动态散射体链的可控性
Controllability for chains of dynamical scatterers
摘要：
本文考虑了一类由相同的混沌细胞组成的线性链组成的力学模型，每个混沌细胞具有两个小的侧孔，并且在其中心包含一个旋转盘。粒子在特征温度和速率下从位于链两端的随机热浴中注入。一旦在系统中，粒子在单元内自由移动，并且将与单元的外边界以及与圆盘经历弹性碰撞。它们之间不相互作用，但可以通过与圆盘的碰撞将能量从一个转移到另一个。系统的状态由粒子的位置和速度以及圆盘的角位置和角速度定义。我们表明，在这个类中的每一个模型是可控的浴，即我们证明了浴的行动可以驱动系统从任何状态到任何其他状态在有限的时间。因此，人们得到的存在，最多一个经常不变的措施，其特点是国家（平衡）。
英文摘要：
In this paper, we consider a class of mechanical models which consists of a linear chain of identical chaotic cells, each of which has two small lateral holes and contains a rotating disk at its center. Particles are injected at characteristic temperatures and rates from stochastic heat baths located at both ends of the chain. Once in the system, the particles move freely within the cells and will experience elastic collisions with the outer boundary of the cells as well as with the disks. They do not interact with each other but can transfer energy from one to another through collisions with the disks. The state of the system is defined by the positions and velocities of the particles and by the angular positions and angular velocities of the disks. We show that each model in this class is controllable with respect to the baths, i.e. we prove that the action of the baths can drive the system from any state to any other state in a finite time. As a consequence, one obtains the existence of at most one regular invariant measure characterizing its states (out of equilibrium).
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