Full counting statistics of chaotic cavities from classical action correlations

Abstract

We present a trajectory-based semiclassical calculation of the full counting statistics of quantum transport through chaotic cavities, in the regime of many open channels. Our method to obtain the $m$th moment of the density of transmission eigenvalues requires two correlated sets of $m$ classical trajectories, therefore generalizing previous works on conductance and shot noise. The semiclassical results agree, for all values of $m$, with the corresponding predictions from random matrix theory.

12 pages, 6 figures; v2-added some references; v3-Substantial changes in presentation (results remain the same): we have removed all reference to quantum graphs, and now treat generic chaotic cavities; v4-Largely expanded, now has 5 sections and an appendix

References in corpus (9)

• Semiclassical Foundation of Universality in Quantum Chaos
• Semiclassical Theory of Chaotic Conductors
• Ehrenfest time dependent suppression of weak localization
• Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry
• Quantum-to-classical correspondence in open chaotic systems
• Ehrenfest-time dependence of weak localization in open quantum dots
• Full counting statistics of chaotic cavities with many open channels
• Shot noise from action correlations
• Full counting statistics of a chaotic cavity with asymmetric leads