Landauer-Büttiker and Thouless conductance (Q2354357)

There are many open problems related to the transport phenomena in quantum mechanics. And in this framework, the paper provides a mathematically rigorous proof of the Thouless conductance formula. The central idea is to establish a connection between the Thouless conductance and the Landauer-Büttiker formula, which will be applied later to crystalline limit. The starting point of the paper is a property satisfied by a one-particle Hamiltonian which has no singular continuous spectrum and which has been previously published elsewhere by the authors.