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 Schrödinger 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.
|Journal||Journal of Mathematical Physics|
|State||Published - 2006|
Bibliographical noteFunding Information:
P.D.H. thanks R. M. Brown, M. Shubin, and especially H. Leschke, for many helpful discussions. P.D.H. is partially supposed by NSF Grant No. DMS-0503784.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics