Magnetoconductance of ballistic chaotic quantum dots: A Brownian motion approach for the $S$-matrix

TL;DR

This paper models the magnetoconductance of ballistic chaotic quantum dots during the transition from orthogonal to unitary symmetry using a Brownian motion approach for the S-matrix, providing exact solutions for eigenvalue correlations.

Contribution

It introduces a Brownian motion ensemble for the S-matrix to analyze magnetoconductance crossover, deriving explicit correlation functions and connecting the model to physical flux parameters.

Findings

Exact expressions for transmission eigenvalue correlations

Quantitative description of weak localization suppression

Model validity extends to larger fluxes for averages

Abstract

Using the Fokker-Planck equation describing the evolution of the transmission eigenvalues for Dyson's Brownian motion ensemble, we calculate the magnetoconductance of a ballistic chaotic dot in in the crossover regime from the orthogonal to the unitary symmetry. The correlation functions of the transmission eigenvalues are expressed in terms of quaternion determinants for arbitrary number $N$ of scattering channels. The corresponding average, variance and autocorrelation function of the magnetoconductance are given as a function of the Brownian motion time $t$. A microscopic derivation of this $S$-Brownian motion approach is discussed and $t$ is related to the applied flux. This exactly solvable random matrix model yields the right expression for the suppression of the weak localization corrections in the large $N$-limit and for small applied fluxes. An appropriate rescaling of $t$ could extend its validity to larger magnetic fluxes for the averages, but not for the correlation functions.