Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2008-01-25
Physics
Condensed Matter
Statistical Mechanics
10 pages
Scientific paper
We study the long-time behavior of the probability density Q_t of the first exit time from a bounded interval [-L,L] for a stochastic non-Markovian process h(t) describing fluctuations at a given point of a two-dimensional, infinite in both directions Gaussian interface. We show that Q_t decays when t \to \infty as a power-law $^{-1 - \alpha}, where \alpha is non-universal and proportional to the ratio of the thermal energy and the elastic energy of a fluctuation of size L. The fact that \alpha appears to be dependent on L, which is rather unusual, implies that the number of existing moments of Q_t depends on the size of the window [-L,L]. A moment of an arbitrary order n, as a function of L, exists for sufficiently small L, diverges when L approaches a certain threshold value L_n, and does not exist for L > L_n. For L > L_1, the probability density Q_t is normalizable but does not have moments.
No associations
LandOfFree
First-exit-time probability density tails for a local height of a non-equilibrium Gaussian interface does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with First-exit-time probability density tails for a local height of a non-equilibrium Gaussian interface, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and First-exit-time probability density tails for a local height of a non-equilibrium Gaussian interface will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-412858