"Integrable Aspects of Universal Quantum Transport in Chaotic Cavities"

The Painleve transcendents discovered at the turn of the XX century by pure mathematical reasoning, have later made their surprising appearance -- much in the way of Wigner's "miracle of appropriateness" -- in various problems of theoretical physics. The notable examples include the two-dimensional Ising model, one-dimensional impenetrable Bose gas, corner and polynuclear growth models, one dimensional directed polymers, string theory, two dimensional quantum gravity, and spectral distributions of random matrices. In this talk, I will show how the ideas of integrability can be utilized to advocate emergence of a one-dimensional Toda Lattice and the fifth Painleve transcendent in the paradigmatic problem of conductance fluctuations in quantum chaotic cavities coupled to the external world via ballistic point contacts. Specifically, the cumulants of the Landauer conductance of a cavity with broken time-reversal symmetry are proven to be furnished by the coefficients of a Taylor-expanded Painleve V function. Further, I will argue that inclusion of tunneling effects inherent in realistic point contacts does not destroy the integrability: in this case, conductance fluctuations are captured by a two-dimensional Toda Lattice.