Gauge-invariant frozen Gaussian approximation method for the schrödinger equation with periodic potentials

Published

Journal Article

© 2016 Society for Industrial and Applied Mathematics. We develop a gauge-invariant frozen Gaussian approximation (GIFGA) method for the Schrödinger 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 [Frozen Gaussian Approximation for High Frequency Wave Propagation in Periodic Media, arXiv:1504.08051, 2015].

Full Text

Duke Authors

Cited Authors

  • Delgadillo, R; Lu, J; Yang, X

Published Date

  • January 1, 2016

Published In

Volume / Issue

  • 38 / 4

Start / End Page

  • A2440 - A2463

Electronic International Standard Serial Number (EISSN)

  • 1095-7200

International Standard Serial Number (ISSN)

  • 1064-8275

Digital Object Identifier (DOI)

  • 10.1137/15M1040384

Citation Source

  • Scopus