Noninteracting trapped fermions : from random matrices to the Kardar-Parisi-Zhang equation

Jeudi 16 novembre 14:00-15:00 - Grégory Schehr - Université Paris-Sud

Résumé : I will consider a system of N one-dimensional free fermions confined by a harmonic well. At zero temperature (T=0), this system is intimately connected to random matrices belonging to the Gaussian Unitary Ensemble. In particular, the density of fermions has, for large N, a finite support and it is given by the Wigner semi-circular law. Besides, close to the edges of the support, the quantum fluctuations are described by the so-called Airy-Kernel (which plays an important role in random matrix theory). What happens at finite temperature T ? I will show that at finite but low temperature, the fluctuations close to the edge, are described by a generalization of the Airy kernel, which depends continuously on temperature. Remarkably, exactly the same kernel arises in the exact solution of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions at finite time. I will also discuss extensions of these results to fermions in higher dimensions.

Lieu : salle 117/119 du bâtiment 425

Noninteracting trapped fermions : from random matrices to the Kardar-Parisi-Zhang equation  Version PDF