University of Sussex
Browse

File(s) not publicly available

Tau-function theory of chaotic quantum transport with ß = 1, 2, 4

journal contribution
posted on 2023-06-20, 14:17 authored by F Mezzadri, Nicholas SimmNicholas Simm
We study the cumulants and their generating functions of the probability distributions of the conductance, shot noise and Wigner delay time in ballistic quantum dots. Our approach is based on the integrable theory of certain matrix integrals and applies to all the symmetry classes ß?{1,2,4} of Random Matrix Theory. We compute the weak localization corrections to the mixed cumulants of the conductance and shot noise for ß = 1, 4, thus proving a number of conjectures of Khoruzhenko et al. (in Phys Rev B 80:(12)125301, 2009). We derive differential equations that characterize the cumulant generating functions for all ß?{1,2,4}. Furthermore, when ß = 2 we show that the cumulant generating function of the Wigner delay time can be expressed in terms of the Painlevé III' transcendant. This allows us to study properties of the cumulants of the Wigner delay time in the asymptotic limit n?8. Finally, for all the symmetry classes and for any number of open channels, we derive a set of recurrence relations that are very efficient for computing cumulants at all orders.

History

Publication status

  • Published

File Version

  • Published version

Journal

Communications in Mathematical Physics

ISSN

0010-3616

Publisher

Springer Verlag

Issue

2

Volume

324

Page range

465-513

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications
  • Mathematical Physics Group Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2018-05-17

First Compliant Deposit (FCD) Date

2018-05-17

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC