Class: Bose Einstein Condensate

Bose Einstein Condensate model.

class comfit.bose_einstein_condensate.bose_einstein_condensate.BoseEinsteinCondensate(dim, **kwargs)

Bases: BaseSystem

__init__(dim, **kwargs)

Initializes a system to simulate a Bose-Einstein Condensate using the Gross-Pitaevskii equation.

Parameters

dimint: The dimension of the system.
kwargsdict, optional: Optional keyword arguments to set additional parameters. see https://comfitlib.com/ClassBoseEinsteinCondensate/

Returns

BoseEinsteinCondensate: The system object representing the BoseEinsteinCondensate simulation.

Examples

>>> bec = BoseEinsteinCondensate(3,xRes=101,yRes=101,zRes=101, gamma=0.5)
Creates a BoseEinsteinCondensate system with 3 dimensions and a spatial resolution of 101 in all directions.
The dissipative factor gamma is set to 0.5.

calc_force_on_external_potential()

Calculates the average force acting on the external potential.

Return type:: ndarray

Returns

numpy.ndarray: Average force on the potential

calc_hamiltonian()

Function that calculates the Hamiltonian

Return type:: float

Returns

float: The Hamiltonian

calc_hamiltonian_density()

Calculates the hamiltonian density

Return type:: ndarray

Returns

numpy.ndarray: The hamiltonian density

calc_harmonic_potential(thomas_fermi_radius)

Calculates a harmonic trap with thomas_fermi_radius being the Thomas-Fermi radius

Return type:: ndarray

Parameters

thomas_fermi_radiusfloat: The Thomas-Fermi radius

Returns

numpy.ndarray: A harmonic potential

calc_kinetic_energy()

Calculates the kinetic energy.

Return type:: float

Returns

float: The kinetic energy

calc_nonlinear_evolution_function_f(psi, t)

Calculates the non-linear evolution term of the dGPE

Return type:: ndarray

Parameters

psinumpy.ndarray: the wavefunction at a given time.

Returns

numpy.ndarray: The non-linear evolution term

calc_nonlinear_evolution_term_comoving_f(psi, t)

Calculates the non-linear evolution term of the dGPE when gamma is not a constant.

Relevant for example in the comoving frame when we have a dissipative frame around the edge.

Return type:: ndarray

Parameters

psinumpy.ndarray: the wavefunction at a given time.

Returns

numpy.ndarray: the non-linear evolution term

calc_superfluid_current()

Calculates the superfluid current

Return type:: ndarray

Returns

numpy.ndarray: The superfluid current

calc_velocity()

Calculates the weighted velocity field

Return type:: ndarray

Returns

numpy.ndarray: The weighted velocity field

calc_vortex_density(psi=None)

Calculates the vortex density of the system.

Return type:: ndarray

Parameters

psinumpy.ndarray, optional: The wavefunction of the system. If None, self.psi[0] is used.

Returns

numpy.ndarray: The vortex density of the system.

calc_vortex_density_singular()

Calculates the vortex density of the system using the singular method.

Return type:: ndarray

Returns

numpy.ndarray: The vortex density of the system.

calc_vortex_nodes(dt_psi=None)

Calculate the positions and charges of vortex nodes based on the defect density.

Return type:: list[dict]

Parameters

dt_psinumpy.ndarray, optional: The time derivative of the wavefunction of the system.

Returns

list of dict

List of dictionaries representing the vortex nodes. Each dictionary contains the following keys:

‘position_index’: The position index of the vortex node in the defect density array.
‘charge’: The charge of the vortex node.
‘position’: The position of the vortex node as a list [x, y].
‘velocity’: The velocity of the vortex node as a list [vx, vy].

calc_vortex_velocity_field(dt_psi, psi=None)

Calculates the vortex velocity field of the system.

Return type:: ndarray

Parameters

dt_psinumpy.ndarray: The time derivative of the wavefunction of the system.
psinumpy.ndarray, optional: The wavefunction of the system. If None, self.psi[0] is used.

