ON STOCHASTIC APPROACHES OF NUCLEAR-DYNAMICS

We present recent developments of stochastic descriptions of nuclear d ynamics. We focus on the newly introduced microscopic descriptions, su ch as stochastic extensions of currently used kinetic equations, as we ll as on more phenomenological, macroscopic approaches. We show to wha t extent these stochastic descriptions may offer a proper picture of n uclear dynamics both in strongly out of equilibrium situations, such a s the ones encountered in energetic heavy-ion collisions or in closer to equilibrium situations such as the deexcitation of hot nuclei by th ermal fission. In Section 1 we present a pedestrian introduction to th e stochastic description of dynamical systems. We start from the eleme ntary Brownian motion and introduce the Langevin and Fokker-Planck des criptions of the motion on that occasion. A few words are then spent t o discuss the numerical methods developed for simulating stochastic eq uations. Section 2 of the paper is devoted to a formal introduction an d discussion of both macroscopic and microscopic stochastic descriptio ns of nuclear dynamics. After a brief introduction reminding general c oncepts of equilibrium statistical physics we focus on microscopic des criptions of the many-body problem. We introduce here the Boltzmann La ngevin equation which will provide a basis for many subsequent discuss ions. After having discussed the obtention of this equation from vario us points of view (from density matrix and Green's function techniques in particular), we consider reduced versions of this equation as well as a Fokker-Planck alternative. Section 3 is devoted to an analysis o f fission by means of Langevin or Fokker-Planck-like approaches. We ma inly discuss phenomenological approaches and spend some time in a deta iled presentation of the ingredients entering these models. We present results obtained in these dynamical calculations when a proper accoun t of particle evaporation is included for describing the fission of ho t nuclei. Critical comparisons with experimental data are also provide d. In Section 4 we focus on the application of the Boltzmann Langevin Equation to various situations encountered in energetic nuclear collis ions. We first remind some typical multifragmentation and subthreshold particle production, such as in particular kaon production. We discus s possible simulations of this equation and present some results in re alistic calculations of collisions. We particularly focus on the dynam ics of collective variables such as the quadrupole moment of the momen tum distribution. We finally discuss other numerical simulations devel oped in the field. The last section before conclusion is devoted to ex tensions presently developed in the field of microscopic stochastic de scriptions of nuclear dynamics. We present as a first step a relativis tic version of the theory, then focus on fluid dynamics reductions. We finally discuss in some detail the recently introduced Stochastic tim e-dependent Hartree-Fock theory, which could provide new interesting d evelopments.