## Extremes and counting statistics for trapped fermions and random matrices

#### by Prof. Pierre Le Doussal

*ENS, Paris*

##### at Condensed Matter Seminar

Mon, 13 Mar 2023, 11:10

Sacta-Rashi Building for Physics (54), room 207

#### Abstract

I will first consider non-interacting fermions, and discuss the zero temperature quantum fluctuations of the number of fermions in some domain in d=1 and d>1. I will show how to calculate explicitly its variance in presence of an arbitrary external potential in d=1 and for some class of potentials in d>1. The connections with random matrix theory will prove useful. Next I will ask about the statistics of extrema of the counting function for some models of interacting fermions on the circle, and solve that problem using statistical mechanics methods. That will lead to new formula for the full counting statistics of interacting fermions in a class of Calogero-Sutherland type models in d=1 (and in particular to a generalisation of the Dyson-Mehta constant beyond the non interacting case).

Based on:

N. Smith, P. Le Doussal, S. Majumdar G. Schehr,

Phys. Rev. E. 103 L030105 (2021) and SciPost Phys 11, 110 (2021)

Y. Fyodorov and P. Le Doussal, Phys. Rev. Lett. 124, 210602 (2020).

Created on 02-03-2023 by Meidan, Dganit (dganit)

Updaded on 07-03-2023 by Meidan, Dganit (dganit)