Related papers: Nonlinear Schr\"odinger Equations for Bose-Einstei…
In the mean-field approximation, a trapped Bose-Einstein condensate at zero temperature is described by the Gross-Pitaevskii equation for the condensate, or equivalently, by the hydrodynamic equations for the number density and the current…
We construct a fully self-consistent non-equilibrium theory for the dynamics of two interacting finite-temperature atomic Bose-Einstein condensates. The condensates are described by dissipative Gross-Pitaevskii equations, coupled to quantum…
We rewrite the complex Klein-Gordon (KG) equation with a mexican-hat scalar field potential in a thermal bath with one loop contribution as a new Gross-Pitaevskii (GP)-like equation. We interpret it as a charged and finite temperature…
We explore the effect of mutual gravitational interaction between ultra-cold gas atoms on the dynamics of Bose-Einstein condensates (BEC). Small amplitude oscillation of BEC is studied by applying variational technique to reduce the…
The dynamics of stability and collapse of a trapped atomic Bose-Einstein condensate (BEC) coupled to a molecular one is studied using the time-dependent Gross-Pitaevskii (GP) equation including a nonlinear interaction term which can…
We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al. (J. Phys. B 35,1555,(2002). The derivation does not rely on the concept of local energy and momentum…
We investigate the phenomenon of Bose-Einstein condensation in ideal bosonic gases confined to axially-symmetric surfaces of revolution. The single-particle Schr\"odinger equation is formulated on a general surface and then explicitly…
Describing partially-condensed Bose gases poses a long-standing theoretical challenge. We present exact stochastic Ehrenfest relations for the stochastic projected Gross-Pitaevskii equation, including both number and energy damping…
We investigate the properties of discrete breathers in a Bose-Einstein condensate with two- and three-body interactions in optical lattice. In the tight-binding approximation the Gross-Pitaevskii equation with periodic potential for the…
We have previously formulated a simple criterion for deducing the intervals of oscillations in the solutions of second-order linear homogeneous differential equations. In this work, we extend analytically the same criterion to the cubic…
Coupled nonlinear Schrodinger equations (CNLS) with an external elliptic function potential model a quasi one--dimensional interacting two-component Bose-Einstein condensate trapped in a standing light wave. New families of stationary…
A Bose-Einstein condensation theory for any integer spin using noncommutative quantum mechanics methods is considered. The effective potential is derived as a multipolar expansion in the non-commutativity parameter ($\theta$) and, at second…
In this work the Klein-Gordon (KG) equation for a complex scalar field with U(1) symmetry endowed in a mexican-hat scalar field potential with thermal and electromagnetic contributions is written as a Gross-Pitaevskii (GP)-like equation.…
We consider a two-dimensional nonlinear Schr{\"o}dinger equation proposed in Physics to model rotational binary Bose-Einstein condensates. The nonlinearity is a logarithmic modification of the usual cubic nonlinearity. The presence of both…
We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schr\"odinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe…
While the Gross--Pitaevskii equation is well-established as the canonical dynamical description of atomic Bose-Einstein condensates (BECs) at zero-temperature, describing the dynamics of BECs at finite temperatures remains a difficult…
We propose an efficient stochastic method to implement numerically the Bogolubov approach to study finite-temperature Bose-Einstein condensates. Our method is based on the Wigner representation of the density matrix describing the non…
The Gross-Pitaevskii equation for polarized molecules is an integro-differential equation, consequently it is complicated for solving. We find a possibility to represent it as a non-integral nonlinear Schrodinger equation, but this equation…
We discuss the zero-temperature hydrodynamics equations of bosonic and fermionic superfluids and their connection with generalized Gross-Pitaevskii and Ginzburg-Landau equations through a single superfluid nonlinear Schrodinger equation.
One-dimensional (1D) Nonlinear Schroedinger Equaation (NLS) provides a good approximation to attractive Bose-Einshtein condensate (BEC) in a quasi 1D cigar-shaped optical trap in certain regimes. 1D NLS is an integrable equation that can be…