Quantum Brownian motion in a general environment. II. Nonlinear coupling and perturbative approach.
Quantum Brownian motion in a general environment. II. Nonlinear coupling and perturbative approach.
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DOI：
10.1103/physrevd.47.1576
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发表时间：
1993-02
期刊：
影响因子：
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通讯作者：
B. Hu;Juan Pablo Paz;Yuhong Zhang
中科院分区：
文献类型：
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作者：
B. Hu;Juan Pablo Paz;Yuhong Zhang
我们发展了一个微扰方案来处理一个量子布朗粒子(坐标[italx])与振子浴(坐标[italq][sub[italn]])的非线性耦合的动力学问题，其中的相互作用作用形式为[lambda][italf]([italx])[italq][sub[italn]][sup[italk]]。我们给出了[italk]=2，3，4阶的影响泛函，导出了局部耗散和白噪声的特例以及非局部耗散和有色噪声的一般情况下的主方程.我们证明了k阶耦合的L阶噪声核与其相应的耗散核之间存在广义的涨落-耗散关系。
We develop a perturbation scheme to treat the dynamics of a quantum Brownian particle (coordinate [ital x]) coupled nonlinearly to a bath of oscillators (coordinates [ital q][sub [ital n]]) with an interaction action in the form [lambda][ital f]([ital x])[ital q][sub [ital n]][sup [ital k]]. We derive the influence functionals for the [ital k]=2,3,4 cases to order [lambda][sup 2] and derive the master equations for the special cases of local dissipation and white noise, as well as the general cases of nonlocal dissipation and colored noise for [ital f]([ital x])=[ital x] and [ital x][sup 2]. We show that a generalized fluctuation-dissipation relation exists between the [ital l]th-order noise kernels of the [ital k]th-order coupling and their corresponding dissipation kernels.