Returns

numpy.ndarray: The vortex velocity field of the system.

conf_dissipative_frame(interface_width=7, frame_width_x=None, frame_width_y=None, frame_width_z=None)

Configures a dissipative frame around the computational domain

This function sets self.gamma so that it has a low value in the bulk and a large value near the edges. This sets a dissipative frame around the computational domain

Return type:: None

Parameters

interface_widthfloat: length of the interface between the low gamma and high gamma regions
frame_width_xfloat: distance from center to the frame in x-direction
frame_width_yfloat: – “ – y-direction
frame_width_zfloat: – “ – z-direction

Returns

None: modify self.gamma

conf_external_potential(V_ext, additive=False)

Sets the external potential of the system.

Return type:: None

Parameters

V_extfunction or float: the external potential
additivebool, optional: whether to add the new potential to the existing potential or not

Returns

None: Modifies the value of self.V_ext

conf_initial_condition_disordered(noise_strength=0.01)

Sets disordered initial condition for the BoseEinsteinCondensate with some thermal fluctuations

Return type:: ndarray

Parameters

noise_strengthfloat: the strength of the noise

Returns

None: Sets the value of self.psi and self.psi_f. self.psi always carries a leading component axis, so self.psi[0] is set to the newly configured disordered state.

conf_initial_condition_thomas_fermi()

Finds the Thomas_Fermi ground state.

Must be preceded by an energy relaxation to find the true ground state

Return type:: None

Returns

None: Sets the value of self.psi and self.psi_f. self.psi always carries a leading component axis, so self.psi[0] is set to the newly configured Thomas-Fermi state.

conf_insert_vortex(charge=1, position=None)

Sets the initial condition for a vortex dipole

Parameters

chargeint: the charge of the vortex
positionlist: the position of the vortex

Returns

None: Modifies the value of self.psi and self.psi_f

conf_insert_vortex_dipole(dipole_vector=None, dipole_position=None)

Sets the initial condition for a vortex dipole configuration in a 2-dimensional system.

Returns

None: Modifies the value of self.psi and self.psi_f

Raises

Exception: If the dimension of the system is not 2.

conf_insert_vortex_filament(position=None, charge=None)

Insert a vortex line into the condensate. The vortex line is assumed to be elongated along the z-axis.

Return type:: None

Parameters

positionarray_like, optional: the position in the xy-plane of the vortex filament (vector)
chargeint, optional: the charge of the vortex filament

Returns

None: Modifies the value of self.psi and self.psi_f

conf_insert_vortex_ring(position=None, radius=None, normal_vector=[0, 0, 1])

Sets the initial condition for a vortex ring configuration in a 3-dimensional system

Return type:: None

Parameters

positionlist, optional: the position of the vortex ring
radiusfloat, optional: the radius of the vortex ring
normal_vectorlist, optional: the normal vector of the vortex ring

Returns

None: Modifies the value of self.psi and self.psi_f

conf_vortex_remover(nodes, area)

Removes vortices

Function that finds and removes vortices outside of the area defined by the corners (x1,y1), (x1,y2), (x2,y1), (x2,y2)

Return type:: None

Parameters

nodeslist: a list containing the vortices
areaarray: list on the format (x1,x2,y1,y2)

Returns

None: Modifies the value of self.psi and self.psi_f

evolve_comoving_dGPE(number_of_steps, vel_x, method='ETD2RK')

Evolver for the dGPE in the comoving frame.

This evolver assume that the stirring is in the x-direction and that gamma is spatialy dependent

Return type:: None

Parameters

number_of_stepsint: the number of time steps that we are evolving the equation
vel_xfloat: velocity in x direction
methodstring: the integration method we want to use. ETD2RK is sett as default

Returns

None: Updates the fields self.psi and self.psi_f

evolve_dGPE(number_of_steps, method='ETD2RK')

Evolver for the dGPE.

Return type:: None

Parameters

number_of_stepsint: the number of time steps that we are evolving the equation
methodstring, optional: the integration method we want to use. ETD2RK is sett as default

Returns

None: Updates the self.psi and self.psi_f

evolve_relax(number_of_steps, method='ETD2RK')

Evolver for the dGPE in imaginary time that relax the equation closer to the ground state

Return type:: None

Parameters

number_of_stepsint: the number of time steps that we are evolving the equation
methodstring: the integration method we want to use. ETD2RK is sett as default

Returns

None: Updates the self.psi and self.psi_f