The density of surface states as the total time delay

Abstract

For a scattering problem of tight-binding Bloch electrons by a weak random surface potential, a generalized Levinson theorem is put forward showing the equality of the total density of surface states and the density of the total time delay. The proof uses explicit formulas for the wave operators in the new rescaled energy and interaction (REI) representation, as well as an index theorem for adequate associated operator algebras.

Suggestions of referees incorporated and errors corrected. To appear in Lett. Math. Phys

References in corpus (3)

• Levinson's theorem for Schroedinger operators with point interaction: a topological approach
• New expressions for the wave operators of Schroedinger operators in R^3
• On the wave operators and Levinson's theorem for potential scattering in R^3

Cited by in corpus (3)

• One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results
• Levinson's theorem: an index theorem in scattering theory
• Dimensional reduction and scattering formulation for even topological invariants