Gauge-invariant frozen Gaussian approximation method for the schrödinger equation with periodic potentials
Abstract
© 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].
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https://hdl.handle.net/10161/14111Published Version (Please cite this version)
10.1137/15M1040384Publication Info
Delgadillo, R; Lu, J; & Yang, X (2016). Gauge-invariant frozen Gaussian approximation method for the schrödinger equation
with periodic potentials. SIAM Journal on Scientific Computing, 38(4). pp. A2440-A2463. 10.1137/15M1040384. Retrieved from https://hdl.handle.net/10161/14111.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Jianfeng Lu
Professor of Mathematics
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm
development for problems from computational physics, theoretical chemistry, materials
science and other related fields.More specifically, his current research focuses include:Electronic
structure and many body problems; quantum molecular dynamics; multiscale modeling
and analysis; rare events and sampling techniques.

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