Universal ground-state properties of free fermions in a d-dimensional trap
Language
en
Article de revue
This item was published in
EPL - Europhysics Letters. 2015-12, vol. 112, n° 6, p. 60001 (1-6)
European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Matrix theory
Probability theory - stochastic processes - and statistics
Fluctuation phenomena - random processes - noise - and Brownian motion
ANR Project
Paris Sciences et Lettres - ANR-10-IDEX-0001
Marcheurs Browniens répulsifs et matrices aléatoires - ANR-11-BS04-0013
Marcheurs Browniens répulsifs et matrices aléatoires - ANR-11-BS04-0013
Origin
Hal imported