Computational methods for the dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations
arXiv:1305.1093 · doi:10.1016/j.cpc.2013.07.012
Abstract
In this paper, we begin with the nonlinear Schrodinger/Gross-Pitaevskii equation (NLSE/GPE) for modeling Bose-Einstein condensation (BEC) and nonlinear optics as well as other applications, and discuss their dynamical properties ranging from time reversible, time transverse invariant, mass and energy conservation, dispersion relation to soliton solutions. Then, we review and compare different numerical methods for solving the NLSE/GPE including finite difference time domain methods and time-splitting spectral method, and discuss different absorbing boundary conditions. In addition, these numerical methods are extended to the NLSE/GPE with damping terms and/or an angular momentum rotation term as well as coupled NLSEs/GPEs. Finally, applications to simulate a quantized vortex lattice dynamics in a rotating BEC are reported.
23 pages 1 figure
References in corpus (7)
- Mathematical theory and numerical methods for Bose-Einstein condensation
- Nature of the superconductor-insulator transition in disordered superconductors
- C programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap
- An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates
- Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions
- Symmetry Breaking and Self-trapping of a Dipolar Bose-Einstein Condensate in a Double-well Potential
- Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap
Cited by in corpus (96)
- Mathematical theory and numerical methods for Bose-Einstein condensation
- Fortran and C programs for the time-dependent dipolar Gross-Pitaevskii equation in an anisotropic trap
- Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by the preconditioned nonlinear conjugate gradient method
- Computation of Ground States of the Gross-Pitaevskii Functional via Riemannian Optimization
- Supersolidity in Two-Dimensional Trapped Dipolar Droplet Arrays
- On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions
- OpenMP Fortran and C programs for solving the time-dependent Gross-Pitaevskii equation in an anisotropic trap
- Mathematical models and numerical methods for spinor Bose-Einstein condensates
- Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime
- Spontaneous Formation of Star-Shaped Surface Patterns in a Driven Bose-Einstein Condensate
- Regularized numerical methods for the logarithmic Schrodinger equation
- Exciting the Goldstone Modes of a Supersolid Spin-Orbit-Coupled Bose Gas
- Controllable non-local interactions between dark solitons in dipolar condensates
- Strongly anisotropic vortices in dipolar quantum droplets
- Localized dark solitons and vortices in defocusing media with spatially inhomogeneous nonlinearity
- Time-of-flight expansion of binary Bose-Einstein condensates at finite temperature
- A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation
- FORTRESS: FORTRAN programs for solving coupled Gross-Pitaevskii equations for spin-orbit coupled spin-1 Bose-Einstein condensate
- Mass- and energy-conserved numerical schemes for nonlinear Schrödinger equations
- Analog cosmological reheating in an ultracold Bose gas
- Universality class of a spinor Bose-Einstein condensate far from equilibrium
- Accurate and efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates via the nonuniform FFT
- Control of Dy Bose-Einstein condensate phases and dynamics with dipolar anisotropy
- A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation
- Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime
- Arbitrarily high-order structure-preserving schemes for the Gross-Pitaevskii equation with angular momentum rotation in three dimensions
- Three-dimensional splitting dynamics of giant vortices in Bose-Einstein condensates
- Turbulence Excitation in Counter-Streaming Paraxial Superfluids of Light
- Optimal nonlinear coherent mode transitions in Bose-Einstein Condensates utilizing spatio-temporal controls
- Quantum turbulence simulations using the Gross-Pitaevskii equation: high-performance computing and new numerical benchmarks
- Unified way for computing dynamics of Bose-Einstein condensates and degenerate Fermi gases
- Monitoring currents in cold-atom circuits
- Energy preserving model order reduction of the nonlinear Schrödinger equation
- A discrete Schrodinger equation via optimal transport on graphs
- Supersolid Stacks in Antidipolar Bose-Einstein Condensates
- Stable vortex structures in colliding self-gravitating Bose-Einstein condensates
- Cavity Induced Collective Behavior in the Polaritonic Ground State
- Two-dimensional symbiotic solitons and vortices in binary condensates with attractive cross-species interaction
- Ground states of Bose-Einstein condensates with higher order interaction
- FACt: FORTRAN toolbox for calculating fluctuations in atomic condensates
- Self-bound vortex lattice in a rapidly rotating quantum droplet
- Uniform error bounds of time-splitting methods for the nonlinear Dirac equation in the nonrelativistic regime without magnetic potential
- Classical linear chain behavior from dipolar droplets to supersolids
- Error estimates of the time-splitting methods for the nonlinear Schrödinger equation with semi-smooth nonlinearity
- Optimal error bounds on time-splitting methods for the nonlinear Schrödinger equation with low regularity potential and nonlinearity
- Optimal error bounds on the exponential wave integrator for the nonlinear Schrödinger equation with low regularity potential and nonlinearity
- Non-perturbative analytical diagonalization of Hamiltonians with application to coupling suppression and enhancement in cQED
- Multi-speed solitary waves of nonlinear Schr{ö}dinger systems: theoretical and numerical analysis
- One-Dimensional Fuzzy Dark Matter Models: Structure Growth and Asymptotic Dynamics
- Zero-dimensional limit of the two-dimensional Lugiato-Lefever equation
- Spontaneous formation and non-equilibrium dynamics of a soliton-shaped Bose-Einstein condensate in a trap
- Rayleigh-Taylor instability in a phase-separated three-component Bose-Einstein condensate
- Tunneling dynamics of Dy supersolids and droplets
- Pseudospectral methods with PML for nonlinear Klein-Gordon equations in classical and non-relativistic regimes
- An explicit and symmetric exponential wave integrator for the nonlinear Schrödinger equation with low regularity potential and nonlinearity
- Analysis of a Crank-Nicolson finite difference scheme for (2+1)D perturbed nonlinear Schrödinger equations with saturable nonlinearity
- Time-dependent spectral renormalization method
- High order exponential integrators for nonlinear Schrödinger equations with application to rotating Bose-Einstein condensates
- Two dimensional Quantum droplets in random repulsive potential
- A Finite Difference Scheme for (2+1)D Cubic-Quintic Nonlinear Schrödinger Equations with Nonlinear Damping
- Equilibrium vortex lattices of a binary rotating atomic Bose-Einstein condensate with unequal atomic masses
- Numerical simulation of nonequilibrium states in a trapped Bose-Einstein condensate
- An efffcient numerical scheme for two-dimensional nonlinear time fractional Schrödinger equation
- Signatures of rigidity and second sound in dipolar supersolids
- Sinusoidal magnetic field induced topological excitations in a spin-orbit coupled spinor condensate
- Atomic soliton transmission and induced collapse in scattering from a narrow barrier
- Mutual transitions between stationary and moving dissipative solitons
- Modeling atom interferometry experiments with Bose-Einstein condensates in power-law potentials
- Magnetization induced skyrmion dynamics of a spin-orbit-coupled spinor condensate under sinusoidally varying magnetic field
- A novel nonlocal potential solver based on nonuniform FFT for efficient simulation of the Davey-Stewartson equations
- Angular Bloch Oscillations and their applications
- Strong interaction induced dimensional crossover in 1D quantum gas
- PT-symmetric and antisymmetric nonlinear states in a split potential box
- High-order mass- and energy-conserving SAV-Gauss collocation finite element methods for the nonlinear Schrödinger equation
- Fresh look at the effects of gravitational tidal forces on a freely-falling quantum particle
- An extended Fourier pseudospectral method for the Gross-Pitaevskii equation with low regularity potential
- A linearized and conservative Fourier pseudo-spectral method for the damped nonlinear Schrödinger equation in three dimensions
- Numerical analysis of the Gross-Pitaevskii Equation with a randomly varying potential in time
- Numerical simulation of the Gross-Pitaevskii equation via vortex tracking
- Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT
- A Lawson-time-splitting extended Fourier pseudospectral method for the Gross-Pitaevskii equation with time-dependent low regularity potential
- Nonlinear dynamics of coupled superfluids
- A Machine-Learning Method for Time-Dependent Wave Equations over Unbounded Domains
- Ground states and dynamics of spin-orbit-coupled Bose-Einstein condensates
- Generation of wave turbulence in dipolar gases driven across their phase transitions
- Bohmian analysis of dark solutions in interfering Bose-Einstein condensates: The dynamical role of underlying velocity fields
- The Finite Element Method for the time-dependent Gross-Pitaevskii equation with angular momentum rotation
- A linearized energy--conservative finite element method for the nonlinear Schrödinger equation with wave operator
- The Gross-Pitaevskii-Poisson model for an ultracold plasma: density waves and solitons
- Time-reversible and norm-conserving high-order integrators for the nonlinear time-dependent Schrödinger equation: Application to local control theory
- Mass- and energy-preserving exponential Runge-Kutta methods for the nonlinear Schrödinger equation
- Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials
- Mathematical Models and Numerical Methods for Bose-Einstein Condensation
- Numerical integrators for continuous disordered nonlinear Schrödinger equation
- Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime
- Instability of the finite-difference split-step method on the background of localized solutions of the generalized nonlinear Schrödinger equation