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Universality and ergodicity in quantum many-body systems: August 26-October 18, 2019

Organized by: Boris Altshuler, Anatoly Dymarsky, Lea Santos, and Jacobus Verbaarschot

Dynamics of quantum many-body systems is attracting extensive attention across different fields of physics: theoretical and experimental condensed matter, AMO physics, high energy theory, quantum information, and others. Remarkable progress has been achieved in the past years understanding thermalization, or lack thereof, of isolated quantum systems, paving new ways to quantitatively probe quantum chaos and connecting many-body systems to quantum gravity. However, this progress is still fragmentary and there are very important basic questions which are not well understood. The program will address, among others, the following questions.

1) What are the characteristic timescales of relaxation and thermalization for many-body quantum systems? The interplay between different timescales and their manifestation in various observables is not clear. One highly contested question is the behavior of the so-called Thouless time, which marks the scale of applicability of Random Matrix Theory to describe correlations of energy spectrum. For the disordered single-particle systems the latter was identified as the timescale of diffusion. For various many-body systems (local 1D systems, Floquet, SYK model) the Thouless time was shown recently to behave very differently.

2) What is the relation between out-of-time-ordered correlators (OTOC) and the timescales marking the onset of universal behavior? This question is in its infancy with very few papers making explicit connection between dynamics of thermalization and quantitative manifestations of quantum chaos.

3) What constitutes ergodic behavior for quantum systems? Ergodicity for quantum systems is often equated with Eigenstate Thermalization, which is only concerned with the value of observables at equilibrium. Can something be said about the approach toward and fluctuations around the asymptotic value?

4) What is the scope of applicability of Random Matrix Theory to many-body systems? Random matrices are known to describe various aspects of quantum chaotic systems, e.g. statistics of energy levels. More recently, there have been several applications of random matrices to describe the late time behavior of various observables, including survival probability, correlation functions, Euclidean partition function, etc. An important question would be to understand which dynamical quantities and to what they extent may exhibit universal behavior and be described by the Random Matrix Theory.

The program is accompanied by a workshop “Applications of Random Matrix Theory to many-body physics,” to be held between September 16-20, 2019, which will be focused on universal behavior of many-body systems.