Signatures of Chaos in the Statistical Distribution of Conductance Peaks in Quantum Dots

Abstract

Analytical expressions for the width and conductance peak distributions of irregularly shaped quantum dots in the Coulomb blockade regime are presented in the limits of conserved and broken time-reversal symmetry. The results are obtained using random matrix theory and are valid in general for any number of non-equivalent and correlated channels, assuming that the underlying classical dynamic of the electrons in the dot is chaotic or that the dot is weakly disordered. The results are expressed in terms of the channel correlation matrix which for chaotic systems is given in closed form for both point-like contacts and extended leads. We study the dependence of the distributions on the number of channels and their correlations. The theoretical distributions are in good agreement with those computed in a dynamical model of a chaotic billiard.

19 pages, RevTex, 11 Postscript figures

References in corpus (11)

• Experimental studies of Chaos and Localization in Quantum Wavefunctions
• How Phase-Breaking Affects Quantum Transport Through Chaotic Cavities
• Quantum chaos in a deformable billiard: Applications to quantum dots
• Crossover from Orthogonal to Unitary Symmetry for Ballistic Electron Transport in Chaotic Microstructures
• Effect of a Voltage Probe on the Phase-Coherent Conductance of a Ballistic Chaotic Cavity
• Spatial Correlation in Quantum Chaotic Systems with Time-reversal Symmetry: Theory and Experiment
• The Statistical Distributions of Level Widths and Conductance Peaks in Irregularly Shaped Quantum Dots
• Comment on "Spatial Correlation in Quantum Chaotic Systems with Time-Reversal Symmetry: Theory and Experiment" by V. N. Prigodin et al [cond-mat/9504089]
• Statistical Properties of Level Widths and Conductance Peaks in a Quantum Dot
• Gaussian Fluctuations in Chaotic Eigenstates
• Magnetoconductance of ballistic chaotic quantum dots: A Brownian motion approach for the $S$-matrix

Cited by in corpus (9)

• The Statistical Theory of Quantum Dots
• Signature of Dynamical Localization in the Lifetime Distribution of Wave-Chaotic Dielectric Resonators
• Nodal portraits of quantum billiards: Domains, lines, and statistics
• The Statistics of Chaotic Tunnelling
• Scarring and the statistics of tunnelling
• Coulomb blockade conductance peak fluctuations in quantum dots and the independent particle model
• Semiclassical spatial correlations in chaotic wave functions
• Periodic orbit effects on conductance peak heights in a chaotic quantum dot
• Ballistic Quantum Dots with Disorder and Interactions: A numerical study on the Robnik-Berry billiard