Ballistic Transport Through Chaotic Cavities: Can Parametric Correlations and the Weak Localization Peak be Described by a Brownian Motion Model?

TL;DR

This paper introduces a Brownian motion model on the S-matrix manifold to describe conductance correlations and weak localization in chaotic cavities, predicting specific behaviors of these phenomena that align with experiments under certain conditions.

Contribution

The paper develops a novel Brownian motion model on the S-matrix manifold to analytically describe parametric correlations and weak localization peaks in ballistic transport.

Findings

Correlation function shape matches weak localization peak

Functions behave as 1 - O(B^2), not linearly

Width scales with square root of number of channels

Abstract

A Brownian motion model is devised on the manifold of S-matrices, and applied to the calculation of conductance-conductance correlations and of the weak localization peak. The model predicts that (i) the correlation function in $B$ has the same shape and width as the weak localization peak; (ii) the functions behave as $\propto 1-{\cal O}(B^2)$, thus excluding a linear line shape; and (iii) their width increases as the square root of the number of channels in the leads. Some of these predictions agree with experiment and with other calculations only in the limit of small $B$ and a large number of channels.