2014年度 第2回中央大学物理学科教室談話会

講演者：Ivan Dornic 氏（CEA Saclay, France）

題　目: Brownian motion in time-dependent potentials and Painlev'e transcendents: a few examples of stochastic integrability　[pdf.file]

日　時：２０１４年６月３０日（月）１６：２０〜１７：５０

場　所：中央大学後楽園キャンパス３号館３階３３０８号教室

　（〒112-8551　文京区春日１-１３-２７；東京メトロ丸の内線,

　　南北線「後楽園駅」または都営地下鉄大江戸線, 三田線「春日駅」

　　から徒歩５分）

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