Integrable theory of quantum transport in chaotic cavities

Abstract

The problem of quantum transport in chaotic cavities with broken time-reversal symmetry is shown to be completely integrable in the universal limit. This observation is utilised to determine the cumulants and the distribution function of conductance for a cavity with ideal leads supporting an arbitrary number $n$ of propagating modes. Expressed in terms of solutions to the fifth Painlevé transcendent and/or the Toda lattice equation, the conductance distribution is further analysed in the large-$n$ limit that reveals long exponential tails in the otherwise Gaussian curve.

4 pages; final version to appear in Physical Review Letters

References in corpus (7)

• Semiclassical Theory of Chaotic Conductors
• Semiclassical Approach to Chaotic Quantum Transport
• Nonlinear statistics of quantum transport in chaotic cavities
• Ehrenfest time dependent suppression of weak localization
• Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry
• Are Bosonic Replicas Faulty?
• Semiclassical theory of the Ehrenfest-time dependence of quantum transport

Cited by in corpus (10)

• Distributions of Conductance and Shot Noise and Associated Phase Transitions
• Systematic approach to statistics of conductance and shot-noise in chaotic cavities
• Efficient semiclassical approach for time delays
• Statistics of thermal to shot noise crossover in chaotic cavities
• Random matrix theory of quantum transport in chaotic cavities with non-ideal leads
• Conductance Distributions in Chaotic Mesoscopic Cavities
• Joint statistics of quantum transport in chaotic cavities
• Correlations of RMT Characteristic Polynomials and Integrability: Hermitean Matrices
• Largest Schmidt eigenvalue of entangled random pure states and conductance distribution in chaotic cavities
• Integrable Aspects of Universal Quantum Transport in Chaotic Cavities