Statistics of fermions in a $d$-dimensional box near a hard wall

Bertrand Lacroix-A-Chez-Toine 1 Pierre Le Doussal 2 Satya N. Majumdar 1 Gregory Schehr 1

EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2017

We study $N$ noninteracting fermions in a domain bounded by a hard wall potential in $d \geq 1$ dimensions. We show that for large $N$, the correlations at the edge of the Fermi gas (near the wall) at zero temperature are described by a universal kernel, different from the universal edge kernel valid for smooth potentials. We compute this $d$ dimensional hard edge kernel exactly for a spherical domain and argue, using a generalized method of images, that it holds close to any sufficiently smooth boundary. As an application we compute the quantum statistics of the position of the fermion closest to the wall. Our results are then extended in several directions, including non-smooth boundaries such as a wedge, and also to finite temperature.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. LPTENS - Laboratoire de Physique Théorique de l'ENS