
# ax4.set_xlim(min(x1)-dx, max(x1)+dx)
# ax4.set_ylim(min(y1)-dy, max(y1)+dy)
offset = WG.tN / 5.0
dx1 = np.diff(x1)
dy1 = np.diff(y1)
plt.plot(x1[:], y1[:], "grey", ls="dotted")
plt.plot(x0, y0, "ro", mew=0.0, mec="r")
plt.plot([WG.x_EP, -WG.x_EP], [WG.y_EP, WG.y_EP], "ko")
plt.quiver(
x1[offset:-1:offset],
y1[offset:-1:offset],
dx1[offset::offset],
dy1[offset::offset],
units="xy",
angles="xy",
headwidth=6.0,
color="k",
zorder=10,
)
# ylim(-0.1,0.1)
# text(WG.x_EP - WG.x_R0*0.2,
# WG.y_EP + WG.y_R0*4, "EP")
##
# save figure
##
# tight_layout()
plt.subplots_adjust( # left=0.125,
bottom=None,
# right=0.9,
top=None,
wspace=0.5,
hspace=0.6,
)
filename = "{0}_{1}".format(filename, kwargs.get("loop_direction"))
f.write(filename + ".cfg")
# plt.savefig(filename + ".pdf")
plt.savefig(filename + ".png")
if write_profile:
xi_lower, _ = WG.get_boundary()
np.savetxt(filename + ".profile", zip(WG.t, xi_lower))
plt.clf()