Volume 120, Number 1, October 2017
|Number of page(s)||5|
|Published online||29 December 2017|
Statistics of fermions in a d-dimensional box near a hard wall
1 LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay - 91405 Orsay, France
2 CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure - 24 rue Lhomond, 75231 Paris Cedex, France
Received: 14 November 2017
Accepted: 8 December 2017
We study N noninteracting fermions in a domain bounded by a hard-wall potential in 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 confining 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 hard wall. Our results are then extended in several directions, including non-smooth boundaries such as a wedge, and also to finite temperature.
PACS: 02.10.Yn – Matrix theory / 02.50.-r – Probability theory, stochastic processes, and statistics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EPLA, 2017
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