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Technology & Science

P23: Non-Perturbative Approaches to Non-Equilibrium Quantum Systems

PhD Student: Stefano De Nicola

Quantum many-body systems exhibit a rich variety of novel phases and phase transitions, ranging from superconductivity to the Quantum Hall Effect. Describing these emergent phenomena has necessitated the development of sophisticated theoretical techniques. However, out of equilibrium, much less is known, and there is a lack of a universal framework and widely applicable techniques. This has led in recent years to the intensive study of non-equilibrium quantum many-body systems, in particular systems subject to time-dependent protocols such as rapid quenches (Calabrese and Cardy) and sweeps.

New developments have opened the way for some very promising directions, including the quench action approach (Caux and Essler) and the use of stochastic differential equations (Gritsev). Advancing this frontier requires expertise from different areas of physics and mathematics, including integrable models out of equilibrium and the dynamics of quantum impurities (Doyon), condensed matter field theory and cold atomic gases (Bhaseen).

The goal of this project is to investigate the non-equilibrium response of quantum many-body systems using these new approaches, and to develop the scope and applications of non-perturbative techniques. There are many possible directions for investigation, including the dynamics of quantum spin systems, entanglement growth, and the behavior of open systems and quantum non-equilibrium steady states. The overarching aim is to distill universal results out of equilibrium and to develop new theoretical tools. Possible application areas include condensed matter systems, cold atoms, quantum optics and quantum information.