We propose a five-parameter dumbbell model to describe the fusion and fission processes of massive nuclei, where the collective variables are: the distance ρ between the center-of-mass of two fusing nuclei, the neck parameter ν, asymmetry D, two deformation variables β_1 and β_2 . The present model has macroscopic qualitative expression of polarization and nuclear collision of head to head, sphere to sphere, waist to waist and so on. The conception of the "projectile eating target" based on open mouth and swallow is proposed to describe the nuclear fusion process, and our understanding of the probability of fusion and quasi-fission is in agreement with some previous work. The calculated fission barriers of a lot of compound nuclei are compared with the experimental data.
We investigate the time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to the whole fusion-fission dynamical process and can be called the reverse Kramers problem. By the passing probability over the saddle point of an inverse harmonic potential multiplying the exponential decay factor of a particle in the metastable potential, we present an approximate expression for the modified passing probability over the barrier, in which the effect of the reflection boundary of the potential is taken into account. Our analytical result and Langevin Monte-Carlo simulation show that the probability of passing and against escaping over the barrier is a non-monotonous function of time and its maximal value is less than the stationary result of the passing probability over the saddle point of an inverse harmonic potential.
The correlated Lvy flight is studied analytically in terms of the fractional Fokker-Planck equation and simulated numerically by using the Langevin equation,where the usual white Lvy noise is generalized to an Ornstein-Uhlenbeck Lvy process(OULP)with a correlation timeτc.We analyze firstly the stable behavior of OULP.The probability density function of Lvy flight particle driven by the OULP in a harmonic potential is exactly obtained,which is also a Lvy-type one withτc-dependence width;when the particle is bounded by a quartic potential,its stationary distribution has a bimodality shape and becomes noticeable with the increase of τc.
A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed,which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling.This model allows ballistic diffusion and classical localization simultaneously,in which the fluctuation-dissipation relation is still satisfied but the Khinchin theorem is broken.The asymptotical equilibrium for a nonergodic system requires the initial thermal equilibrium,however,when the system starts from nonthermal conditions,it does not approach the equilibration even though a nonlinear potential is used to bound the particle,this can be confirmed by the zeroth law of thermodynamics.In the dynamics of Brownian localization,due to the memory damping function inducing a constant term,our results show that the stationary distribution of the system depends on its initial preparation of coordinate rather than momentum.The coupled oscillator chain with a fixed end boundary acts as a heat bath,which has long been used in studies of collinear atom/solid-surface scattering and lattice vibration,we investigate this problem from the viewpoint of nonergodicity.
