FLUCTUATION-DISSIPATION THEOREM
FLUCTUATION-DISSIPATION THEOREM
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DOI：
10.1088/0034-4885/29/1/306
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发表时间：
1966-01-01
影响因子：
18.1
通讯作者：
KUBO, R
中科院分区：
文献类型：
--
作者：
KUBO, R
线性响应理论给出了涨落耗散定理的一般证明，该定理指出给定系统对外部扰动的线性响应是用处于热平衡状态的系统的涨落性质来表示的。这个定理可以用一个描述涨落的随机方程来表示，它是经典布朗运动理论中常见的朗之万方程的推广。在这个广义方程中，摩擦力变得滞后或频率相关，且随机力不再是白色的。它们之间通过一个推广的奈奎斯特定理联系在一起，该定理实际上是涨落耗散定理的另一种表述。这一观点可以应用于一大类不可逆过程，包括多粒子系统中的集体模，正如Mori已经证明的那样。作为例证，简要讨论了密度响应问题。
The linear response theory has given a general proof of the fluctuation-dissipation theorem which states that the linear response of a given system to an external perturbation is expressed in terms of fluctuation properties of the system in thermal equilibrium. This theorem may be represented by a stochastic equation describing the fluctuation, which is a generalization of the familiar Langevin equation in the classical theory of Brownian motion. In this generalized equation the friction force becomes retarded or frequency-dependent and the random force is no more white. They are related to each other by a generalized Nyquist theorem which is in fact another expression of the fluctuation-dissipation theorem. This point of view can be applied to a wide class of irreversible process including collective modes in many-particle systems as has already been shown by Mori. As an illustrative example, the density response problem is briefly discussed.