Nonequilibrium dynamics of a fast oscillator coupled to Glauber spins

Details Nonequilibrium dynamics of a fast oscillator coupled to Glauber spins Nonequilibrium dynamics of a fast oscillator coupled to Glauber spins

2010-07-11

arxiv.org/abs/1007.1806v1

J. Stat. Mech. (2010) P09019

Physics

Condensed Matter

Statistical Mechanics

30 pages, 9 figures

Scientific paper

10.1088/1742-5468/2010/09/P09019

A fast harmonic oscillator is linearly coupled with a system of Ising spins that are in contact with a thermal bath, and evolve under a slow Glauber dynamics at dimensionless temperature $\theta$. The spins have a coupling constant proportional to the oscillator position. The oscillator-spin interaction produces a second order phase transition at $\theta=1$ with the oscillator position as its order parameter: the equilibrium position is zero for $\theta>1$ and non-zero for $\theta< 1$. For $\theta<1$, the dynamics of this system is quite different from relaxation to equilibrium. For most initial conditions, the oscillator position performs modulated oscillations about one of the stable equilibrium positions with a long relaxation time. For random initial conditions and a sufficiently large spin system, the unstable zero position of the oscillator is stabilized after a relaxation time proportional to $\theta$. If the spin system is smaller, the situation is the same until the oscillator position is close to zero, then it crosses over to a neighborhood of a stable equilibrium position about which keeps oscillating for an exponentially long relaxation time. These results of stochastic simulations are predicted by modulation equations obtained from a multiple scale analysis of macroscopic equations.

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