arXiv 0905.14572009-05-10cond-mat.stat-mech

长程相互作用系统的统计力学注记

Notes on the Statistical Mechanics of Systems with Long-Range Interactions

David Mukamel

备注：: Notes of lectures given at a Summer School in Les Houches (France), 4-29 August 2008

摘要：

本文综述了在$d$维中具有长程成对相互作用（LRI）的系统的热力学和动力学性质，这些系统在大距离r处衰变为1/r^{d+σ}。确定了两大类这样的系统：（a）相互作用衰减缓慢的系统，称为“强”LRI，其中能量是超广泛的。这些系统的特点是不寻常的性质，如系综的不等价性，负比热，缓慢衰减的相关性和遍历性打破。（b）相互作用势衰减较快的系统，其中能量是加性的，因此导致不太显著的效应。这些相互作用影响系统的热力学行为附近的相变，长程相关性是自然存在的。长程关联经常出现在动力学涉及守恒量的系统中。驱动系统的稳态特性被认为是在上述框架内。

英文摘要：

Thermodynamic and dynamical properties of systems with long range pairwise interactions (LRI) which decay as 1/r^{d+σ} at large distances r in $d$ dimensions are reviewed in these Notes. Two broad classes of such systems are identified: (a) systems with a slow decay of the interactions, termed "strong" LRI, where the energy is super-extensive. These systems are characterized by unusual properties such as inequivalence of ensembles, negative specific heat, slow decay of correlations and ergodicity breaking. And (b) systems with faster decay of the interaction potential where the energy is additive, thus resulting in less dramatic effects. These interaction affect the thermodynamic behavior of systems near phase transitions, where long range correlations are naturally present. Long range correlations are often present in systems driven out of equilibrium when the dynamics involves conserved quantities. Steady state properties of driven systems are considered within the framework outlined above.

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摘要：

英文摘要：

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