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

TL;DR

This paper reviews the statistical properties of Wigner time delay in quantum scattering, especially in disordered systems, and discusses its application to transport phenomena in coherent conductors, integrating random matrix theory and nonlinear transport models.

Contribution

It provides a comprehensive review of Wigner time delay concepts, including new insights into disordered systems and their relation to transport in coherent conductors.

Findings

Statistical properties of Wigner time delay in disordered systems analyzed.

Relation between Wigner time delay and exponential functionals of Brownian motion established.

Application of Wigner-Smith matrix to nonlinear and AC transport in coherent conductors discussed.

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 B\"uttiker 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.