2006/12/24 by Aleksei V. Chechkin, Chechkin, Aleksei V., Oleksii Sliusarenko +5 · 2 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Spectroscopy and Quantum Chemical Studies #Statistical Mechanics (cond-mat.stat-mech) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.cond-mat/0612618
openalex publication_date 2006/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the barrier crossing of a particle driven by white symmetric Levy\nnoise of index \α and intensity DD for three different generic types of\npotentials: (a) a bistable potential; (b) a metastable potential; and (c) a\ntruncated harmonic potential. For the low noise intensity regime we recover the\npreviously proposed algebraic dependence on D of the characteristic escape\ntime, T\esc\≃ C(\α)/D\μ(\α), where C(\α) is\na coefficient. It is shown that the exponent \μ(\α) remains\napproximately constant, \μ\≈ 1 for 0<\α<2; at \α=2 the\npower-law form of T\esc changes into the known exponential\ndependence on 1/D; it exhibits a divergence-like behavior as \α\napproaches 2. In this regime we observe a monotonous increase of the escape\ntime T\esc with increasing \α (keeping the noise intensity\nD constant). The probability density of the escape time decays exponentially.\nIn addition, for low noise intensities the escape times correspond to barrier\ncrossing by multiple Levy steps. For high noise intensities, the escape time\ncurves collapse for all values of \α. At intermediate noise intensities,\nthe escape time exhibits non-monotonic dependence on the index \α, while\nstill retaining the exponential form of the escape time density.\n