Non-equilibrium dynamics of one-dimensional infinite particle systems with a hard-core interaction
Non-equilibrium dynamics of one-dimensional infinite particle systems with a hard-core interaction
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具有核心相互作用的一维无限粒子系统的非平衡动力学
DOI：
10.1007/bf01614551
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发表时间：
1977
影响因子：
2.4
通讯作者：
J. Fritz
中科院分区：
文献类型：
--
作者：
R. Dobrushin;J. Fritz
考虑一维粒子相互作用的无限大牛顿运动方程系统，其作用势为有限范围的硬核奇点势，其作用势为硬核间距离的倒数。证明了有限比能的初始构型极限解的存在性，并构造了运动半群，如果无穷大附近的能量涨落仅随离原点距离的小次方增加.在这种情况下，还证明了解的唯一性，并且解是初始数据的弱连续函数。允许的一组初始配置进行了广泛的一类概率措施，包括吉布斯领域与不同的潜力。在没有硬核的情况下，极限解构造的初始配置与对数级的能量和密度波动。
An infinite system of Newton's equation of motion is considered for one-dimensional particles interacting by a finite-range hard-core potential of singularity like an inverse power of distance between the hard cores. Existence of limiting solutions is proved for initial configurations of finite specific energy and the semigroup of motion is constructed if energy fluctuations near infinity increase only as a small power of distance from the origin. In this case uniqueness of solutions is also proved and the solution is a weakly continuous function of initial data. The allowed set of initial configurations carries a wide class of probability measures including Gibbsian fields with different potentials. In the absence of hard cores limiting solutions are constructed for initial configurations with a logarithmic order of energy and density fluctuations.