DEAN, David S.; LE DOUSSAL, Pierre; MAJUMDAR, Satya N.; SCHEHR, Grégory

doi:10.1209/0295-5075/112/60001

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http://creativecommons.org/licenses/by-sa/

DEAN, David S.
Laboratoire Ondes et Matière d'Aquitaine [LOMA]

LE DOUSSAL, Pierre
Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] [LPTENS]

MAJUMDAR, Satya N.
Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS]

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Article de revue

Este ítem está publicado en

EPL - Europhysics Letters. 2015-12, vol. 112, n° 6, p. 60001 (1-6)

European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing

Resumen en inglés

The ground-state properties of N spinless free fermions in a d-dimensional confining potential are studied. We find that any n-point correlation function has a simple determinantal structure that allows us to compute several properties exactly for large N. We show that the average density has a finite support with an edge, and near this edge the density exhibits a universal (valid for a wide class of potentials) scaling behavior for large N. The associated edge scaling function is computed exactly and generalizes to any d the edge electron gas result of Kohn and Mattsson in d = 3 (Kohn W. and Mattsson A. E., Phys. Rev. Lett., 81 (1998) 3487). In addition, we calculate the kernel (that characterizes any n-point correlation function) for large N and show that, when appropriately scaled, it depends only on dimension d, but has otherwise universal scaling forms, at the edges. The edge kernel, for higher d, generalizes the Airy kernel in one dimension, well known from the random matrix theory.< Leer menos

Palabras clave en inglés

Matrix theory

Probability theory - stochastic processes - and statistics

Fluctuation phenomena - random processes - noise - and Brownian motion

DOI

http://dx.doi.org/10.1209/0295-5075/112/60001

Proyecto ANR

Paris Sciences et Lettres - ANR-10-IDEX-0001
Marcheurs Browniens répulsifs et matrices aléatoires - ANR-11-BS04-0013

Orígen

Importado de Hal

Centros de investigación

Laboratoire Ondes et Matière d'Aquitaine (LOMA) - UMR 5798