Wigner time delay and related concepts -- Application to transport in coherent conductors

Abstract

The concepts of Wigner time delay and Wigner-Smith matrix allow to characterize temporal aspects of a quantum scattering process. The article reviews the statistical properties of the Wigner time delay for disordered systems; the case of disorder in 1D with a chiral symmetry is discussed and the relation with exponential functionals of the Brownian motion underlined. Another approach for the analysis of time delay statistics is the random matrix approach, from which we review few results. As a pratical illustration, we briefly outline a theory of nonlinear transport and AC transport developed by Büttiker and coworkers, where the concept of Wigner-Smith time delay matrix is a central piece allowing to describe screening properties in out-of-equilibrium coherent conductors.

39 pages, LaTeX, 15 pdf figures; contribution to a special issue in Physica E "Frontiers in quantum electronic transport - in memory of Markus Büttiker" ; v5: (version updated after publication) section 4.1.1 reorganised and completed, table of section 7.2 corrected, refs. added ; v6: new subsections 3.5, 4.2 and 5.3.2, refs added

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