2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217738The problem of quantum transport in chaotic cavities with broken time-reversal symmetry is shown to be completely integrable in the universal limit. This observation is utilised to determine the cumulants and the distribution function of conductance for a cavity with ideal leads supporting an arbitrary number $n$ of propagating modes. Expressed in terms of solutions to the fifth Painlevé transcendent and/or the Toda lattice equation, the conductance distribution is further analysed in the large-$n$ limit that reveals long exponential tails in the otherwise Gaussian curve.4 pages; final version to appear in Physical Review LettersMesoscale and Nanoscale PhysicsHigh Energy Physics - TheoryMathematical PhysicsChaotic DynamicsExactly Solvable and Integrable Systemstext