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摘要翻译：
质点的摩擦系数可以依赖于它的位置，就像当质点靠近壁时一样。我们用一个带有乘性噪声的一般朗之万方程来表述具有这种状态相关摩擦系数的粒子的动力学，该方程的计算需要引入特定的规则。两个常见的惯例，Ito和Stratonovich提供了评价噪声的替代规则，但其他惯例是可能的。我们证明了粒子的分布函数在很长时间内接近玻尔兹曼分布的要求，表明必须在朗之万方程中加入漂移项。这个漂移项与扩散系数乘以一个因子的导数成正比，这个因子取决于用于定义乘性噪声的约定。我们在一些具有空间变化扩散系数的例子中探索了这一结果的后果。我们还导出了任意解释噪声的路径积分表示，并将其用于简单系统中相关的微扰研究。
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英文标题：
《State-dependent diffusion: thermodynamic consistency and its path
integral formulation》
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作者：
A.W.C. Lau, T.C. Lubensky
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Soft Condensed Matter 软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alternative rules for evaluation of the noise, but other conventions are possible. We show the requirement that a particle's distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation. This drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise. We explore the consequences of this result in a number examples with spatially varying diffusion coefficients. We also derive path integral representations for arbitrary interpretation of the noise, and use it in a perturbative study of correlations in a simple system.
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PDF链接：
https://arxiv.org/pdf/707.2234
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