具有刚性排斥势的碰撞粒子链中的热传导
Heat conduction in a chain of colliding particles with stiff repulsive potential
摘要：
一维台球，即质量相等的碰撞粒子链，是完全可积系统的著名例子。具有不同粒子的台球一般是不可积的，但在热力学极限下仍然表现出热传导系数（HCC）的发散。传统的台球模型意味着粒子之间的瞬时（零时间）碰撞。我们解除这个条件，考虑最近邻相互作用势为幂律势的刚性碰撞粒子链中的热输运。瞬时碰撞对应于相互作用势中无限幂的极限;对于有限幂，相互作用需要非零时间。这种模型的修改导致了深刻的物理后果--多粒子，特别是三粒子碰撞的概率变得非零。与等粒子的可积台球模型相反，修正模型在大系统尺寸下表现出热传导系数的饱和。此外，识别的散射事件与三重粒子碰撞导致简单的定义的特征平均自由程和动力学描述的热输运。这种方法允许预测HCC极限值的温度和密度依赖性。后一种依赖性是非常违反直觉的-HCC与链中的颗粒密度成反比。这两个预测都证实了直接数值模拟。
英文摘要：
One-dimensional billiard, i.e. a chain of colliding particles with equal masses, is well-known example of completely integrable system. Billiards with different particles are generically not integrable, but still exhibit divergence of a heat conduction coefficient (HCC) in thermodynamic limit. Traditional billiard models imply instantaneous (zero-time) collisions between the particles. We lift this condition and consider the heat transport in a chain of stiff colliding particles with power-law potential of the nearest-neighbor interaction. The instantaneous collisions correspond to the limit of infinite power in the interaction potential; for finite powers, the interactions take nonzero time. This modification of the model leads to profound physical consequence -- probability of multiple, in particular, triple particle collisions becomes nonzero. Contrary to the integrable billiard of equal particles, the modified model exhibits saturation of the heat conduction coefficient for large system size. Moreover, identification of scattering events with the triple particle collisions leads to simple definition of characteristic mean free path and kinetic description of the heat transport. This approach allows prediction both of temperature and density dependencies for the HCC limit values. The latter dependence is quite counterintuitive - the HCC is inversely proportional to the particle density in the chain. Both predictions are confirmed by direct numeric simulations.
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