A new approach to solve the Boltzmann-Langevin equation for fermionic systems

TL;DR

This paper introduces a novel method to incorporate phase-space fluctuations in fermionic transport theories, accurately implementing the Boltzmann-Langevin equation and ensuring proper fluctuation reproduction in various dimensions.

Contribution

The authors develop a new procedure based on Bauer et al.'s method, ensuring the Pauli principle is respected and fluctuations are accurately modeled in fermionic systems.

Findings

Good reproduction of fluctuations in continuum limit

Validated in 1D and 2D idealized systems

Successfully applied to full 3D systems

Abstract

We present a new method to introduce phase-space fluctuations in transport theories, corresponding to a full implementation of the Boltzmann-Langevin equation for fermionic systems. It is based on the procedure originally developed by Bauer et al. for transport codes employing the test particle method. In the new procedure, the Pauli principle is carefully checked, leading to a good reproduction of the correct fluctuations in the ``continuum limit'' ($h \to 0$). Accurate tests are carried out in one and two dimensional idealized systems, and finally results for a full 3D application are shown. We stress the reliability of this method, which can be easily plugged into existing tranport codes using test particles, and its general applicability to systems characterized by instabilities, like for instance multifragmentation processes.