Lower entropy bounds and particle number fluctuations in a Fermi sea
In this letter we demonstrate, in an elementary manner, that given a partition of the single particle Hilbert space into orthogonal subspaces, a Fermi sea may be factored into pairs of entangled modes, similar to a BCS state. We derive expressions for the entropy and for the particle number fluctuations of a subspace of a Fermi sea, at zero and finite temperatures, and relate these by a lower bound on the entropy. As an application we investigate analytically and numerically these quantities for electrons in the lowest Landau level of a quantum Hall sample.
Copyright © Institute of Physics and IOP Publishing Limited 2006. Received 21 October 2005, in final form 30 November 2005. Published 11 January 2006. Print publication: Issue 4 (27 January 2006) I thank J D Bekenstein, J Lebowitz, L S Levitov, B Shapiro, A Retzker and M Reznikov for useful remarks.