Random-matrix theory of thermal conduction in superconducting quantum dots

We calculate the probability distribution of the transmission eigenvalues T-n of Bogoliubov quasiparticles at the Fermi level in an ensemble of chaotic Andreev quantum dots. The four Altland-Zirnbauer symmetry classes (determined by the presence or absence of time-reversal and spin-rotation symmetries) give rise to four circular ensembles of scattering matrices. We determine P({T-n}) for each ensemble, characterized by two symmetry indices beta and gamma. For a single d-fold degenerate transmission channel we thus obtain the distribution P(g) proportional to g(-1+beta/2)(1-g)(gamma/2) of the thermal conductance g (in units of d pi(2)k(2)(B)T(0)/6h at low temperatures T-0). We show how this single-channel limit can be reached using a topological insulator or superconductor, without running into the problem of fermion doubling.