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Communications in Mathematical Physics

, Volume 326, Issue 1, pp 251–286 | Cite as

Wave Packets in Honeycomb Structures and Two-Dimensional Dirac Equations

  • Charles L. Fefferman
  • Michael I. WeinsteinEmail author
Article

Abstract

In a recent article (Fefferman and Weinstein, in J Am Math Soc 25:1169–1220, 2012), the authors proved that the non-relativistic Schrödinger 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.

Keywords

Brillouin Zone Dirac Equation Weinstein Conical Singularity Conical Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of Applied Physics and Applied MathematicsColumbia UniversityNew YorkUSA

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