Das Debankur, Vink Richard, Krüger Matthias
Institut für Theoretische Physik, Georg-August-Universität Göttingen, 37073 Göttingen, Germany.
Institut für Materialphysik, Georg-August-Universität Göttingen, 37073 Göttingen, Germany.
J Phys Condens Matter. 2024 Feb 29;36(21). doi: 10.1088/1361-648X/ad2b1d.
We analytically study friction and dissipation of a driven bead in a 1D harmonic chain, and analyze the role of internal damping mechanism as well as chain length. Specifically, we investigate Dissipative Particle Dynamics and Langevin Dynamics, as paradigmatic examples that do and do not display translational symmetry, with distinct results: For identical parameters, the friction forces can differ by many orders of magnitude. For slow driving, a Goldstone mode traverses the entire system, resulting in friction of the driven bead that grows arbitrarily large (Langevin) or gets arbitrarily small (Dissipative Particle Dynamics) with system size. For a long chain, the friction for DPD is shown to be bound, while it shows a singularity (i.e. can be arbitrarily large) for Langevin damping. For long underdamped chains, a radiation mode is recovered in either case, with friction independent of damping mechanism. For medium length chains, the chain shows the expected resonant behavior. At the resonance, friction is non-analytic in damping parameter, depending on it as. Generally, no zero frequency bulk friction coefficient can be determined, as the limits of small frequency and infinite chain length do not commute, and we discuss the regimes where 'simple' macroscopic friction occurs.
我们对一维谐波链中受驱动珠子的摩擦和耗散进行了分析研究，并分析了内部阻尼机制以及链长的作用。具体而言，我们研究了耗散粒子动力学和朗之万动力学，它们分别是不显示和平移对称性的典型例子，结果截然不同：对于相同的参数，摩擦力可能相差多个数量级。对于缓慢驱动，一个戈德斯通模贯穿整个系统，导致受驱动珠子的摩擦力随系统尺寸增大而任意增大（朗之万动力学）或任意减小（耗散粒子动力学）。对于长链，耗散粒子动力学的摩擦力是有界的，而朗之万阻尼则显示出奇异性（即可以任意大）。对于长的欠阻尼链，在任何一种情况下都会恢复辐射模，摩擦力与阻尼机制无关。对于中等长度的链，链表现出预期的共振行为。在共振时，摩擦力在阻尼参数上是非解析的，其依赖关系为 。一般来说，无法确定零频率的体摩擦系数，因为小频率极限和无限链长极限不可交换，并且我们讨论了出现“简单”宏观摩擦的区域。
