Benchmarks

These three scripts profile the execution time of certain functions within the spinor-gpe package. The first one measures the time for the main time-evolution propagation function TensorPropagator.full_step(). The second and third measure the execution times for the forward and inverse 2D FFT functions and the Hadamard product, respectively.

The scripts share the following physical and numerical parameters. Individual differeces in these parameters are noted in each file.

Physical Parameters

Atom number

\(\quad N_{\rm at} = 100\)

Atomic mass, Rubidium-87

\(\quad m = 1.4442 \times 10^{-25}~[\rm kg]\)

Trap frequencies

\(\quad (\omega_x, \omega_y, \omega_z) = 2 \pi \times (50, 50, 2000)~[{\rm Hz}]\)

\(\quad (\omega_x, \omega_y, \omega_z) = \omega_x \times (1, \gamma, \eta) = (1, 1, 40)~[\omega_x]\)

Harmonic oscillator length, x-axis

\(\quad a_x = \sqrt{\hbar / m \omega_x} = 1.525~[{\mu\rm m}]\)

3D scattering length, Rubidium-87

\(\quad a = 5.313~[{\rm nm}]\)

\(\quad a_{\rm sc} = a / a_x = 0.00348~[a_x]\)

Scattering 2D scale

\(\quad g_{\rm sc}^{2\rm D} = \sqrt{8\pi\eta}~a_{\rm sc} = 0.1105~[\omega_x a_x^2]\)

Scattering coupling

\(\quad (g_{\rm uu}, g_{\rm dd}, g_{\rm ud}) = g_{\rm sc}^{2 \rm D} \times (1, 1, 1.04)~[\omega_x a_x^2]\)

Chemical potential

\(\quad \mu = \sqrt{4 N_{\rm at} a_{\rm sc} \gamma \sqrt{\eta / 2 \pi}} = 1.875~[\omega_x]\)

Thomas-Fermi radius

\(\quad R_{\rm TF} = \sqrt{2 \mu} = 1.937~[a_x]\)

Initial population fractions

\(\quad (p_0, p_1) = (0.5, 0.5)\)

Raman wavelength

\(\quad \lambda_L = 790.1~[{\rm nm}]\)

Numerical Parameters

Number of grid points

\(\quad (N_x^{(\rm min)}, N_y^{(\rm min)}) = (64, 64)~{\rm to}~(4096, 4096)\)

r-grid half-size

\(\quad (x^{\rm max}, y^{\rm max}) = (8, 8)~[a_x]\)

r-grid spacing

\(\quad (\Delta x, \Delta y) = (0.25, 0.25)~{\rm to}~(0.003906, 0.003906)~[a_x]\)

k-grid half-size

\(\quad (k_x^{\rm max}, k_y^{\rm max}) = \pi / (\Delta x, \Delta y)\)

\(\quad (k_x^{\rm max}, k_y^{\rm max}) = (12.566, 12.566)~{\rm to}~(804.25, 804.25)~[a_x^{-1}]\)

k-grid spacing

\(\quad (\Delta k_x, \Delta k_y) = \pi / (x^{\rm max}, y^{\rm max})\)

\(\quad (\Delta k_x, \Delta k_y) = (0.3927, 0.3927)~[a_x^{-1}]\)

Time scale

\(\quad \tau_0 = 1 / \omega_x = 0.00318~[{\rm s/rad}]\)

\(\quad \tau_0 = 1~[\omega_x^{-1}]\)

Time step duration, imaginary

\(\quad \Delta \tau_{\rm im} = 1 / 50~[-i \tau_0]\)

Number of time steps, imaginary

\(\quad N_{\rm im} = 1\)

FFT and iFFT Time

Hadamard Time

Propagation Time