Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-12-12
Phys. Rev. E 84, 061151 (2011)
Physics
Condensed Matter
Statistical Mechanics
5 pages, 4 figures, revised, accepted for publication on Phys. Rev. E
Scientific paper
10.1103/PhysRevE.84.061151
Long-lived quasistationary states, associated with stationary stable solutions of the Vlasov equation, are found in systems with long-range interactions. Studies of the relaxation time in a model of $N$ globally coupled particles moving on a ring, the Hamiltonian Mean Field model (HMF), have shown that it diverges as $N^\gamma$ for large $N$, with $\gamma \simeq 1.7$ for some initial conditions with homogeneously distributed particles. We propose a method for identifying exact inhomogeneous steady states in the thermodynamic limit, based on analysing models of uncoupled particles moving in an external field. For the HMF model, we show numerically that the relaxation time of these states diverges with $N$ with the exponent $\gamma \simeq 1$. The method, applicable to other models with globally coupled particles, also allows an exact evaluation of the stability limit of homogeneous steady states. In some cases it provides a good approximation for the correspondence between the initial condition and the final steady state.
Buyl Pierre de
Mukamel David
Ruffo Stefano
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