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Landauer-Büttiker and Thouless conductance. (English) Zbl 1323.82026
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.

82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
82C70 Transport processes in time-dependent statistical mechanics
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