# Project Details

### Description

Statement ofWork In the last three decades, quantum chaos, an interdisciplinary field focusing on the quantum manifestations of classical chaos, has received a great deal of attention from a number of physics communities. Indeed, the quantization of chaotic Hamiltonian systems and the signatures of classical chaos in quantum regimes are fundamental to physics and have direct applications in disciplines such as condensed matter physics, atomic physics, nuclear physics, optics, and acoustics. Issues that have been pursued include energy-level statistics, statistical properties of wave functions, quantum chaotic scattering, electronic transport in quantum dots, localization, and the effect of magnetic field, etc. Existing works on quantum chaos are concerned almost exclusively with non-relativistic quantum mechanical systems described by the Schrodinger equation, where the dependence of the particle energy on the momentum is quadratic. A fundamental issue, which we propose to address, is whether phenomena in non-relativistic quantum chaos can occur in relativistic quantum systems described by the Dirac equation, where the energy-momentum relation is linear. This issue is of great interest at the present due to the discovery of graphene in which the underlying quantum dynamics can be relativistic. Another area of tremendous recent interest in condensed matter physics to which relativistic quantum mechanics is directly relevant is topological insulators, materials that are surface conducting but bulkily insulating. In a topological insulator, the surface energy band exhibits structures that are characteristic of massless Dirac fermions. For both graphene and topological insulators, relativistic quantum behaviors occur in two dimensions. To understand the relativistic quantum manifestations of classical chaos thus not only is fundamental to advance physics, but also will have significant impact on nanoscale devices based on graphene or topological insulators. Our proposed research represents a ne

Status | Finished |
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Effective start/end date | 2/28/08 → 9/30/14 |

### Funding

- DOD-NAVY: Office of Naval Research (ONR): $700,000.00