• Example 1: Unitary Fermi Gas is confided in a 1D (smooth) squared well
• Example 2: Soliton in the unitary Fermi gas.
• Example 3: Unitary Fermi Gas confined in 2D harmonic trap
• Archival examples

Example 1: Unitary Fermi Gas is confided in a 1D (smooth) squared well

Target: generate solution in a 1D potential well V_{\textrm{ext}}(x,y,z)\rightarrow V_{\textrm{ext}}(x), with bulk density corresponding k_F=1.

Code: st-wslda-1d

Settings:

• only-trap_predefines.h
• only-trap_problem-definition.h
• only-trap_logger.h
• only-trap_input.txt

Output:

• only-trap.stdout

Simple plotting script:

import numpy as np
import matplotlib.pyplot as plt
from wdata.io import WData, Var

data = WData.load("only-trap.wtxt")

fig, ax = plt.subplots()
ax.plot(data.xyz[0], data.rho_a[-1]*2, color='red', label=r'density', lw=3.0) # plot last frame [-1]
ax.set(xlabel='x', ylabel=r'$n(x)$')
ax2 = ax.twinx()  # instantiate a second axes that shares the same x-axis
ax2.plot(data.xyz[0], np.angle(data.delta[-1])/np.pi, color='blue', label=r'arg. of phase', lw=2.0, ls="--") # plot last frame [-1]
ax2.set(ylabel=r'$V_{ext}(x)$')
fig.legend(loc="upper left", bbox_to_anchor=(0.3,0.3), bbox_transform=ax.transAxes)
fig.savefig("only-trap.png")

Example 2: Soliton in the unitary Fermi gas.

Target: on top of the Example 1 imprint soliton.

Code: st-wslda-1d

Settings:

• soliton-x0_predefines.h
• soliton-x0_problem-definition.h
• soliton-x0_logger.h
• soliton-x0_input.txt

Output:

• soliton-x0.stdout

Simple plotting script:

import numpy as np
import matplotlib.pyplot as plt
from wdata.io import WData, Var

data = WData.load("soliton-x0.wtxt")

fig, ax = plt.subplots()
ax.plot(data.xyz[0], data.rho_a[-1]*2, color='red', label=r'density', lw=3.0) # plot last frame [-1]
ax.set(xlabel='x', ylabel=r'$n(x)$')
ax2 = ax.twinx()  # instantiate a second axes that shares the same x-axis
ax2.plot(data.xyz[0], np.angle(data.delta[-1])/np.pi, color='blue', label=r'arg. of phase', lw=2.0, ls="--") # plot last frame [-1]
ax2.set(ylabel=r'$Arg[\Delta](x)/\pi$')
fig.legend(loc="upper left", bbox_to_anchor=(0.15,0.3), bbox_transform=ax.transAxes)
fig.savefig("soliton-x0.png")

Example 3: Unitary Fermi Gas confined in 2D harmonic trap

Target: find a static solution of gas confined in harmonic trap:

V_{\textrm{ext}}(x,y,z) = \frac{m\omega_x^2 x^2}{2} + \frac{m\omega_y^2 y^2}{2}

Code: st-wslda-2d

Note: in the computation, a smoothed harmonic potential was used, see Fig. 4 of arXiv:1711.05803

Settings:

• trap-2d_predefines.h
• trap-2d_problem-definition.h
• trap-2d_logger.h
• trap-2d_input.txt

Output:

• trap-2d.stdout

Archival examples

For other examples you can see here.