Magnetoconductance Autocorrelation Function for Few--Channel Chaotic Microstructures

Abstract

Using the Landauer formula and a random matrix model, we investigate the autocorrelation function of the conductance versus magnetic field strength for ballistic electron transport through few-channel microstructures with the shape of a classically chaotic billiard coupled to ideal leads. This function depends on the total number M of channels and the parameter t which measures the difference in magnetic field strengths. Using the supersymmetry technique, we calculate for any value of M the leading terms of the asymptotic expansion for small t. We pay particular attention to the evaluation of the boundary terms. For small values of M, we supplement this analytical study by a numerical simulation. We compare our results with the squared Lorentzian suggested by semiclassical theory and valid for large M. For small M, we present evidence for non--analytic behavior of the autocorrelation function at t = 0.

40 pages, 4 figures, submitted to Annals of Physics (NY)

References in corpus (7)

• Mesoscopic Transport Through Ballistic Cavities: A Random S-Matrix Theory Approach
• Weak-Localization in Chaotic Versus Non-Chaotic Cavities: A Striking Difference in the Line Shape
• Crossover from Orthogonal to Unitary Symmetry for Ballistic Electron Transport in Chaotic Microstructures
• Single-particle Green's functions of the Calogero-Sutherland model at couplings λ= 1/2, 1, and 2
• Magnetoconductance of ballistic chaotic quantum dots: A Brownian motion approach for the $S$-matrix
• Crossover of magnetoconductance autocorrelation for a ballistic chaotic quantum dot
• Ballistic Transport Through Chaotic Cavities: Can Parametric Correlations and the Weak Localization Peak be Described by a Brownian Motion Model?

Cited by in corpus (8)

• The Statistical Theory of Quantum Dots
• Statistical properties of the spectrum of the QCD Dirac operator at low energy
• Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
• Microscopic Spectrum of the QCD Dirac Operator in Three Dimensions
• Variance of transmitted power in multichannel dissipative ergodic structures invariant under time reversal
• Conductance fluctuations and weak localization in chaotic quantum dots
• Asymptotic Expansion for the Magnetoconductance Autocorrelation Function
• Ergodicity of Random-Matrix Theories: The Unitary Case