Thermal transport through non-ideal Andreev quantum dots

TL;DR

This paper analyzes thermal transport in non-ideal Andreev quantum dots within symmetry classes D and C, deriving joint probability density functions using random matrix theory, including a new matrix model for class C.

Contribution

It introduces a novel random matrix model for class C Andreev quantum dots and derives explicit joint probability density functions for thermal transport.

Findings

Derived joint probability density functions for classes D and C.

Introduced a new random matrix model for class C.

Provided explicit formulas for non-ideal lead coupling.

Abstract

We consider the scenario of thermal transport through two types of Andreev quantum dots which are coupled to two leads, belonging to the Class D and Class C symmetry classes. Using the random matrix description we derive the joint probability density function (j.p.d.f.) in term of Hypergeometric Function of Matrix Arguments when we consider one lead to be attached ideally and one lead non ideally. For the class C ensemble we derive a more explicit representation of the j.p.d.f. which results in a new type of random matrix model.