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 wavepackets, 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.
Original language | English (US) |
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Pages (from-to) | 251-286 |
Number of pages | 36 |
Journal | Communications In Mathematical Physics |
Volume | 326 |
Issue number | 1 |
DOIs | |
State | Published - Nov 29 2014 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics