量子準位ダイナミックスの確率過程理論(筑波大学開学20周年記念第2回『非平衡系の統計物理-現状と展望』シンポジウム,研究会報告)

Abstract

We are motivated by the recent theoretical analyses of Zakrzewski and Delande (Z-D) on curvature distribution of chaotic quantum levels to construct a unified theory which is capable of predicting the nonuniversal feature of the distribution P(K) : while P(K) for large values of the curvature K of an irregular quantum level, embedded in a level diagram moving as a parameter λ (i.e. K = d^2E/dλ^2), has the universal power law P(K)～K^<-(v+2)>, P(K) for K &ap; 0 is different for different individual systems with variety of sharpened peaks, as we have demonstrated previously. We utilize the stochastic frequency modulation theory of Kubo who formulated the motional narrowing of resonant line shape in the context of Gaussian stochastic processes. Thus, a satisfactory scheme of interpolating the two limiting forms of P(K) proposed by Z-D has been achieved.