玻尔兹曼重量的有效性和失效
Validity and Failure of the Boltzmann Weight
摘要：
利用分子动力学方法，在$d$维晶格（$d=1,2,$和3）上研究了具有长程相互作用的经典惯性XY模型的动力学和热统计性质.旋光分子间的相互作用随距离$r_{ij}$衰减，类似于~ $1/r_{ij}^α$（$α\geq 0$），其中$α\to\infty$和$α=0$分别对应于最近邻相互作用和无限程相互作用.我们验证了动量概率分布是麦克斯韦在短距离政权，而$q$ -高斯出现在长距离政权。此外，在后一种情况下，个体能量概率分布的特征在于长尾，对应于$q$指数函数。目前的调查强烈表明，在长程制度，中央属性属于玻尔兹曼-吉布斯统计力学的范围内，通过比率$α/d$依赖于$d$和$α$。
英文摘要：
The dynamics and thermostatistics of a classical inertial XY model, characterized by long-range interactions, are investigated on $d$-dimensional lattices ($d=1,2,$ and 3), through molecular dynamics. The interactions between rotators decay with the distance $r_{ij}$ like~$1/r_{ij}^α$ ($α\geq 0$), where $α\to\infty$ and $α=0$ respectively correspond to the nearest-neighbor and infinite-range interactions. We verify that the momenta probability distributions are Maxwellians in the short-range regime, whereas $q$-Gaussians emerge in the long-range regime. Moreover, in this latter regime, the individual energy probability distributions are characterized by long tails, corresponding to $q$-exponential functions. The present investigation strongly indicates that, in the long-range regime, central properties fall out of the scope of Boltzmann-Gibbs statistical mechanics, depending on $d$ and $α$ through the ratio $α/d$.
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