Applying a macroscopic reduction procedure on the improved quantum molecular dynamics (ImQMD) model, the energy dependences of the nucleus-nucleus potential, the friction parameter, and the random force characterizing a one-dimensional Langevin-type
description of the heavy-ion fusion process are investigated. Systematic calculations with the ImQMD model show that the fluctuation-dissipation relation found in the symmetric head-on fusion reactions at energies just above the Coulomb barrier fades out when the incident energy increases. It turns out that this dynamical change with increasing incident energy is caused by a specific behavior of the friction parameter which directly depends on the microscopic dynamical process, i.e., on how the collective energy of the relative motion is transferred into the intrinsic excitation energy. It is shown microscopically that the energy dissipation in the fusion process is governed by two mechanisms: One is caused by the nucleon exchanges between two fusing nuclei, and the other is due to a rearrangement of nucleons in the intrinsic system. The former mechanism monotonically increases the dissipative energy and shows a weak dependence on the incident energy, while the latter depends on both the relative distance between two fusing nuclei and the incident energy. It is shown that the latter mechanism is responsible for the energy dependence of the fusion potential and explains the fading out of the fluctuation-dissipation relation.
Macroscopic parameters as well as precise information on the random force characterizing the Langevin type description of the nuclear fusion process around the Coulomb barrier are extracted from the microscopic dynamics of individual nucleons by expl
oiting the numerical simulation of the improved quantum molecular dynamics. It turns out that the dissipation dynamics of the relative motion between two fusing nuclei is caused by a non-Gaussian distribution of the random force. We find that the friction coefficient as well as the time correlation function of the random force takes particularly large values in a region a little bit inside of the Coulomb barrier. A clear non-Markovian effect is observed in the time correlation function of the random force. It is further shown that an emergent dynamics of the fusion process can be described by the generalized Langevin equation with memory effects by appropriately incorporating the microscopic information of individual nucleons through the random force and its time correlation function.
A revised version will be uploaded later. In this Letter, it is shown that the one-time-pad key in the Vernam cipher can be repeatedly used with unconditional security using quantum media. The security proof is given with two explicit protocols, and the error rate threshold is analyzed.
