Quantum Monte-Carlo method applied to Non-Markovian barrier transmission

Abstract

In nuclear fusion and fission, fluctuation and dissipation arise due to the coupling of collective degrees of freedom with internal excitations. Close to the barrier, both quantum, statistical and non-Markovian effects are expected to be important. In this work, a new approach based on quantum Monte-Carlo addressing this problem is presented. The exact dynamics of a system coupled to an environment is replaced by a set of stochastic evolutions of the system density. The quantum Monte-Carlo method is applied to systems with quadratic potentials. In all range of temperature and coupling, the stochastic method matches the exact evolution showing that non-Markovian effects can be simulated accurately. A comparison with other theories like Nakajima-Zwanzig or Time-ConvolutionLess ones shows that only the latter can be competitive if the expansion in terms of coupling constant is made at least to fourth order. A systematic study of the inverted parabola case is made at different temperatures and coupling constants. The asymptotic passing probability is estimated in different approaches including the Markovian limit. Large differences with the exact result are seen in the latter case or when only second order in the coupling strength is considered as it is generally assumed in nuclear transport models. On opposite, if fourth order in the coupling or quantum Monte-Carlo method is used, a perfect agreement is obtained.

10 pages, 6 figures, to be published in Phys. Rev. C

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• Neutron pair transfer in sub-barrier capture process
• Search of systematic behavior of breakup probability in reactions with weakly bound projectiles at energies around Coulomb barrier
• Exact description of non-Markovian effect in open quantum system: the discretized environment method
• Sub-barrier capture reactions with ${}^{16,18}$O and ${}^{40,48}$Ca beams
• A new approach for open quantum systems based on a phonon number representation of a harmonic oscillator bath
• Threshold energy for sub-barrier fusion hindrance phenomenon
• Production of exotic isotopes in complete fusion reactions with radioactive beams
• Quasifission at extreme sub-barrier energies