Diffusion over a saddle with a Langevin equation

Abstract

The diffusion problem over a saddle is studied using a multi-dimensional Langevin equation. An analytical solution is derived for a quadratic potential and the probability to pass over the barrier deduced. A very simple solution is given for the one dimension problem and a general scheme is shown for higher dimensions.

13 pages, use revTeX, to appear in Phys. Rev. E61

References in corpus (3)

• Levy Flights in External Force Fields: Langevin and Fractional Fokker-Planck Equations, and their Solutions
• Levy flights in quenched random force fields
• Computing probabilities of very rare events for Langevin processes: a new method based on importance sampling

Cited by in corpus (13)

• Coupled-channels calculations for nuclear reactions: from exotic nuclei to superheavy elements
• Isospin dependence of reactions ${}^{48}$Ca+${}^{243-251}$Bk
• Time-dependent Hartree-Fock plus Langevin approach for hot fusion reactions to synthesize the $Z=120$ superheavy element
• Hot fusion reactions with deformed nuclei for synthesis of superheavy nuclei: an extension of the fusion-by-diffusion model
• Quantum Statistical Effects on Fusion Dynamics of Heavy-Ions
• Quantum effect in the diffusion along a potential barrier: Comments on the synthesis of superheavy elements
• Quantum Monte-Carlo method applied to Non-Markovian barrier transmission
• Influence of microscopic transport coefficients on the formation probabilities for super-heavy elements
• Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect
• Non-Markovian diffusion over a parabolic potential barrier: influence of the friction-memory function
• Fusion Hindrance in the Heavy Ion Reactions -- Border Between the Normal and Hindered Fusions
• Analysis of the Fusion Hindrance in Mass-symmetric Heavy Ion Reactions
• Optimal path of diffusion over the saddle point and fusion of massive nuclei