科研之友
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摘要
We consider the dynamics of finite size disordered systems as defined by a master equation satisfying detailed balance. The master equation can be mapped onto a Schrodinger equation in configuration space, where the quantum Hamiltonian H has the generic form of an Anderson localization tight-binding model. The largest relaxation time t(eq) governing the convergence towards Boltzmann equilibrium is determined by the lowest non-vanishing eigenvalue E(1) = 1/t(eq) of H (the lowest eigenvalue being E(0) = 0). So the relaxation time teq can be computed without simulating the dynamics by any eigenvalue method able to compute the first excited energy E1. Here we use the 'conjugate gradient' method to determine E1 for each disordered sample and present numerical results on the statistics of the relaxation time teq over disordered samples of a given size for two models: (i) for the random walk in a self-affine potential of Hurst exponent H on a two-dimensional square of size L x L, we find the activated scaling ln t(eq)(L) similar to L(psi) with psi = H as expected; (ii) for the dynamics of the Sherrington-Kirkpatrick spin glass model of N spins, we find the growth ln t(eq)(N) similar to N(psi) with psi = 1/3 in agreement with most previous Monte Carlo measures. In addition, we find that the rescaled distribution of (ln t(eq)) decays as e(-u eta) for large u with a tail exponent of order eta similar or equal to 1.36. We give a rare-event interpretation of this value, that points towards a sample-to-sample fluctuation exponent of order psi(width) similar or equal to 0.26 for the barrier.
- 出版日期2009-12
- 单位中国地震局
