This award supports theoretical research and education aimed to advance understanding of robust properties of quantum mechanical systems far from the steady state of equilibrium. The study of nonequilibrium systems lies at the forefront of experimental and theoretical research, and will likely play an important role in future technology. However, current understanding of nonequilibrium systems is limited. In particular, there are no systematic theoretical approaches like the ones that exist for systems that are in equilibrium. This project will address fundamental questions regarding the relationship between the evolution of nonequilibrium systems and the geometry of their states, and contribute to understanding the nature of steady states, phases, and phase transitions in systems that receive periodic external stimuli. In addition, the PI aims to develop new computational methods for simulating the dynamics of quantum systems. The predictions of this project will be compared with current state-of-the-art experiments, and could stimulate new experiments.

NSF funds will fully support one graduate student, and in addition will contribute to the training of students and postdocs both from Boston University and other institutions through discussions and collaborations. It is anticipated that the results of this work will be published in scientific journals, and will be reported at various conferences, seminars, schools, and colloquia aimed at a broader audience. The PI will write pedagogical reviews and lecture notes aimed at both graduate and undergraduate student audiences.

Technical Abstract

This award supports theoretical research and education focused on addressing fundamental questions about the nature of non- equilibrium interacting systems, and the practical applications of conceptual advances to specific experimental setups. The PI aims to address the relation between quantum dynamics and geometry, investigate emergent equations of motion of slow macroscopic degrees of freedom coupled to interacting correlated systems, understand the nature of non-equilibrium steady states in driven systems, and find systematic ways of interpolating between quantum and classical dynamics. Specific problems, which will be addressed, include microscopic derivation of dynamics of slow degrees of freedom, like positions and shapes of macroscopic objects, coupled to fast interacting quantum systems; finding general relations among kinematic coefficients like mass tensor, response functions and the quantum geometric tensor; and finding leading corrections to conventional Hamiltonian dynamics. The PI will also carry out the theoretical analysis of steady states and transient dynamics in periodically driven systems both isolated and coupled to the environment. This work will aim at understanding energy localization and ergodicity, emergent conservation laws, phases and phase transitions and others. The third topic will focus on developing new numerical methods for simulating quantum dynamics. The key idea is to extend semiclassical methods to higher dimensional phase space by introducing extra degrees of freedom representing correlation functions. The PI aims to apply these ideas to specific experimentally relevant setups. The proposal will also involve close collaboration with experimental groups that focus on explaining existing results and the implementation of theoretical ideas in new experiments.

NSF funds will fully support one graduate student, and in addition will contribute to the training of students and postdocs both from Boston University and other institutions through discussions and collaborations. It is anticipated that the results of this work will be published in scientific journals, and will be reported at various conferences, seminars, schools, and colloquia aimed at a broader audience. The PI will write pedagogical reviews and lecture notes aimed at both graduate and undergraduate student audiences.

Agency
National Science Foundation (NSF)
Institute
Division of Materials Research (DMR)
Application #
1506340
Program Officer
Daryl Hess
Project Start
Project End
Budget Start
2015-09-01
Budget End
2018-08-31
Support Year
Fiscal Year
2015
Total Cost
$348,754
Indirect Cost
Name
Boston University
Department
Type
DUNS #
City
Boston
State
MA
Country
United States
Zip Code
02215