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arXiv · 0712.1752

Out of equilibrium phase transitions in mean field Hamiltonian dynamics

Pierre-Henri Chavanis·Giovanni De Ninno·Duccio Fanelli·Stefano Ruffo
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Abstract

Systems with long-range interactions display a short-time relaxation towards Quasi-Stationary States (QSSs), whose lifetime increases with system size. With reference to the Hamiltonian Mean Field (HMF) model, we here review Lynden-Bell's theory of ``violent relaxation''. The latter results in a maximum entropy scheme for a water-bag initial profile which predicts the presence of out-of-equilibrium phase transitions} separating homogeneous (zero magnetization) from inhomogeneous (non-zero magnetization) QSSs. Two different parametric representations of the initial condition are analyzed and the features of the phase diagram are discussed. In both representations we find a second order and a first order line of phase transitions that merge at a tricritical point. Particular attention is payed to the condition of existence and stability of the homogenous phase.

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Pierre-Henri Chavanis, Giovanni De Ninno, Duccio Fanelli, Stefano Ruffo. 2007-12-11. Out of equilibrium phase transitions in mean field Hamiltonian dynamics. https://doi.org/10.1142/9789812818805_0001

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