摩擦力的几种哈密顿模型II
Some Hamiltonian Models of Friction II
摘要：
在本文中，我们考虑了一个非常重的示踪粒子在一个非常密集的，非相互作用玻色气体介质中的运动。我们证明，在一定的平均场的限制，示踪粒子将减速，并在介质中的某个地方休息。摩擦是由无隙模式的切伦科夫辐射发射到气体中引起的。在数学上，系统的半线性积分-微分方程，介绍了在[FSSG 10]，描述了一个示踪剂粒子在色散介质中进行了研究，并证明了衰减性能的解决方案。这项工作是[FGS 10]的扩展;它是一个扩展，因为没有假设示踪粒子和介质之间的相互作用的弱耦合限制。使用的技术方法是分散估计和收缩原则。
英文摘要：
In the present paper we consider the motion of a very heavy tracer particle in a medium of a very dense, non-interacting Bose gas. We prove that, in a certain mean-field limit, the tracer particle will be decelerated and come to rest somewhere in the medium. Friction is caused by emission of Cerenkov radiation of gapless modes into the gas. Mathematically, a system of semilinear integro-differential equations, introduced in [FSSG10], describing a tracer particle in a dispersive medium is investigated, and decay properties of the solution are proven. This work is an extension of [FGS10]; it is an extension because no weak coupling limit for the interaction between tracer particle and medium is assumed. The technical methods used are dispersive estimates and a contraction principle.
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