gpe.Examples.tutorial

Example code from the tutorial.

Classes

StateHOConvergence1	State with tools to check convergence for a 1D HO GPE.
StateHOConvergence2	State with tools to check convergence for a 2D HO GPE.

Module Contents

class StateHOConvergence1(**kw)

Bases: gpe.bec.HOMixin, gpe.bec.StateGPEBase

State with tools to check convergence for a 1D HO GPE.

This is a simple state with default parameters forming a trapped gas in a 1D harmonic oscillator. It has some functions for checking and plotting convergence.

The state is specified by the parameter dmu = mu / (hbar*w/2) - 1. If dmu = 0, we will have no interactions (but don’t do this: use a small, non-zero value), while larger values will approach the TF limit.

Nx = 64

Lx = 14.0

dmu = 0.74

w = 1.0

g = 1.0

init()

Initialize the state.

This method defines the basis positions, momenta, etc. for use later on. We define these here rather than in the constructor __init__() so that the user can change them later and the reinitialize the state. We also call this function from the pre_evolve_hook() so that it is called before any evolution takes place. For this reason, we should not modify the state here.

get_convergence(full_output=False)

Return (ir, uv) convergence factors.

These are the ratios of the density at the edge vs maximum density in position (IR) and momentum (UV) space.

Parameters:

full_output (bool) – If True, return (ir, uv, x, nx, k, nk).

plot_convergence(ax=None, legend=True, **kw)

Plot the convergence in axis axs[0].

Parameters:

• ax (Axes) – Plot convergence in ax if provided.

• legend (bool) – If True, include the legend.

• **kw (dict) – All other arguments are passed to plot().

Returns:

ax

Return type:

Axes

get_gtilde()

Return the dimensionless interaction parameter.

plot(axs=None, plot_convergence=False, **kw)

Plot the state in axis ax.

Parameters:

• axs ([Axes]) – List of axes. Plot in axs[0] if provided. plot the convergence in axs[1], if provided and plot_convergence is True.

• plot_convergence (bool) – If True, include the convergence plot.

• **kw (dict) – All other arguments are passed to plot().

Returns:

ax

Return type:

Axes

get_initialized_state(fix_N=False, minimize_kw={})

Return a minimized state.

class StateHOConvergence2(**kw)

Bases: StateHOConvergence1

State with tools to check convergence for a 2D HO GPE.

This is a simple state with default parameters forming a trapped gas in a 2D harmonic oscillator. It has some functions for checking and plotting convergence.

The state is specified by the parameter dmu = mu / (hbar*w/2) - 1. If dmu = 0, we will have no interactions (but don’t do this: use a small, non-zero value), while larger values will approach the TF limit.

Nx = 64

Lx = 14.0

dmu = 0.74

w = 1.0

g = 1.0

get_convergence(full_output=False)

Return (ir, uv) convergence factors.

These are the ratios of the density at the edge vs maximum density in position (IR) and momentum (UV) space.

Parameters:

full_output (bool) – If True, return (ir, uv, r, nr, k, nk).

plot_convergence(ax=None, legend=True, **kw)

Plot the convergence in axis axs[0].

Parameters:

• ax (Axes) – Plot convergence in ax if provided.

• legend (bool) – If True, include the legend.

• **kw (dict) – All other arguments are passed to plot().

Returns:

ax

Return type:

Axes

plot(axs=None, plot_convergence=False, **kw)

Plot the state in axis ax.

Parameters:

• axs ([Axes]) – List of axes. Plot in axs[0] if provided. plot the convergence in axs[1], if provided and plot_convergence is True.

• plot_convergence (bool) – If True, include the convergence plot.

• **kw (dict) – All other arguments are passed to plot().

Returns:

ax

Return type:

Axes