Basic properties of the current-current correlation measure for random Schroedinger operators

Journal Article · Wed Nov 15 00:00:00 EST 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2378618· OSTI ID:20861426

Hislop, Peter D; Lenoble, Olivier ^[1]

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1. Mathematics Department, University of Kentucky, Lexington, Kentucky 40506-0027 (United States)

The current-current correlation measure plays a crucial role in the theory of conductivity for disordered systems. We prove a Pastur-Shubin-type formula for the current-current correlation measure expressing it as a thermodynamic limit for random Schroedinger operators on the lattice and the continuum. We prove that the limit is independent of the self-adjoint boundary conditions and independent of a large family of expanding regions. We relate this finite-volume definition to the definition obtained by using the infinite-volume operators and the trace-per-unit volume.

• OSTI ID: 20861426
• Journal Information: Journal of Mathematical Physics, Vol. 47, Issue 11; Other Information: DOI: 10.1063/1.2378618; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
CORRELATIONS
LATTICE FIELD THEORY
MATHEMATICAL OPERATORS
MEASURE THEORY
RANDOMNESS
SCHROEDINGER EQUATION
THERMODYNAMIC PROPERTIES