Joint statistics of quantum transport in chaotic cavities

¹ School of Mathematics, University of Bristol - University Walk, Bristol BS8 1TW, UK
² Dipartimento di Matematica, Università di Bari - I-70125 Bari, Italy
³ Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Bari - I-70126 Bari, Italy
⁴ Dipartimento di Fisica and MECENAS, Università di Bari - I-70126 Bari, Italy
⁵ King's College London, Department of Mathematics - Strand, London WC2R 2LS, UK

Received: 24 February 2015
Accepted: 29 May 2015

Abstract

We study the joint statistics of conductance G and shot noise P in chaotic cavities supporting a large number N of open electronic channels in the two attached leads. We determine the full phase diagram in the -plane, employing a Coulomb gas technique on the joint density of transmission eigenvalues, as dictated by random matrix theory. We find that in the region of typical fluctuations, conductance and shot noise are uncorrelated and jointly Gaussian, and away from it they fluctuate according to a different joint rate function in each phase of the -plane. Different functional forms of the rate function in different regions emerge as a direct consequence of third-order phase transitions in the associated Coulomb gas problem.