Integrable Theory of Quantum Transport in Chaotic Cavities

2008/06/30 by Vladimir Al. Osipov, Eugene Kanzieper · 3 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum chaos and dynamical systems #Quantum many-body systems #cond-mat.mes-hall #hep-th #math-ph #math.MP #nlin.CD #nlin.SI

paper · pdf · doi:10.1103/physrevlett.101.176804

published as Phys.Rev.Lett.101:176804,2008 · 4 pages; final version to appear in Physical Review Letters

arxiv created 2008/09/25 · openalex publication_date 2008/10/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 utilized 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 analyzed in the large-n limit that reveals long exponential tails in the otherwise Gaussian curve.

Citations

• Semiclassical prediction for shot noise in chaotic cavities
• Shot Noise in Semiclassical Chaotic Cavities
• Semiclassical theory of the Ehrenfest time dependence of quantum transport in ballistic quantum dots
• Random-matrix theory of quantum transport
• Fredholm determinants, differential equations and matrix models

Cited by

• Statistics of thermal to shot noise crossover in chaotic cavities
• Largest Schmidt eigenvalue of random pure states and conductance distribution in chaotic cavities
• Integrable Aspects of Universal Quantum Transport in Chaotic Cavities