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

Journal Article · Thu Jul 01 00:00:00 EDT 2010 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2010.01.025· OSTI ID:21333917

Jin, Shi ^[1]; Huang, Zhongyi ^[2]

---

1. Department of Mathematics, University of Wisconsin, Madison, WI 53706 (United States)
2. Department of Mathematical Sciences, Tsinghua University, Beijing 10084 (China)

The linear Schroedinger equation with periodic potentials is an important model in solid state physics. The most efficient direct simulation using a Bloch decomposition-based time-splitting spectral method requires the mesh size to be O({epsilon}) where {epsilon} is the scaled semiclassical parameter. In this paper, we generalize the Gaussian beam method introduced in Jin et al. to solve this problem asymptotically. We combine the technique of Bloch decomposition and the Eulerian Gaussian beam method to arrive at an Eulerian computational method that requires mesh size of O({radical}({epsilon})). The accuracy of this method is demonstrated via several numerical examples.

• OSTI ID: 21333917
• Journal Information: Journal of Computational Physics, Vol. 229, Issue 13; Other Information: DOI: 10.1016/j.jcp.2010.01.025; PII: S0021-9991(10)00048-3; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BLOCH EQUATIONS
BOLTZMANN-VLASOV EQUATION
PERIODICITY
POTENTIALS
SCHROEDINGER EQUATION
SEMICLASSICAL APPROXIMATION
SIMULATION
SOLID STATE PHYSICS