Scattering matrix ensemble for time-dependent transport through a chaotic quantum dot

TL;DR

This paper develops a random scattering matrix approach for analyzing time-dependent transport in chaotic quantum dots, providing a unified framework that reproduces known results and extends to current noise analysis.

Contribution

It calculates the first four moments of the scattering matrix distribution for time-dependent chaotic quantum dots, establishing a foundational approach for such systems.

Findings

Scattering matrix distribution is nearly Gaussian for large N.

Results unify previous Hamiltonian approach findings.

Application to current noise is discussed.

Abstract

Random matrix theory can be used to describe the transport properties of a chaotic quantum dot coupled to leads. In such a description, two approaches have been taken in the literature, considering either the Hamiltonian of the dot or its scattering matrix as the fundamental random quantity of the theory. In this paper, we calculate the first four moments of the distribution of the scattering matrix of a chaotic quantum dot with a time-dependent potential, thus establishing the foundations of a ``random scattering matrix approach'' for time-dependent scattering. We consider the limit that the number of channels $N$ coupling the quantum dot the reservoirs is large. In that limit, the scattering matrix distribution is almost Gaussian, with small non-Gaussian corrections. Our results reproduce and unify results for conductance and pumped current previously obtained in the Hamiltonian approach. We also discuss an application to current noise.