The semiclassically scaled time-dependent multi-particle Schrödinger equation describes,
inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational …

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 …

We present the asymptotic transitions from microscopic to macroscopic physics, their
computational challenges and the asymptotic-preserving (AP) strategies to compute …

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 …

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 …

Kinetic limits for waves in a random medium Page 1 Kinetic limits for waves in a random
medium Guillaume Bal∗ Tomasz Komorowski † Lenya Ryzhik ‡ September 30, 2010 Contents …

We construct quantum algorithms to compute the solution and/or physical observables of
nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations …

In this paper, a fourth-order compact and energy conservative difference scheme is
proposed for solving the two-dimensional nonlinear Schrödinger equation with periodic …