# Quantum Journal Club: Christophe Texier

## Correlations of occupation numbers in the canonical ensemble

### Christophe Texier (LPTMS, Université Paris-Sud)

The connection between the statistical physics of non-interaction indistinguishable particles in quantum mechanics and the theory of symmetric functions will be reviewed. Then, I will study the $p$-point correlation function $\overline{n_1\cdots n_p}$ of occupation numbers in the canonical ensemble ; in the grand canonical ensemble, they are trivially obtained from the independence of individual quantum states, however the constraint on the number of particles makes the problem non trivial in the canonical ensemble. I will show several representations of these correlation functions. I will illustrate the main formulae by revisiting the problem of Bose-Einstein condensation in a 1D harmonic trap in the canonical ensemble, for which we have obtained several analytical results. In particular, in the temperature regime dominated by quantum correlations, the distribution of the ground state occupancy is shown to be a truncated Gumbel law.

Ref: Olivier Giraud, Aurélien Grabsch & Christophe Texier, Correlations of occupation numbers in the canonical ensemble and application to BEC in a 1D harmonic trap, Phys. Rev. A 97, 053615 (2018).

Date/Time : 26/11/2018 - 11:00 - 12:00