Tau-Function Theory of Quantum Chaotic Transport with beta=1,2,4

摘要: We study the cumulants and their generating functions of probability distributions conductance, shot noise Wigner delay time in ballistic quantum dots. Our approach is based on integrable theory certain matrix integrals applies to all symmetry classes beta=1,2,4 Random Matrix Theory. compute weak localization corrections mixed conductance for beta=1,4, thus proving a number conjectures Khoruzhenko et al. (Phys. Rev. B, Vol. 80 (2009), 125301). derive differential equations that characterize cumulant beta=1,2,4. Furthermore, we show function can be expressed terms Painleve' III' transcendant. This allows us properties asymptotic limit n -> infinity. Finally, any open channels, set recurrence relations are very efficient computing at orders.