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Wave Packets in Honeycomb Structures and Two-Dimensional Dirac Equations

Author(s): Fefferman, Charles L.; Weinstein, Michael I.

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Abstract: In a recent article (Fefferman and Weinstein, in J Am Math Soc 25:1169-1220, 2012), the authors proved that the non-relativistic Schrodinger operator with a generic honeycomb lattice potential has conical (Dirac) points in its dispersion surfaces. These conical points occur for quasi-momenta, which are located at the vertices of the Brillouin zone, a regular hexagon. In this paper, we study the time-evolution of wave-packets, which are spectrally concentrated near such conical points. We prove that the large, but finite, time dynamics is governed by the two-dimensional Dirac equations.
Publication Date: Feb-2014
Electronic Publication Date: 29-Nov-2013
Citation: Fefferman, Charles L, Weinstein, Michael I. (2014). Wave Packets in Honeycomb Structures and Two-Dimensional Dirac Equations. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 326 (251 - 286). doi:10.1007/s00220-013-1847-2
DOI: doi:10.1007/s00220-013-1847-2
ISSN: 0010-3616
EISSN: 1432-0916
Pages: 251 - 286
Type of Material: Journal Article
Version: Author's manuscript

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