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.

Args:

dimint

The dimension of the system.

kwargsdict, optional

Optional keyword arguments to set additional parameters. see https://comfitlib.com/ClassBoseEinsteinCondensate/

Returns:

The system object representing the BoseEinsteinCondensate simulation. BoseEinsteinCondensate object

Example:

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

Args:

None

Returns:

Average force on the potential (numpy.ndarray)

calc_hamiltonian()

Function that calculates the Hamiltonian

Return type:

float

Args:

None

Returns:

The Hamiltonian

calc_hamiltonian_density()

Calculates the hamiltonian density

Return type:

ndarray

Args:

None

Returns:

The hamiltonian density (numpy.ndarray)

calc_harmonic_potential(R_tf)

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

Return type:

ndarray

Args:

R_tf (float): The Thomas-Fermi radius

Returns:

A harmonic potential

calc_kinetic_energy()

Calculates the kinetic energy.

Return type:

float

Args:

None

Returns:

The kinetic energy (float)

calc_nonlinear_evolution_function_f(psi, t)

Calculates the non-linear evolution term of the dGPE

Return type:

ndarray

Args:

psi: the wavefunction at a given time. (numpy.ndarray)

Returns:

The non-linear evolution term (numpy.ndarray)

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

Args:

psi: the wavefunction at a given time. (numpy.ndarray)

Returns:

the non-linear evolution term (numpy.ndarray)

calc_superfluid_current()

Calculates the superfluid current

Return type:

ndarray

Args:

None

Returns:

The superfluid current (numpy.ndarray)

calc_velocity()

Calculates the weighted velocity field

Return type:

ndarray

Args:

None

Returns:

The weighted velocity field (numpy.ndarray)

calc_vortex_density(psi=None)

Calculates the vortex density of the system.

Return type:

ndarray

Args:

psi: The wavefunction of the system. (numpy.ndarray)

Returns:

The vortex density of the system. numpy.ndarray

calc_vortex_density_singular()

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

Return type:

ndarray

Args:

None

Returns:

The vortex density of the system. (numpy.ndarray)

calc_vortex_nodes(dt_psi=None)

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

Return type:

list[dict]

Args:

dt_psi: The time derivative of the wavefunction of the system. (numpy.ndarray)

Returns:

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

Args:

dt_psi: The time derivative of the wavefunction of the system. (numpy.ndarray) psi: The wavefunction of the system. (numpy.ndarray)

Returns:

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

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

Args:

d: length of the interface between the low gamma and high gamma regions (float) frame_width_x: distance fom center to the frame in x-direction (float) frame_width_y: – “ – y-direction (float) frame_width_z: – “ – z-direction (float)

Returns:

modify self.gamma

conf_external_potential(V_ext, additive=False)

Sets the external potential of the system.

Return type:

None

Args:

V_ext (function or float): the external potential additive (bool, optional): whether to add the new potential to the existing potential or not

Returns:

Modifies the value of self.V_ext

conf_initial_condition_Thomas_Fermi()

Finds the Thomas_Fermi ground state.

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

Return type:

None

Args:

None

Returns:

Sets the value of self.psi and self.psi_f

conf_initial_condition_disordered(noise_strength=0.01)

Sets disordered initial condition for the BoseEinsteinCondensate with some thermal flcutiations

Return type:

ndarray

Args:

noise_strength: the strength of the noise

Returns:

Sets the value of self.psi and self.psi_f

conf_insert_vortex(charge=1, position=None)

Sets the initial condition for a vortex dipole

Args:

charge (int): the charge of the vortex position (list): the position of the vortex

Returns:

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.

Args:

None

Returns:

Modifies the value of self.psi and self.psi_f

Raises:

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

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

Args:

position: the position of the vortex ring (list) radius: the radius of the vortex ring (float) normal_vector: the normal vector of the vortex ring (list)

Returns:

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

Args:

nodes (list) a list containing the vortices Area (array) list on the format (x1,x2,y1,y2)

Returns:

Modifies the value of self.psi and self.psi_f

evolve_comoving_dGPE(number_of_steps, velx, 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

Args:

number_of_steps: the number of time steps that we are evolving the equation (int) velx: velocity in x direction (float) method: the integration method we want to use. ETD2RK is sett as default (string)

Returns:

Updates the fields self.psi and self.psi_f

evolve_dGPE(number_of_steps, method='ETD2RK')

Evolver for the dGPE.

Return type:

None

Args:

number_of_steps: the number of time steps that we are evolving the equation (int) method: the integration method we want to use. ETD2RK is sett as default (string, optional)

Returns:

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

Args:

number_of_steps: the number of time steps that we are evolving the equation (int) method: the integration method we want to use. ETD2RK is sett as default (string)

Returns:

Updates the self.psi and self.psi_f