Order and chaos in dissipative quantum matter

University of Cambridge

No physical system is truly isolated from its surroundings. Interactions with the environment and noise are, to some degree, unavoidable, leading to exchanges of energy and information (dissipation). Openness is particularly important in the microscopic quantum realm: It can be a hindrance, say, for quantum computers, with losses limiting their accuracy; Or it can be a resource, as in atomic physics, where experimental advances now allow us to engineer special states of matter stabilized by dissipation.

Whether to avoid or exploit it, a deeper theoretical understanding of openness is paramount. Much is known in the case of a few particles interacting weakly with each other. But the most interesting physics occurs in strongly interacting many-body systems, which are notoriously difficult to analyze even in isolated settings. One very fruitful approach is to replace these complex systems with simpler toy models possessing the main features of interest. A more radical approach is to forget details altogether and model them as completely random. This is the content of the celebrated quantum chaos conjecture: chaotic (complicated) quantum systems behave as if they were random.

My research lies at the interface of several areas of physics (condensed matter, high-energy theory, and quantum information science) and focuses on the quantum chaos approach to the nonequilibrium and open realms. It revolves around the following questions: (i) How to study the dynamics of far-from-equilibrium strongly-interacting many-body quantum systems? (ii) What are the universal properties of complex dissipative quantum matter? (iii) How to define, detect, and quantify quantum chaos in the presence of dissipation?

To address these questions, I propose investigating dissipative versions of celebrated toy models of strongly- interacting systems, namely the Sachdev-Ye-Kitaev model (a model of infinitely strongly-coupled electrons) and quantum-circuit models of quantum computers. The questions I aim to address include the following: How to engineer transitions from order to chaos and special steady-states in dissipative systems with strong interactions? How to relate chaos in space with chaos in time? How are chaos and randomness related in the presence of dissipation? And what are the best tools to distinguish dissipative order from chaos?