Time evolution for infinitely many hard spheres
Time evolution for infinitely many hard spheres
复制标题
无限多个硬球的时间演化
DOI：
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发表时间：
1976
期刊：
影响因子：
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通讯作者：
R. Alexander
中科院分区：
文献类型：
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作者：
R. Alexander
AbstractWe construct the time evolution for infinitely many particles in ℝv interacting by the hard-sphere potential
$$Phi (x) = left{ {egin{array}{*{20}c} { + infty } \ 0 \ end{array} }
ight. egin{array}{*{20}c} {|x|< a} \ {|x| geqq a} \ end{array}$$
. Because there are abundant examples of hard-sphere configurations with more than one solution to the Newtonian equations of motion, we introduce the concept of aregular solution, in which the growth of velocities and crowding of particles at infinity are limited. We prove that (1) regular solutions exist with probability one in every equilibrium state, and (2) any configuration of the infinite system is the initial point of at most one regular solution. Equilibrium states are invariant under the time-evolution.
AbstractWe construct the time evolution for infinitely many particles in ℝv interacting by the hard-sphere potential
$$Phi (x) = left{ {egin{array}{*{20}c} { + infty } \ 0 \ end{array} }
ight. egin{array}{*{20}c} {|x|< a} \ {|x| geqq a} \ end{array}$$
. Because there are abundant examples of hard-sphere configurations with more than one solution to the Newtonian equations of motion, we introduce the concept of aregular solution, in which the growth of velocities and crowding of particles at infinity are limited. We prove that (1) regular solutions exist with probability one in every equilibrium state, and (2) any configuration of the infinite system is the initial point of at most one regular solution. Equilibrium states are invariant under the time-evolution.