Abstract

Scarring in quantum systems with classical chaotic dynamics is one of the most remarkable phenomena in modern physics. Previous works were concerned mostly with nonrelativistic quantum systems described by the Schrödinger equation. The question remains outstanding of whether truly relativistic quantum particles that obey the Dirac equation can scar. A significant challenge is the lack of a general method for solving the Dirac equation in closed domains of arbitrary shape. In this paper, we develop a numerical framework for obtaining complete eigensolutions of massless fermions in general two-dimensional confining geometries. The key ingredients of our method are the proper handling of the boundary conditions and an efficient discretization scheme that casts the original equation in a matrix representation. The method is validated by (1) comparing the numerical solutions to analytic results for a geometrically simple confinement and (2) verifying that the calculated energy level-spacing statistics of integrable and chaotic geometries agree with the known results. Solutions of the Dirac equation in a number of representative chaotic geometries establish firmly the existence of scarring of Dirac fermions.

Original languageEnglish (US)
Article number016702
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume86
Issue number1
DOIs
StatePublished - Jul 11 2012

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Dirac Equation
Billiards
Dirac equation
Paul Adrien Maurice Dirac
Fermions
fermions
Quantum Systems
geometry
scars
Discretization Scheme
Matrix Representation
Chaotic Dynamics
Energy Levels
ingredients
confining
Spacing
casts
energy levels
spacing
Physics

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Scarring of Dirac fermions in chaotic billiards. / Ni, Xuan; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 86, No. 1, 016702, 11.07.2012.

Research output: Contribution to journalArticle

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