Exploiting nonlinear dynamics for sensor applications
Abstract
Quantum chaos is referred to as the study of quantum manifestations of chaotic dynamics in the corresponding classical system, a field that has been extremely active for more than three decades. In closed chaotic Hamiltonian systems, the basic phenomena that have been and continue to be studied include energy level-spacing statistics and quantum scarring. In open Hamiltonian systems, quantum chaotic scattering has been investigated extensively. Quite recently, due to tremendous development of graphene science, relativistic quantum manifestations of classical chaos have become an interesting area of study. In studies of quantum chaos, the typical setting was that of single-particle quantum dynamics, whereas many-body effects such as electron-electron interactions were ignored. While there were previous studies of the interplay between many-body interactions and classical chaos, these were exclusively for nonrelativistic quantum systems described by the Schr¨odinger equation. To investigate the effect of chaos on relativistic quantum systems incorporating many-body interactions is an outstanding problem, yet it is not only fundamental to physics, but also important for practical development of relativistic quantum devices. To study quantum chaos in the presence of many-body interactions, we propose to study the Hubbard model for graphene systems. This paradigmatic model to treat interacting particles in a lattice was originally conceived to describe the transition between conducting and insulating systems. For electrons in a solid, comparing with the conventional tight-binding model described by the single electron Hamiltonian, the Hubbard model contains a potential term to treat the manybody effect through the mechanism of on-site Coulomb interaction. There has been a great deal of interest in the Hubbard model due to its relevance to frontier problems in condensed matter physics such as high-temperature superconductivity and the trapping of untracold atoms in optical lattices. As we argue in this proposal, while the Hubbard model is much more challenging and sophisticated than the tight-binding model, it can serve as a paradigm to gain significant physical insights into many-body quantum manifestations of distinct types of classical dynamics. To be concrete, we focus on graphene systems and study the particular phenomenon of quantum resonant tunneling. The typical setting of a quantum tunneling system consists of two symmetric potential wells separated by a potential barrier in between. The whole system, which includes the left and right wells and the barrier, is closed, and its geometrical shape can be chosen to yield characteristically distinct types of dynamics in the classical limit. For example, if the whole system has a rectangular domain, the classical dynamics is integrable, but fully developed chaos can arise if the system has a stadium or a bowtie shape. Recently, it has been discovered that, in both nonrelativistic and relativistic quantum systems under the setting of single electron tunneling, classical chaos can regularize quantum tunneling dynamics. Here by “regularizing” we mean that the vast spread in the tunneling rate in any small energy interval typically seen in the integrable geometry can be greatly suppressed when the underlying domain generates chaos in the classical limit.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 08, 2016
- Source ID
- N000141512405
Entities
People
- Ying-Cheng Lai
Organizations
- Arizona State University
- Office of Naval Research
- United States Navy