LPTMS PhD Proposal: Quantum entanglement in fermionic systems via random matrix theory

Responsables:

Satya MAJUMDAR + 33 (0)1 69 15 64 65

Grégory SCHEHR + 33 (0)1 69 15 76 41

During the last few years, it has been shown that non-interacting fermions in presence of a trap can be studied using the powerful techniques of random matrix theory, and more generally of determinantal point processes. This toolbox allowed to study analytically the interplay between quantum and thermal fluctuations in challenging physical situations where standard approaches of many-body physics, like the Local Density Approximation, fail.

Currently, there is an intense activity, both experimental and theoretical, concerning the relation between quantum entanglement and the thermodynamic entropy in many-body quantum systems. Many results remain currently conjectural. In this project, we would like to explore these questions, for instance the quantum entanglement at finite temperature, in a class of solvable models of trapped fermions, that are known to be related to RMT models at zero temperature.