Lecturer: Prof. Eugene Kanzieper
Affiliation: Department of Applied Mathematics,
Faculty of Sciences,
H.I.T. - Holon Institute of Technology
Abstract:
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.