Speakers & Program

— Andrei BERNEVIG (Princeton Univ.): "Topological Matter".

— Tomaž PROSEN (Lujbjana Univ.) : "Many-body quantum chaos and random matrix theory".

One of the key goals of quantum chaos is to establish a clean relationship between the observed universal spectral fluctuations of simple quantum systems and random matrix theory. For single particle systems with fully chaotic classical counterparts, the problem has been essentially solved by M. V. Berry within the so-called diagonal approximation of semiclassical periodic-orbit sums.
In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming at the forefront also for simple many-body quantum systems, such as locally interacting spin chains. Such systems seem to display two universal types of of behavior which are nowadays usually termed as `many-body localized phase' and `ergodic phase’. In the ergodic phase, the spectral fluctuations are typically excellently described by random matrix theory, despite simplicity of interactions and lack of any external source of disorder.
After giving a broad overview of the problem and its history, I will outline a heuristic derivation of random matrix spectral form factor for clean non-integrable spin chains, a prominent example of which is the Ising chain in a tilted (transverse + longitudinal) periodically kicking magnetic field. I will also present a specific model of the same type with nearest-neighbor interactions where random matrix spectral form factor can be rigorously proven. These models, which I will discuss in some detail, provide exactly solvable models of many-body quantum chaos.

References:
P. Kos, M. Ljubotina, T. Prosen, Phys. Rev. X 8, 021062 (2018)
B. Bertini, P. Kos, T. Prosen, Phys. Rev. Lett. 121, 264101 (2018)
A. Chan, A. De Luca, J. T. Chalker, Phys. Rev.  X 8, 041019 (2018)
A. Chan, A. De Luca, J. T. Chalker, Phys. Rev. Lett. 121, 060601 (2018)

— Adam NAHUM (Oxford Univ.) : "Entanglement and information spreading".

For many purposes, a nonzero temperature makes the dynamics of nonintegrable quantum many-body systems effectively classical. For example, the effective coarse-grained description of local correlation functions is typically some form of classical hydrodynamics. In this short course I will discuss the dynamics of 'nonlocal' quantum observables that cannot be described with conventional hydrodynamics. These include the entanglement entropy and other observables which characterise the spreading of quantum information after a quantum quench. I will describe simple many-body systems, random unitary circuits, that allow calculations via exact mappings to archetypal classical statistical mechanics problems: directed polymers, membranes, growing clusters, etcetera. I will use these mappings to motivate a more general phenomenology of information spreading in chaotic systems.

— Gregory SCHEHR (CNRS & LPTMS, Orsay Univ.) : "Growth processes and integrability".

Stochastic growth models in the Kardar-Parisi-Zhang (KPZ) universality class are cornerstones of non-equilibrium statistical physics. As such, they have been extensively studied, both in theoretical physics as well as in mathematics. In these lectures, I will review the spectacular progresses that have been achieved, during the last twenty years, for the KPZ universality class in 1+1 dimensions. 
In particular, I will present the connections between these growth models and random matrix theory or closely related objects, like non-intersecting random walks. I will also discuss more recent developments, including in particular relations to trapped fermions at finite temperature.

— Jean-Marie STEPHAN (CNRS & Univ. Lyon 1) : "Extreme boundary conditions and random tilings".

Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as illustrated by the famous 'arctic circle theorem' for domino tilings in two dimensions. 
In these lectures, I will discuss such examples in the context of critical phenomena, and their relation to 1+1d quantum spin or particle models in trapping potentials. All those turn out to share a common feature: they are inhomogeneous, in the sense that local densities now depend on position in the bulk. I will explain how such problems may be understood using semiclassical arguments, and how field theoretical techniques may be adapted to understand long range correlations in general. If time permits I will also discuss the various connections to KPZ-type scaling at the edge, and similar but different hydrodynamic treatments of quantum integrable systems put far from equilibrium.

— Jorge KUCHAN (CNRS & LPENS) : "Probability distribution and correlations of matrix elements of operators in chaotic systems: completing ETH".

— Fabian ESSLER (Oxford Univ.) : "Non-equilibrium dynamics in split one-dimensional Bose gases".

— Benoit DOUÇOT (CNRS & LPTHE) : "The Floquet spectrum of superconducting multiterminal quantum dots".