Séminaire de groupe
Finitetemperature free fermions and the KardarParisiZhang equation at finite time 
Gregory Schehr 
LPTMS, Universite ParisSud 
mercredi 30 septembre 2015 , 10h00 
Salle de séminaire du groupe de Physique Statistique 
I shall consider a system of N onedimensional free fermions confined by a harmonic well. At zero temperature (T=0), it is wellknown that 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 semicircular law. Besides, close to the edges of the support, the quantum fluctuations are described by the socalled AiryKernel (which plays an important role in randommatrix theory). What happens at finite temperature T ? I shall 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 KardarParisiZhang (KPZ) equation in 1+1 dimensions at finite time. <br> If time permits, I shall also present recent results for fermions in higher dimensions. 
