pde_opt.numerics.equations.gross_pitaevskii
This module contains various Gross-Pitaevskii equation classes.
Classes
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Gross-Pitaevskii equation in 2D with time-splitting and control. |
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Gross-Pitaevskii equation in 2D with time-splitting and control. |
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Gross-Pitaevskii equation in 2D with time-splitting and rotation. |
- class pde_opt.numerics.equations.gross_pitaevskii.GPE2DTSControl(domain: Domain, k: float, e: float, lights: Callable, trap_factor: float = 1.0)[source]
Gross-Pitaevskii equation in 2D with time-splitting and control.
The Gross-Pitaevskii equation describes the dynamics of Bose-Einstein condensates. The equation is:
\[i\hbar \frac{\partial \psi}{\partial t} = \left[-\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r}, t) + g|\psi|^2\right]\psi\]where ψ is the wave function, V is the external potential, and g is the interaction strength. The external potential includes a harmonic trap and control field:
\[V(\mathbf{r}, t) = \frac{1}{2}m\omega^2\left[(1+\epsilon)x^2 + (1-\epsilon)y^2\right] + V_{control}(\mathbf{r}, t)\]- k: float
Interaction strength parameter
- e: float
Trap ellipticity parameter
- lights: Callable
Function for the control field
- trap_factor: float = 1.0
Scaling factor for the harmonic trap
- fft = None
- ifft = None
- A_term = None
- dx = None
- class pde_opt.numerics.equations.gross_pitaevskii.GPE2DTSRot(domain: Domain, k: float, e: float, omega: float)[source]
Gross-Pitaevskii equation in 2D with time-splitting and rotation.
The Gross-Pitaevskii equation describes the dynamics of Bose-Einstein condensates. The equation is:
\[i\hbar \frac{\partial \psi}{\partial t} = \left[-\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r}) + g|\psi|^2 - \Omega L_z\right]\psi\]where ψ is the wave function, V is the external potential, g is the interaction strength, and Ω is the rotation frequency with L_z being the angular momentum operator. The external potential includes a harmonic trap:
\[V(\mathbf{r}) = \frac{1}{2}m\omega^2\left[(1+\epsilon)x^2 + (1-\epsilon)y^2\right]\]- k: float
Interaction strength parameter
- e: float
Trap ellipticity parameter
- omega: float
Rotation frequency
- class pde_opt.numerics.equations.gross_pitaevskii.GPE2DTSPiston(domain: Domain, k: float, e: float, piston: Callable)[source]
Gross-Pitaevskii equation in 2D with time-splitting and control.
The Gross-Pitaevskii equation describes the dynamics of Bose-Einstein condensates. The equation is:
\[i\hbar \frac{\partial \psi}{\partial t} = \left[-\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r}, t) + g|\psi|^2\right]\psi\]where ψ is the wave function, V is the external potential, and g is the interaction strength. The external potential includes a harmonic trap and control field:
\[V(\mathbf{r}, t) = \frac{1}{2}m\omega^2\left[(1+\epsilon)x^2 + (1-\epsilon)y^2\right] + V_{control}(\mathbf{r}, t)\]- k: float
Interaction strength parameter
- e: float
Trap ellipticity parameter
- piston: Callable
Function for the piston field
- fft = None
- ifft = None
- A_term = None
- dx = None