第２回　物理学教室談話会

内容: 題目：　Brownian motion in time-dependent potentials and Painlev\'e transcendents: a few examples of stochastic integrability

概要：
We show how the determination of the distribution of a certain imaginary
exponential of Brownian motion --- a stylized model of phase-noise --- can
be recast in terms of the first-passage properties of a particle diffusing in
an explicitely time-dependent potential. We uncover that the latter involves
the particular Sine-Gordon Painlev\'e III transcendent. This representation
parallels a characterization of the celebrated Tracy-Widom distribution,
and vindicates a recently proposed general scheme linking non-stationary
Schr\"odinger (or Fokker-Planck) equations to Painlev\'e equations.
Another salient example of this correspondence is provided by the critical
scaling correlations of the two-dimensional Ising model, which are
associated to the Sinh-Gordon Painlev\'e III.

問い合わせ先：中大・理工・物理　香取眞理
e-mail: katori@phys.chuo-u.ac.jp
tel: (03) 3817-1776