# Séminaires du Tuesday 06 March

## Séminaire du LPTMS: Shuang Wu

#### 11:00:00

## Thouless bandwidth formula in the Hofstadter model

### Shuang Wu (LPTMS, Université Paris-Sud)

I will show a method of D. J. Thouless to calculate the Hofstadter spectrum bandwidth in relation to the Catalan constant. And I will present how we generalize Thouless bandwidth formula to its n-th moment and obtain a closed expression in terms of polygamma, zeta and Euler numbers.

## Séminaire du LPTMS: Giulio Bertoli

#### 11:30:00

## Finite temperature disordered bosons in two dimensions

### Giulio Bertoli (LPTMS, Université Paris-Sud)

In this talk, I will present a study of the phase transitions in a two dimensional weakly interacting Bose gas in a random potential at finite temperatures. It is possible to identify superfluid, normal fluid and insulator phases. The study of the effect of interaction between particles on localization demonstrates that interacting particles can undergo a many-body localization-delocalization transition, that is the transition from insulator to fluid state. I will also discuss the influence of disorder on the BKT transition between superfluid and normal fluid, in order to construct the phase diagram. At T=0 one has a tricritical point, where the three phases coexist. It is shown that the truncation of the energy distribution function at the trap barrier, which is a generic phenomenon in evaporative cooling of cold atoms, limits the growth of the localization length, so that the insulator phase is present at any temperature.

- Reference: G. Bertoli, V.P. Michal, B.L. Altshuler, G.V. Shlyapnikov,
*Finite temperature disordered bosons in two dimensions*, preprint cond-mat.dis-nn arXiv:1708.03628