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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.|
|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|
|Pages:||251 - 286|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||COMMUNICATIONS IN MATHEMATICAL PHYSICS|
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