# Project Details

### Description

NONTECHNICAL SUMMARY This award supports fundamental theoretical research and education to advance conceptual understanding of quantum mechanical systems of many particles, for example electrons in materials, that are far from the balanced state of equilibrium. The detailed study of nonequilibrium processes has been hampered over the years by the very short time scales that characterize the response of the system to external impulse, and the difficulty of isolating such systems from the environment. With the appearance of diverse new systems accessible to experiments, including nanoelectronic and nanomechanical devices, molecular electronic devices, optical systems, and cold atom gases trapped in beams of laser light, many limitations have been overcome and great progress has been made to control and fine tune many fundamental experiments to probe nonequilibrium systems. This award addresses a need to develop in parallel the theoretical tools to describe them.The PI will focus on systems that undergo an abrupt change, or quench, and investigate how the system responds with time. The systems to be investigated are described by a class of models that have experimental realizations in trapped cold atom systems or nanodevices. Theoretical tools will be developed to explore the time evolution of these systems. The PI aims to use these tools to go further to probe and identify the fundamental principles that underlie thermodynamics for systems that are far from equilibrium. The PI will address several questions, including: What drives a system to reach equilibrium? What aspects of the dynamics apply to many systems independent of specific details, and which ones are specific to a particular system? When a system is in a nonequilibrium steady state does it maximize entanglement, a quantum mechanical property that links different parts of the system that may be far from each other?The projects describe detailed experimental systems and are used to discover the concepts that govern them. Combining both the theoretical analysis with specific study of experimental systems provides an excellent platform for the training of graduate students. The PI will convey the underlying science and research results to a broad range of audiences from high school students to the general public.TECHNICAL SUMMARYThis award supports the theoretical research and education on the nonequilibrium dynamics of strongly correlated systems. The emphasis is placed on quench evolution in systems described by integrable Hamiltonians that can be realized by experiments. The PI will develop the theoretical tools needed to investigate the dynamics of nonequilibrium systems. He will pursue generalizations of the Yudson representation to finite volume that are necessary to allow the expression of an arbitrary initial state in terms of the Bethe Ansatz eigenstates of the Hamiltonian and hence its evolution. The PI will investigate a variety of systems, including:The Gaudin-Yang model describes multicomponent particles, fermions or bosons moving on the continuous line interacting via short range potential. The PI will study the interaction quench of a Fermi sea with attractive and repulsive interactions with the purpose of understanding the different phases that ensue. Of particular interest is the quench into a finite momentum condensed state, driven by an imbalance of spin-up and spin-down electrons. Similar questions arise on the lattice for systems described by the Hubbard Hamiltonian.The Sine-Gordon model can describe a large number of systems in a variety of contexts. The PI will study this model in the physical context of the quench from a Mott insulator to a superfluid that takes place when the strength of the periodic potential is reduced, a quantum phase transition much studied experimentally.Quantum impurity systems, typically given by the Kondo and Anderson Hamiltonians, appear in many contexts. With these Hamiltonians, the PI will investigate the quench dynamics of: i. an impurity coupled to a lead to determine time evolution of the Kondo effect, ii. An impurity attached to two leads held at different chemical potential to determine and the time evolution of the non equilibrium current driven by the voltage.This award also supports educational activities integrated with the research at the graduate level. The results of the research will be incorporated into the PI's graduate level courses on quantum many-body physics and condensed matter theory and into a book the PI is writing.

Status | Finished |
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Effective start/end date | 10/1/14 → 9/30/17 |

### Funding

- National Science Foundation (National Science Foundation (NSF))