Effect of chaos on relativistic quantum tunneling

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. editor’s choice Copyright c © EPLA, 2012 To understand the effect of chaos in the classical limit on quantum behaviors has been a field of interest and active pursuit [1]. This field, named quantum chaos, finds applications in many fields in physics such as condensedmatter physics, atomic physics, nuclear physics, optics, and acoustics. Previous works on quantum chaos focused almost exclusively on non-relativistic quantum systems. A fundamental question is whether phenomena in nonrelativistic quantum chaos can occur in relativistic quantum systems described by the Dirac equation. This field of relativistic quantum chaos [2] is of particular importance because of the relevance of the Dirac equation to graphene systems [3]. Recently, the remarkable phenomenon of chaosregularized quantum tunneling has been uncovered [4], where classical chaos can suppress, significantly, the spread in the tunneling rate commonly seen in systems whose classical dynamics are regular. For example, consider the system in fig. 1, which consists of two symmetrical cavities connected by a one-dimensional potential barrier along the line of symmetry. When the classical dynamics in each cavity is integrable, for sufficiently large energy the tunneling rate can assume many (a)E-mail: [email protected] (a) (b)