标题： 冷迹线在热浴中的统计力学 显示英文标题

标题： Statistical mechanics of a cold tracer in a hot bath

摘要： 我们研究了零温粒子与热布朗粒子浴线性相互作用的动力学。从最一般的线性耦合浴模型出发，我们精确地消除了浴的自由度，将示踪粒子的动力学映射到广义朗之万方程，允许示踪粒子上存在任意外部势。我们将这一结果应用于确定通过弹簧连接到$N$个相同浴粒子的示踪粒子的命运，或者插入到热粒子的谐振链中的情况。在前一种“完全连接”的情况下，我们发现示踪粒子在大$N$下会进入有效平衡态，在有限$N$下进入违反FDT（详细涨落定理）的状态，而在后一种“环”模型中，示踪粒子从未满足FDT。然后，我们对于大但有限的$N$对完全连接模型进行摄动研究，展示了不可逆性的特征，如麦尔电流、非玻尔兹曼统计和正熵产生。最后，我们将研究范围缩小到示踪粒子上的谐波外部势，从而能够精确求解任意线性模型下示踪粒子和浴的动力学。我们应用这些发现表明，处于热晶格中的冷示踪粒子以长程方式抑制晶格的波动，并将这一结果推广到线性弹性场理论中。 显示英文摘要

摘要： We study the dynamics of a zero-temperature particle interacting linearly with a bath of hot Brownian particles. Starting with the most general model of a linearly-coupled bath, we eliminate the bath degrees of freedom exactly to map the tracer dynamics onto a generalized Langevin equation, allowing for an arbitrary external potential on the tracer. We apply this result to determine the fate of a tracer connected by springs to $N$ identical bath particles or inserted within a harmonic chain of hot particles. In the former "fully-connected" case, we find the tracer to transition between an effective equilibrium regime at large $N$ and an FDT-violating regime at finite $N$, while in the latter "loop" model the tracer never satisfies an FDT. We then study the fully-connected model perturbatively for large but finite $N$, demonstrating signatures of irreversibility such as ratchet currents, non-Boltzmann statistics, and positive entropy production. Finally, we specialize to harmonic external potentials on the tracer, allowing us to exactly solve the dynamics of both the tracer and the bath for an arbitrary linear model. We apply our findings to show that a cold tracer in a hot lattice suppresses the fluctuations of the lattice in a long-ranged manner, and we generalize this result to linear elastic field theories.