Mathematical and computational methods for semiclassical Schrödinger equations
We consider time-dependent (linear and nonlinear) Schrödinger equations in a
semiclassical scaling. These equations form a canonical class of (nonlinear) dispersive …
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 …
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 …
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
Singular perturbation problems are of common occurrence in all branches of applied
mathematics and engineering. These problems are encountered in various fields such as …
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 …
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 …
open boundary conditions, is presented. This method improves the sub-band decomposition …
Semi-classical limit of Schrödinger–Poisson equations in space dimension n⩾ 3
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 …
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
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 …
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.
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 …
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
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 …
dimensional Schrödinger equations with periodic potentials. This is a prominent model in …
A numerical study of the Gaussian beam methods for Schrödinger-Poisson equations
As an important model in quantum semiconductor devices, the Schrödinger-Poisson
equations have generated widespread interests in both analysis and numerical simulations …
equations have generated widespread interests in both analysis and numerical simulations …