A semiclassical matrix model for quantum chaotic transport

Abstract

We propose a matrix model which embodies the semiclassical approach to the problem of quantum transport in chaotic systems. Specifically, a matrix integral is presented whose perturbative expansion satisfies precisely the semiclassical diagrammatic rules for the calculation of general counting statistics. Evaluating it exactly, we show that it agrees with corresponding predictions from random matrix theory. This uncovers the algebraic structure behind the equivalence between these two approaches, and opens the way for further semiclassical calculations.

8 pages, 2 figures

References in corpus (10)

• Periodic-Orbit Theory of Universality in Quantum Chaos
• Semiclassical Theory of Chaotic Conductors
• Semiclassical Approach to Chaotic Quantum Transport
• Ehrenfest time dependent suppression of weak localization
• Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry
• Ehrenfest-time dependence of weak localization in open quantum dots
• Full counting statistics of chaotic cavities from classical action correlations
• Universality in chaotic quantum transport: The concordance between random matrix and semiclassical theories
• Shot noise from action correlations
• Semiclassical approach to universality in quantum chaotic transport

Cited by in corpus (15)

• Semiclassical roots of universality in many-body quantum chaos
• Efficient semiclassical approach for time delays
• Combinatorial theory of the semiclassical evaluation of transport moments I: Equivalence with the random matrix approach
• Integer moments of complex Wishart matrices and Hurwitz numbers
• Statistics of time delay and scattering correlation functions in chaotic systems II. Semiclassical Approximation
• Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions
• Energy-dependent correlations in the $S$-matrix of chaotic systems
• Semiclassical treatment of quantum chaotic transport with a tunnel barrier
• Expansion of polynomial Lie group integrals in terms of certain maps on surfaces, and factorizations of permutations
• Semiclassical approach to $S$ matrix energy correlations and time delay in chaotic systems
• Semiclassical calculation of time delay statistics in chaotic quantum scattering
• Full perturbative calculation of spectral correlation functions for chaotic systems in the unitary symmetry class
• Exponentially small quantum correction to conductance
• Quantum transport in chaotic cavities with tunnel barriers
• Electronic transport in three-terminal chaotic systems with a tunnel barrier