scholarly journals Statistical Mechanics of systems with long range interactions

2008 ◽  
Author(s):  
David Mukamel ◽  
Alessandro Campa ◽  
Andrea Giansanti ◽  
Giovanna Morigi ◽  
Francesco Sylos Labini
Keyword(s):  
Statistical Mechanics ◽  
Long Range ◽  
Long Range Interactions

scholarly journals Generalized Statistics and the Formation of a Quark-Gluon Plasma

2003 ◽  
Vol 12 (03) ◽  
pp. 395-405 ◽  
Author(s):  
A. M. Teweldeberhan ◽  
H. G. Miller ◽  
R. Tegen
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Statistical Mechanics ◽  
Long Range ◽  
Quark Gluon Plasma ◽  
Gluon Plasma ◽  
Extensive Form ◽  
Small Deviations ◽  
Long Range Interactions ◽  
Dominant Part

The aim of this paper is to investigate the effect of a non-extensive form of statistical mechanics proposed by Tsallis on the formation of a quark-gluon plasma (QGP). We suggest to account for the effects of the dominant part of the long-range interactions among the constituents in the QGP by a change in the statistics of the system in this phase, and we study the relevance of this statistics for the phase transition. The results show that small deviations (≈ 10%) from Boltzmann–Gibbs statistics in the QGP produce a noticeable change in the phase diagram, which can, in principle, be tested experimentally.

Statistical mechanics and long range interactions

2006 ◽  
Vol 7 (3-4) ◽  
pp. 414-421 ◽  
Author(s):  
Julien Barré ◽  
Freddy Bouchet
Keyword(s):  
Statistical Mechanics ◽  
Long Range ◽  
Long Range Interactions

scholarly journals Statistical mechanics and dynamics of solvable models with long-range interactions

2009 ◽  
Vol 480 (3-6) ◽  
pp. 57-159 ◽  
Author(s):  
Alessandro Campa ◽  
Thierry Dauxois ◽  
Stefano Ruffo
Keyword(s):  
Statistical Mechanics ◽  
Long Range ◽  
Solvable Models ◽  
Long Range Interactions

scholarly journals The world of long-range interactions: A bird’s eye view

2017 ◽  
Vol 32 (09) ◽  
pp. 1741018 ◽  
Author(s):  
Shamik Gupta ◽  
Stefano Ruffo
Keyword(s):  
Statistical Mechanics ◽  
Long Range ◽  
Degrees Of Freedom ◽  
Large Deviation ◽  
Mean Field ◽  
Coulomb Systems ◽  
Two Dimensions ◽  
Slow Relaxation ◽  
Long Range Interactions ◽  
Non Equilibrium

In recent years, studies of long-range interacting (LRI) systems have taken center stage in the arena of statistical mechanics and dynamical system studies, due to new theoretical developments involving tools from as diverse a field as kinetic theory, non-equilibrium statistical mechanics, and large deviation theory, but also due to new and exciting experimental realizations of LRI systems. In the first, introductory, Section 1, we discuss the general features of long-range interactions, emphasizing in particular the main physical phenomenon of non-additivity, which leads to a plethora of distinct effects, both thermodynamic and dynamic, that are not observed with short-range interactions: Ensemble inequivalence, slow relaxation, broken ergodicity. In Section 2, we discuss several physical systems with long-range interactions: mean-field spin systems, self-gravitating systems, Euler equations in two dimensions, Coulomb systems, one-component electron plasma, dipolar systems, free-electron lasers. In Section 3, we discuss the general scenario of dynamical evolution of generic LRI systems. In Section 4, we discuss an illustrative example of LRI systems, the Kardar–Nagel spin system, which involves discrete degrees of freedom, while in Section 5, we discuss a paradigmatic example involving continuous degrees of freedom, the so-called Hamiltonian mean-field (HMF) model. For the former, we demonstrate the effects of ensemble inequivalence and slow relaxation, while for the HMF model, we emphasize in particular the occurrence of the so-called quasistationary states (QSSs) during relaxation towards the Boltzmann–Gibbs equilibrium state. The QSSs are non-equilibrium states with lifetimes that diverge with the system size, so that in the thermodynamic limit, the systems remain trapped in the QSSs, thereby making the latter the effective stationary states. In Section 5, we also discuss an experimental system involving atoms trapped in optical cavities, which may be modelled by the HMF system. In Section 6, we address the issue of ubiquity of the quasistationary behavior by considering a variety of models and dynamics, discussing in each case the conditions to observe QSSs. In Section 7, we investigate the issue of what happens when a long-range system is driven out of thermal equilibrium. Conclusions are drawn in Section 8.

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