Asymptotic Expansion for the Magnetoconductance Autocorrelation Function

TL;DR

This paper derives asymptotic expansions for the autocorrelation function of magnetoconductance in chaotic microstructures, analyzing its behavior for large magnetic field differences and channel numbers, and compares with semiclassical predictions.

Contribution

It provides the leading terms of the autocorrelation function's asymptotic expansion for large parameters, extending previous calculations and clarifying the function's behavior.

Findings

Asymptotic expansion for large magnetic field difference t

Asymptotic expansion for large number of channels M

Comparison with semiclassical squared Lorentzian model

Abstract

We complement a recent calculation (P.B. Gossiaux and the present authors, Ann. Phys. (N.Y.) in press) of the autocorrelation function of the conductance versus magnetic field strength for ballistic electron transport through microstructures with the shape of a classically chaotic billiard coupled to ideal leads. The function depends on the total number M of channels and the parameter t which measures the difference in magnetic field strengths. We determine the leading terms in an asymptotic expansion for large t at fixed M, and for large M at fixed t/M. We compare our results and the ones obtained in the previous paper with the squared Lorentzian suggested by semiclassical theory.