CAREER: Wave Function Structure and Transport in Quantum Chaotic Systems

Tulane University, New Orleans LA

Investigators

Abstract

The research focus is on statistical properties of wave functions and quantum transport in systems with a non-integrable classical limit. Experiments and applications motivating this work come from fields as diverse as current flow through two-dimensional nanostructures, Coulomb blockade conductance in quantum dots, microwaves in irregularly-shaped electromagnetic resonators, energy transport in large structural acoustic systems, chemical reaction statistics, asymmetric optical resonators, and Casimir forces for nontrivial geometries. Specific closely interrelated research topics covered by this proposal are as follows. (1) Interaction matrix element fluctuations in quantum dots: For realistic chaotic geometries and experimentally relevant dot sizes, interaction matrix variance as computed from single-electron wave functions may exceed by a factor of 3 or 4 the variance predicted by a random wave model, with important implications for reconciling experimentally measured conductance peak spacing statistics with Hartree-Fock calculations. Future work includes obtaining a better understanding of wave function correlations beyond naive leading-order semiclassical approximation, and investigation of intriguing connections with mode competition in chaotic laser resonators. (2) Branched flow through weak random potentials: Images of electron flow in a two-dimensional electron gas show unexpected branching behavior, which may be explained by singularities in the classical flow. Ongoing work includes extension of the theory to the experimentally important parameter regimes of finite wave-length and rms potential height, allowing comparison with nanostructure experiments and with microwave cavity experiments that are now under development, as well as with recent studies of long-range ocean acoustics. (3) Bootstrapping of long-time transport behavior: Short-time quantum behavior, including phase information, may be used to predict nonrandom long-time transport and stationary properties; applications include ballistic and diffusive quantum dots, as well as energy transport in acoustic systems. (4) Long-time semiclassical accuracy: Ongoing work suggests the semiclassical propagator at long times is more accurate in chaotic than in regular systems in two dimensions, with implications for quantum fidelity and quantization ambiguity. Future work includes extending the methods to higher-dimensional and interacting systems, and to higher-order semi-classical approximations, as well as exploring the validity of semiclassical calculations for Casimir energies. Broader impacts of the proposal include: (1) building of a diverse research group of undergraduate and graduate students, with active participation of gender, racially, and disability underrepresented groups, including involvement in diversity-enhancement programs such as LSAMP, and encouraging collaboration with researchers in atomic physics, condensed matter physics, and chemistry; (2) development of new courses in "Computational physics" and "Chaos and nonlinear dynamics", targeted toward upper division undergraduate and beginning graduate students, and including collaboration with faculty in mathematics and engineering; (3) promoting undergraduate research involvement through publication of pedagogical articles accessible to students; (4) teaching of relevant introductory graduate and upper level undergraduate courses in quantum and classical mechanics, with emphasis on classical/quantum correspondence; and (5) continuation of effective, highly rated teaching of the introductory physics curriculum, with a focus on modern physics in the second semester and incorporating the use of innovative technology to encourage students interested in careers in physics and related fields of science.