Petruccione Francesco, Vacchini Bassano
School of Pure and Applied Physics, Howard College, University of KwaZulu-Natal, Durban, 4041, South Africa.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Apr;71(4 Pt 2):046134. doi: 10.1103/PhysRevE.71.046134. Epub 2005 Apr 22.
A fully quantum treatment of Einstein's Brownian motion is given, stressing in particular the role played by the two original requirements of translational invariance and connection between dynamics of the Brownian particle and atomic nature of the medium. The former leads to a clearcut relationship with a generator of translation-covariant quantum-dynamical semi-groups recently characterized by Holevo, the latter to a formulation of the fluctuation-dissipation theorem in terms of the dynamic structure factor, a two-point correlation function introduced in seminal work by Van Hove, directly related to density fluctuations in the medium and therefore to its atomistic, discrete nature. A microphysical expression for the generally temperature dependent friction coefficient is given in terms of the dynamic structure factor and of the interaction potential describing the single collisions. A comparison with the Caldeira-Leggett model is drawn, especially in view of the requirement of translational invariance, further characterizing general structures of reduced dynamics arising in the presence of symmetry under translations.
本文给出了对爱因斯坦布朗运动的全量子处理，特别强调了平移不变性的两个原始要求以及布朗粒子动力学与介质原子性质之间的联系所起的作用。前者导致与最近由霍列沃表征的平移协变量子动力学半群的生成元有明确的关系，后者导致根据动态结构因子（范霍夫在开创性工作中引入的两点关联函数，与介质中的密度涨落直接相关，因此与介质的原子性、离散性质直接相关）来表述涨落耗散定理。根据动态结构因子和描述单次碰撞的相互作用势，给出了通常依赖于温度的摩擦系数的微观物理表达式。与卡尔德雷拉 - 莱格特模型进行了比较，特别是考虑到平移不变性的要求，进一步刻画了在平移对称性存在的情况下出现的约化动力学的一般结构。
