In this work, we discuss the resonance states of a quantum particle in a periodic potential
plus a static force. Originally, this problem was formulated for a crystal electron subject to a …

The achievement of Bose–Einstein condensation in ultra-cold vapours of alkali atoms has
given enormous impulse to the study of dilute atomic gases in condensed quantum states …

In this paper, we mainly review recent results on mathematical theory and numerical
methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation …

In this paper, we begin with the nonlinear Schrödinger/Gross–Pitaevskii equation
(NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics as well …

We study the numerical solution of the time-dependent Gross–Pitaevskii equation (GPE)
describing a Bose–Einstein condensate (BEC) at zero or very low temperature. In …

In this paper, we present a continuous normalized gradient flow (CNGF) and prove its
energy diminishing property, which provides a mathematical justification of the imaginary …

The phenomenon of Bose–Einstein condensation is a phase transition originally predicted
by Bose and Einstein in 1924. In particular, it was shown that below a critical temperature T …

Here we develop simple numerical algorithms for both stationary and non-stationary
solutions of the time-dependent Gross–Pitaevskii (GP) equation describing the properties of …

We show that an explicit time-marching method previously developed for the numerical
study of the dynamics of Bose-Einstein condensates can be profitably adapted to the …

Abstract We create Bose-Einstein condensates of 87 Rb in a static magnetic trap with a
superimposed blue-detuned 1D optical lattice. By displacing the magnetic trap center we are …