Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

点击翻译按钮获取中文摘要

NONTECHNICAL SUMMARYThis award supports theoretical research with a general aim to understand interacting quantum mechanical systems that are out of equilibrium, with a particular focus on "quantum chaos". In everyday life chaos is usually defined as a mess, or more accurately, as a lack of any order. In classical physics, chaos is mathematically defined through very strong sensitivity of a particle's trajectory to slight perturbations. This sensitivity is behind many phenomena surrounding us, from unstable weather patterns to the emergence of equilibrium statistical physics, with the most fundamental example being the second law of thermodynamics. In quantum systems, on the other hand, particles do not have well defined trajectories, since their positions and velocities cannot be defined at the same time due to the uncertainty principle. Accordingly, defining and understanding chaos in the microscopic world in a quantum mechanical language becomes more subtle and has been a subject of active debate in the last four decades. This project explores new ways of defining quantum chaos through sensitivity of quantum states to small perturbations. Through this language it aims to establish direct connections between quantum and classical chaos and explore how it emerges as we increase the number of particles in the system. Another focus of the project is finding ways of suppressing chaos in interacting quantum systems by active dynamical control, which should lead to developing efficient computational and energy transfer schemes. These schemes, in turn, can be used in future technologies to develop fast and efficient quantum computers, quantum simulators, and quantum heat engines or refrigerators. This award also supports educational and outreach activities which involve training students at both graduate and undergraduate levels in topics at the forefront of condensed matter and statistical physics, delivering public talks and lectures, and developing a new book on quantum mechanics, which covers modern advances in the field that are not typically found in standard textbooks.TECHNICAL SUMMARYThis award supports research aimed at developing new theoretical approaches for understanding non-equilibrium interacting systems and on applying these approaches to existing and future experimental setups. The research has three main thrusts: (1) The first theme of the project focuses on a method recently developed by the PI, which characterizes quantum chaos through adiabatic deformations expressed through the adiabatic gauge potential. The PI will analyze universal properties of the transition between integrable and chaotic regimes driven by weak integrability breaking perturbations, apply this method to disordered, periodically driven and other systems, and extend it to classical nonlinear systems like the Fermi-Pasta-Ulam-Tsingou problem to analyze emergence of chaos. (2) The second closely related theme of the project focuses on finding approximate local adiabatic gauge potentials, which can be used to identify approximate local conservation laws in nonintegrable systems. The goal is to develop efficient local counter-diabatic and fast-forward protocols that suppress dissipation in interacting systems, which is important for both efficient information and energy processing. This project will aim to design such protocols in driven Floquet systems, finite-temperature systems, and non-linear systems with locally unbounded spectrum. A particular emphasis will be on developing experimentally relevant protocols, which can be realized in different setups like superconducting qubits, cold atoms and trapped ions. (3) The third theme of the project will focus on investigating the connections between quantum and classical chaos by using a formalism recently developed by the PI that shows a correspondence between classical Hamiltonian systems and quantum eigenstates even away from the semi-classical limit.This award also supports educational and outreach activities which involve training students at both graduate and undergraduate levels in topics at the forefront of condensed matter and statistical physics, delivering public talks and lectures, and developing a new book on quantum mechanics, which covers modern advances in the field that are not typically found in standard textbooks.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.