VERMOUTH · noVEl appRoaches to the quantuM bOUnds To cHaos

noVEl appRoaches to the quantuM bOUnds To cHaos

In recent years, experimental and technological progress in quantum simulation and computation has stimulated enormous theoretical interest in the coherent dynamics of complex quantum systems. This has motivated a renaissance for the study of quantum chaos, which has become a broad multidisciplinary field, with concepts and approaches stemming from condensed matter, high energy physics and quantum information theory. These different interdisciplinary approaches have emphasised the existence of a set of bounds imposed by quantum effects on the physical properties of many-body systems, such as viscosity, conductivity or Lyapunov exponent. They are characterized by a time scale which only depends on temperature and the Planck constant and for this reason they have been dubbed ``"Planckian bounds". Their remarkable feature is that they are all saturated by models of black holes. However, there are several outstanding open questions regarding such quantum constraints. I) Are these bounds a coincidence or they are potentially indicative of a deep principle in quantum mechanics? II) What is the relation between the bound to chaos and the Planckian one? III) What are the physical properties of the systems saturating these bounds? The purpose of this proposal is to tackle several issues at the intersection of these fields from the perspective of standard quantum statistical mechanics. In particular, the project intends to explain the bounds as a direct consequence of the quantum Fluctuation-Dissipation Theorem (FDT), one of the cornerstones of equilibrium physics.

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