Paper Info
Title
Gauge-Invariant Frozen Gaussian Approximation Method for the Schrödinger Equation with Periodic Potentials.
Abstract
We develop a gauge-invariant frozen Gaussian approximation (GIFGA) method for the Schrodinger equation (LSE) with periodic potentials in the semiclassical regime. The method generalizes the Herman-Kluk propagator for LSE to the case with periodic media. It provides an efficient computational tool based on asymptotic analysis on phase space and Bloch waves to capture the high-frequency oscillations of the solution. Compared to geometric optics and Gaussian beam methods, GIFGA works in both scenarios of caustics and beam spreading. Moreover, it is invariant with respect to the gauge choice of the Bloch eigenfunctions and thus avoids the numerical difficulty of computing gauge- dependent Berry phase. We numerically test the method by several one-dimensional examples; in particular, the first order convergence is validated, which agrees with our companion analysis paper
Year
DOI
Venue
2016
10.1137/15M1040384
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
DocType
Volume
Schrodinger equation,periodic potential,semiclassical regime,frozen Gaussian approximation,gauge-invariant
Journal
38
Issue
ISSN
Citations 
4
1064-8275
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Ricardo Delgadillo100.34
Jianfeng Lu213638.65
Xu Yang3459.17