Mathematical and computational methods for semiclassical Schrödinger equations

S **, P Markowich, C Sparber - Acta Numerica, 2011‏ - cambridge.org
We consider time-dependent (linear and nonlinear) Schrödinger equations in a
semiclassical scaling. These equations form a canonical class of (nonlinear) dispersive …

[HTML][HTML] Multi-scale dynamics of the interaction between waves and mean flows: From nonlinear WKB theory to gravity-wave parameterizations in weather and climate …

U Achatz, YH Kim, GS Voelker - Journal of Mathematical Physics, 2023‏ - pubs.aip.org
The interaction between small-scale waves and a larger-scale flow can be described by a
multi-scale theory that forms the basis for a new class of parameterizations of subgrid-scale …

[HTML][HTML] Methods for solving singular perturbation problems arising in science and engineering

M Kumar - Mathematical and Computer Modelling, 2011‏ - Elsevier
Singular perturbation problems are of common occurrence in all branches of applied
mathematics and engineering. These problems are encountered in various fields such as …

[PDF][PDF] Ramanujan-type congruences for three colored Frobenius partitions

J Lovejoy - Journal of Number Theory, 2000‏ - Citeseer
RAMANUJAN-TYPE CONGRUENCES FOR THREE COLORED FROBENIUS PARTITIONS 1.
Introduction Since their discovery by Ramanujan, the partit Page 1 RAMANUJAN-TYPE …

An accelerated algorithm for 2D simulations of the quantum ballistic transport in nanoscale MOSFETs

NB Abdallah, M Mouis, C Negulescu - Journal of Computational Physics, 2007‏ - Elsevier
An accelerated algorithm for the resolution of the coupled Schrödinger/Poisson system, with
open boundary conditions, is presented. This method improves the sub-band decomposition …

Semi-classical limit of Schrödinger–Poisson equations in space dimension n⩾ 3

T Alazard, R Carles - Journal of Differential Equations, 2007‏ - Elsevier
We prove the existence of solutions to the Schrödinger–Poisson system on a time interval
independent of the Planck constant, when the do** profile does not necessarily decrease …

Bloch decomposition-based Gaussian beam method for the Schrödinger equation with periodic potentials

S **, H Wu, X Yang, Z Huang - Journal of Computational Physics, 2010‏ - Elsevier
The linear Schrödinger equation with periodic potentials is an important model in solid state
physics. The most efficient direct simulation using a Bloch decomposition-based time …

[PDF][PDF] A semi-Lagrangian time splitting method for the Schrödinger equation with vector potentials.

S **, Z Zhou - Commun. Inf. Syst., 2013‏ - Citeseer
In this paper, we present a time splitting scheme for the Schrodinger equation in the
presence of electromagnetic eld in the semi-classical regime, where the wave function …

A Bloch Decomposition–Based Split-Step Pseudospectral Method for Quantum Dynamics with Periodic Potentials

Z Huang, S **, PA Markowich, C Sparber - SIAM Journal on Scientific …, 2007‏ - SIAM
We present a new numerical method for accurate computations of solutions to (linear) one-
dimensional Schrödinger equations with periodic potentials. This is a prominent model in …

A numerical study of the Gaussian beam methods for Schrödinger-Poisson equations

S **, H Wu, X Yang - Journal of Computational Mathematics, 2010‏ - JSTOR
As an important model in quantum semiconductor devices, the Schrödinger-Poisson
equations have generated widespread interests in both analysis and numerical simulations …