gpe.tube2

Dynamics in elongated harmonic traps.

See Expansion.md for details.

Attributes

u

Classes

StateGPEdrZ

Effective 1D model for an elongated cloud implementing a modified form

Module Contents

u

class StateGPEdrZ(ws=None, Omega=None, delta=None, **kw)

Bases: gpe.bec2.State

Effective 1D model for an elongated cloud implementing a modified form of the dr-GPE with dynamic rescaling in the y and z directions but not in the x direction. The state here is \(\Phi(Z, t)\) but get_density() has been modified to include the correct scaling.

get_ws(t=None)

Return the trapping frequencies at time t.

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.

property w0_perp

Average perpendicular frequency at time t=0.

get_sigma2s(abs_Phi2s=None)

get_central_density(TF=False)

Return the physical density (3d) along the central axis of the trap.

Parameters:

TF (bool) – If True, then assume the transverse cloud is a TF profile (otherwise use the internal Gaussian anzatz.)

get_V_GPU()

Return the complete potential V - internal and external.

get_energy_density(a=True, b=True, ab=True)

Return the energy density.

Parameters:

• a (bool) – Include the energies associated with this species. This includes the kinetic energy and the self-interaction, but no inter-species interactions.

• b (bool) – Include the energies associated with this species. This includes the kinetic energy and the self-interaction, but no inter-species interactions.

• ab (bool) – Include only the interaction energy.

_rhs(q, t)

RHS for lambda(t) ODE.

get_lambdas()

_get_n_TF(V_TF, V_ext=None, m=None, g=None, state=None)

Return the total TF density. Assumes gaa = gbb = gab and populates only the lower band.

Parameters:

V_g (float) – (V_TF - V)/g. The density will vanish where V=V_TF.

get_mus_from_Vs_TF(Vs_TF)

Return the corrected chemical potential from Vs_TF.

Parameters:

Vs_TF ((float, float)) – External potentials at the Thomas Fermi “radius”. (The external potential is evaluated at this position and this is used to get mu.)

get_Vs_TF_from_mus(mus)

Return Vs_TF from the chemical potentials mus.

Parameters:

mus ((float, float)) – Physical chemical potentials (i.e. what you would pass to the minimizer).