Semi‐classical counting function with application to quantum current

Article type: Research Article

Authors: Butler, J.

Affiliations: Département de Mathématiques, Bât. 425, Université de Paris‐Sud, 91405 Orsay cedex, France E‐mail: Jonathan.Butler@math.u‐psud.fr

Note: [] Author supported by European Union TMR grant FMRX‐960001.

Abstract: We obtain a new two‐term asymptotic formula for the counting function of eigenvalues of h pseudodifferential operators in the limit as h→0. Recent results concerning clustering of eigenvalues obtained in [7] follow in corollary and, as an application, we consider the semi‐classical behaviour of the quantum current studied recently in [2].

Journal: Asymptotic Analysis, vol. 27, no. 3-4, pp. 195-218, 2001