Abstract

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics - all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Original languageEnglish (US)
Article number052101
JournalChaos
Volume28
Issue number5
DOIs
StatePublished - May 1 2018

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Quantum Chaos
Chaos theory
chaos
Chaos
Quantum Mechanics
Paul Adrien Maurice Dirac
Quantum theory
Spintronics
Insulator
Graphene
Dirac Equation
quantum mechanics
Fingerprint
Energy Levels
Quantum Systems
Resonant tunneling
Magnetoelectronics
Scattering
Electronics
Statistics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Relativistic quantum chaos - An emergent interdisciplinary field. / Lai, Ying-Cheng; Xu, Hong Ya; Huang, Liang; Grebogi, Celso.

In: Chaos, Vol. 28, No. 5, 052101, 01.05.2018.

Research output: Contribution to journalReview article

Lai, Ying-Cheng ; Xu, Hong Ya ; Huang, Liang ; Grebogi, Celso. / Relativistic quantum chaos - An emergent interdisciplinary field. In: Chaos. 2018 ; Vol. 28, No. 5.
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