Dynamics of hard rods with initial domain wall state
Dynamics of hard rods with initial domain wall state
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DOI：
10.1088/1742-5468/aa7abf
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发表时间：
2017-03
期刊：
影响因子：
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通讯作者：
B. Doyon;H. Spohn
中科院分区：
文献类型：
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作者：
B. Doyon;H. Spohn
受多体量子系统非平衡动力学最新研究结果的启发，我们研究了具有初始畴壁条件的一维经典硬棒问题。硬棒是一个可积系统，从某种意义上说，对于每个速度，粒子的密度是局部守恒的。 Boldrighini等人(1983 J. Stat. Phys. 31 577)证明，在流体动力学时空尺度上，硬棒流体满足包含所有守恒定律的欧拉型方程。我们在线提供这些方程的通解，初始条件是左半部分和右半部分渐近地处于不同状态。该解决方案被解释为由一系列接触不连续性组成，每个接触不连续性对应一个速度。这是最近在量子可积系统中解决的传输问题的经典对应。我们还讨论了纳维-斯托克斯（粘性）修正，并研究了它对接触不连续性扩大和熵产生的影响。
Inspired by recent results on the non-equilibrium dynamics of many-body quantum systems, we study the classical hard rod problem in one dimension with initial domain wall condition. Hard rods are an integrable system, in the sense that for each velocity the density of particles is locally conserved. It was proven by Boldrighini et al (1983 J. Stat. Phys. 31 577) that on the hydrodynamic space-time scale, the fluid of hard rods satisfies Euler-type equations which comprise all conservation laws. We provide the general solution to these equations on the line, with an initial condition where the left and right halves are, asymptotically, in different states. The solution is interpreted as being composed of a continuum of contact discontinuities, one for each velocity. This is a classical counterpart of the transport problem solved recently in quantum integrable systems. We also discuss the Navier–Stokes (viscous) corrections, and study its effect on the broadening of the contact discontinuity and on entropy production.