Séminaire - Spectres en géométrie hyperbolique : Low-Temperature Quantum Bounds on Curved Manifolds
Description
Nalini Anantharaman
Géométrie spectrale
Collège de France
Année 2023-2024
Séminaire - Spectres en géométrie hyperbolique : Low-Temperature Quantum Bounds on Curved Manifolds
Silvia Pappalardi
Université de Cologne
Résumé
In the past few years, there has been considerable activity around a set of quantum bounds on transport coefficients (viscosity, conductivity) and chaos (Lyapunov exponents), relevant at low temperatures. The interest comes from the fact that black-hole models seem to saturate all of them. However, the relation between the different bounds and physical properties of the systems saturating the is still a matter of ongoing research.
In this talk, I will discuss how one can gain physical intuition by studying classical and quantum free dynamics on curved manifolds. Thanks to the curvature, such models display chaotic dynamics up to low temperatures, and – as I will show how – they violate the bounds in the classical limit.
The talk aims to discuss three different ways in which quantum effects arise to enforce the bounds in practice. For instance, I will show how chaotic behavior is limited by the quantum effects of the curvature itself. As an illustrative example, I will consider the simple case of a free particle on a two-dimensional manifold, constructed by joining the surface of constant negative curvature – a paradigmatic model of quantum chaos – to a cylinder. The resulting phenomenology can be generalized to the case of several (constant) curvatures. The presence of a hierarchy of length scales enforces the bound to chaos up to zero temperature.
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