TY - JOUR
T1 - Wave packets in honeycomb structures and two-dimensional dirac equations
AU - Fefferman, Charles L.
AU - Weinstein, Michael I.
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2013.
PY - 2014/11/29
Y1 - 2014/11/29
N2 - 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.
AB - 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.
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U2 - 10.1007/s00220-013-1847-2
DO - 10.1007/s00220-013-1847-2
M3 - Article
AN - SCOPUS:85027955664
SN - 0010-3616
VL - 326
SP - 251
EP - 286
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 1
ER -