Related papers: Explicit Symplectic Integrators for Massive Point …
Numerous exact solutions to the nonlinear mean-field equations of motion are constructed for multicomponent Bose-Einstein condensates on one, two, and three dimensional optical lattices. We find both stationary and nonstationary solutions,…
In recent publications, the construction of explicit symplectic integrators for Schwarzschild and Kerr type spacetimes is based on splitting and composition methods for numerical integrations of Hamiltonians or time-transformed Hamiltonians…
We present a comprehensive study of modulational instability (MI) in a binary Bose-Einstein condensate with spin-orbit coupling, confined to a deep optical lattice. The system is modeled by a set of discrete Gross-Pitaevskii equations.…
Completely Liouville integrable Hamiltonian system with two degrees of freedom is considered. This Hamiltonian system describes the dynamics of two vortex filaments in a Bose-Einstein condensate enclosed in a cylindrical trap and dynamics…
Symplectic integrators are the tool of choice for many researchers studying dynamical systems because of their good long-term energy conservation properties. For systems with a dominant central mass, symplectic integrators are also highly…
We put forward the use of total-variation-diminishing (or more generally, strong stability preserving) implicit-explicit Runge-Kutta methods for the time integration of the equations of motion associated with the semiconvection problem in…
By applying a position-dependent detuning to a spin-orbit-coupled Hamiltonian with equal Rashba and Dresselhaus coupling, we exploit the behavior of the angular momentum of a harmonically trapped Bose-Einstein condensed atomic gas and…
Magnetic dipole-dipole interaction dominated Bose-Einstein condensates are discussed under spinful situations. We treat the spin degrees of freedom as a classical spin vector, approaching from large spin limit to obtain an effective minimal…
We present bright-dark vector solitons in quasi-one-dimensional spinor (F=1) Bose-Einstein condensates. Using a multiscale expansion technique, we reduce the corresponding nonintegrable system of three coupled Gross-Pitaevskii equations…
Symplectic integrators offer vastly superior performance over traditional numerical techniques for conservative dynamical systems, but their application to \emph{dissipative} systems is inherently difficult due to dissipative systems' lack…
We report on the existence and stability of freely moving solitons in a spatially inhomogeneous Bose- Einstein condensate with helicoidal spin-orbit (SO) coupling. In spite of the periodically varying parameters, the system allows for the…
Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually…
We prove that a class of A-stable symplectic Runge--Kutta time semidiscretizations (including the Gauss--Legendre methods) applied to a class of semilinear Hamiltonian PDEs which are well-posed on spaces of analytic functions with analytic…
We present a new method to propagate rotating Bose-Einstein condensates subject to explicitly time-dependent trapping potentials. Using algebraic techniques, we combine Magnus expansions and splitting methods to yield any order methods for…
We derive a non-equilibrium finite-temperature kinetic theory for a binary mixture of two interacting atomic Bose-Einstein condensates and use it to explore the degree of hydrodynamicity attainable in realistic experimental geometries.…
We propose a novel mixed finite-element formulation for geometrically exact (Simo--Reissner) beams that introduces the moment vector as additional independent field. The specific mixed form allows for an element-local, discontinuous…
A two-dimensional rapidly rotating Bose-Einstein condensate in a harmonic plus quartic trap is expected to have unusual vortex states that do not occur in a pure harmonic trap. At a critical rotation speed $\Omega_h$, a central hole appears…
This work is concerned with the construction and analysis of structure-preserving Galerkin methods for computing the dynamics of rotating Bose-Einstein condensate (BEC) based on the Gross-Pitaevskii equation with angular momentum rotation.…
Maintaining conservation laws in the fully discrete setting is critical for accurate long-time behavior of numerical simulations and requires accounting for discrete conservation properties in both space and time. This paper derives…
We revisit a classic study [D. S. Hall {\it et al.}, Phys. Rev. Lett. {\bf 81}, 1539 (1998)] of interpenetrating Bose-Einstein condensates in the hyperfine states $\ket{F = 1, m_f = -1}\equiv\ket{1}$ and $\ket{F = 2, m_f = +1}\equiv\ket{2}$…