The role of diffusion coefficients in the dynamics of nuclear processes

The dissipation process in open quantum systems at initial time before the setting of the equilibrium state plays a key role in such physical processes, as quantum-optical processes, nuclear fission and fusion and deep inelastic collisions of heavy ions. The goal of a given work is to demonstrate the advanced method for the calculation of non-stationary diffusion coefficients of the collective system, in case when the collective subsystem and thermostat are linearly coupled in the coordinate and momentum. As a result of the interaction between the degrees of freedom of collective and intrinsic subsystems, the transport and diffusion coefficients on coordinate, momentum and coordinate-momentum appear in the system. The Langevin formalism which is effective in description of fluctuation and dissipative processes in macroscopic systems has been introduced in derivation of equations of motion. In the kinetic theory the Leaving's method significantly simplifies a procedure of calculation of non-stationary quantum and thermal fluctuations and provides a clear picture of the dynamics of the process. The microscopic Hamiltonian of the system (thermostat plus collective system) is given. For example, while describing the interaction of nuclei at low energies, the coupling in the coordinate responses for the influence of the mean field of each nucleus on the single-particle motion in other nucleus whereas the last term describes the relation between the currents of intrinsic and collective motion. In the procedure of solving the second order Heisenberg equations, the integro-differential quantum stochastic Langevin Equations are obtained directly. Knowing its solution we may write the equations for the first and second moments which provide us the expressions for the transport and diffusion coefficients. In the figure the time dependencies of diffusion coefficients at the temperature T=0.1 MeV are given. In our calculations we consider the case of a large mass μ=448m0 (m0 is a nucleon mass) and small value of ℎω=1 MeV. Solid, dashed, dotted, dash-dotted and short-dashed curves correspond to the friction coefficients λq=0, 0.5ω, ω, 2ω an 3ω, respectively