We present a simple and systematic procedure to determine the effective dynamics of a Brownian particle coupled to a rapidly fluctuating correlated medium, modeled as a scalar Gaussian field, under spatial confinement. The method allows us, in particular, to address the case in which the fluctuations of the medium are suppressed in the vicinity of the particle, as described by a quadratic coupling in the underlying Hamiltonian. As a consequence of the confinement of the correlated medium, the resulting effective Fokker-Planck equation features spatially dependent drift and diffusion coefficients. We apply our method to simplified fluid models of binary mixtures and microemulsions near criticality containing a colloidal particle, and we analyze the corrections to the stationary distribution of the particle position and the diffusion coefficient.

中文翻译：

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受限相关介质中的示踪粒子：绝热消除方法

我们提出了一个简单而系统的程序来确定在空间限制下耦合到快速波动的相关介质的布朗粒子的有效动力学，该介质被建模为标量高斯场。该方法特别允许我们解决介质波动在粒子附近被抑制的情况，如底层哈密顿量中的二次耦合所描述的那样。由于相关介质的限制，得到的有效 Fokker-Planck 方程具有空间相关的漂移和扩散系数。我们将我们的方法应用于包含胶体颗粒的接近临界的二元混合物和微乳液的简化流体模型，并分析了对颗粒位置和扩散系数的平稳分布的校正。