恒温动力学模型的混沌传播
Propagation of Chaos for a Thermostated Kinetic Model
摘要：
我们考虑一个在d维环面上运动的N个点粒子系统。每个粒子都受到均匀场E和随机速度守恒碰撞的影响。这个模型是Drude-Lorentz模型的一个变体。为了避免被外场加热，粒子还与保持系统总动能恒定的高斯恒温器相互作用。恒温器诱导粒子之间的平均场类型的相互作用。在这里，我们证明，从产品措施，在大N限制，一个粒子的速度分布满足自洽的Vlasov-Boltzmann方程。这是一个后果的“传播的混乱”，我们也证明了这个模型。
英文摘要：
We consider a system of N point particles moving on a d-dimensional torus. Each particle is subject to a uniform field E and random speed conserving collisions. This model is a variant of the Drude-Lorentz model of electrical conduction. In order to avoid heating by the external field, the particles also interact with a Gaussian thermostat which keeps the total kinetic energy of the system constant. The thermostat induces a mean-field type of interaction between the particles. Here we prove that, starting from a product measure, in the large N limit, the one particle velocity distribution satisfies a self consistent Vlasov-Boltzmann equation.. This is a consequence of "propagation of chaos", which we also prove for this model.
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