第１０７回「非線形・統計力学とその周辺」セミナーのご案内

日時：平成２２年２月１８日（木）１５時から

場所：京都大学工学部総合校舎２階２１３講義室（吉田キャンパス）

講演者：
宗像 豊哲 (京都大学 情報学研究科 数理工学専攻)

講演題目：

森理論再訪：‘力学的’なランダム力とセルフコンシステントな構造

講演要旨：

Projection operator method, due to Zwanzig and Mori, has been playing important roles in equilibrium and nonequilibrium statistical mechanics. Especially the generalized Langevin equation (GLE,Mori, 1965), not only gave microscopic justification of stochastic approaches to dynamics in many-body systems but also presented systemtic methodologies to formulate irreversible processes and transport coefficients. In my talk, I first review 'stochastic' Brownian motion, with introduction of Langevin eq., fluctuation -dissipation theorem. Then I turn to GLE, which is derived anew based on 'natural' trajectories of Hamiltonian dynamics in a phase space. Next I point out some new structural aspects of GLE, such as linear functional relation and a self-consistent structure(SCS). I conclude my talk with some examples, in which I could calculate the 'mechanical' random force and its correlation function(kernel). It is noted that such calculations are made possible only through the SCS.