论文标题
经过高密度边界条件的连续体中的经典颗粒
Classical particles in the continuum subjected to high density boundary conditions
论文作者
论文摘要
我们考虑一个限制在有限区域中的经典颗粒系统的连续系统$ \ mathbb {r}^d $通过在存在非自由边界条件的情况下通过超级且脾气暴躁的对潜力进行交互。我们证明，系统压力的热力学极限在任何固定的反温度$β$和任何固定的逃逸性$λ$都不取决于$λ$以外的粒子产生的边界条件，其密度可能会以距离距离距离的距离的距离增加，这取决于速度的速度差异很大，这是对越快的距离的较大差异。特别是，如果这对潜在的$ v（x-y）$是Lennard-Jones类型的，即它以$ c/\ | x-y \ | x-y \ | |^{d+p} $（带有$ p> 0 $）（$ \ | x-y \ | $是$ x $和$ y $之间的euclidean距离，则在$ x $和$ y的限制之间存在限制的情况，随着距离的距离$ r $的距离，分布量为$ρ（1+ r^q）$，其中$ρ$是系统的任何正常数（甚至超过密度$ρ_0（β，λ）$的密度$ρ_0（β，λ）$，通过自由边界条件进行评估）和$ q \ le Q \ le {1 \ le {1 \ fory 2} \ min \ min \ min \ min \ min \ \ f \^$ {1，p \} $。
We consider a continuous system of classical particles confined in a finite region $Λ$ of $\mathbb{R}^d$ interacting through a superstable and tempered pair potential in presence of non free boundary conditions. We prove that the thermodynamic limit of the pressure of the system at any fixed inverse temperature $β$ and any fixed fugacity $λ$ does not depend on boundary conditions produced by particles outside $Λ$ whose density may increase sub-linearly with the distance from the origin at a rate which depends on how fast the pair potential decays at large distances. In particular, if the pair potential $v(x-y)$ is of Lennard-Jones type, i.e. it decays as $C/\|x-y\|^{d+p}$ (with $p>0$) where $\|x-y\|$ is the Euclidean distance between $x$ and $y$, then the existence of the thermodynamic limit of the pressure is guaranteed in presence of boundary conditions generated by external particles which may be distributed with a density increasing with the distance $r$ from the origin as $ρ(1+ r^q)$, where $ρ$ is any positive constant (even arbitrarily larger than the density $ρ_0(β,λ)$ of the system evaluated with free boundary conditions) and $q\le {1\over 2}\min\{1, p\}$.
