Effect of chaos on relativistic quantum tunneling

¹ School of Electrical, Computer and Energy Engineering, Arizona State University - Tempe, AZ 85287, USA
² Institute of Computational Physics and Complex Systems, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University - Lanzhou, Gansu 730000, China
³ Department of Physics, Arizona State University - Tempe, AZ 85287, USA
⁴ Code 6362, Naval Research Laboratory - Washington, DC 20375, USA

^a xuan.ni@asu.edu

Received: 27 March 2012
Accepted: 21 May 2012

Abstract

We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical periodic orbits can exist, which suppress quantum tunneling, and the effect becomes less severe as the underlying classical dynamics in the cavity is chaotic, leading to regularization of tunneling dynamics even in the relativistic quantum regime. Similar phenomena have been observed in graphene. A physical theory is developed to explain the phenomenon based on the spectrum of complex eigenenergies of the non-Hermitian Hamiltonian describing the effectively open cavity system.