Szego limit theorem for operators with discontinuous symbols and applications to entanglement entropy

Details Szego limit theorem for operators with discontinuous symbols and applications to entanglement entropy Szego limit theorem for operators with discontinuous symbols and applications to entanglement entropy

2002-12-16

arxiv.org/abs/math/0212215v4

Int. Math. Res. Not. 2006, Art. ID 95181, 23 pp.

Mathematics

Functional Analysis

18 pages, major revision, to appear in Int. Math. Res. Not

Scientific paper

10.1155/IMRN/2006/95181

The main result in this paper is a one term Szego type asymptotic formula with a sharp remainder estimate for a class of integral operators of the pseudodifferential type with symbols which are allowed to be non-smooth or discontinuous in both position and momentum. The simplest example of such symbol is the product of the characteristic functions of two compact sets, one in real space and the other in momentum space. The results of this paper are used in a study of the violation of the area entropy law for free fermions in [18]. This work also provides evidence towards a conjecture due to Harold Widom.

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