Stochastic TDHF in an exactly solvable model

TL;DR

This paper demonstrates that Stochastic Time-Dependent Hartree-Fock (STDHF) effectively models electron-electron collisions in a solvable schematic system, closely matching exact solutions at higher energies, and discusses its limitations.

Contribution

It introduces and tests STDHF in a Lipkin-Meshkov-Glick inspired model, showing its accuracy and limitations compared to exact solutions.

Findings

STDHF reproduces entropy evolution well at high excitation energies.

Limitations are observed for low energy excitations and memory effects.

Model parameters influence the accuracy of STDHF predictions.

Abstract

We apply in a schematic model a theory beyond mean-field, namely Stochastic Time-Dependent Hartree-Fock (STDHF), which includes dynamical electron-electron collisions on top of an incoherent ensemble of mean-field states by occasional 2-particle-2-hole ($2p2h$) jumps. The model considered here is inspired by a Lipkin-Meshkov-Glick model of $\Omega$ particles distributed into two bands of energy and coupled by a two-body interaction. Such a model can be exactly solved (numerically though) for small $\Omega$. It therefore allows a direct comparison of STDHF and the exact propagation. The systematic impact of the model parameters as the density of states, the excitation energy and the bandwidth is presented and discussed. The time evolution of the STDHF compares fairly well with the exact entropy, as soon as the excitation energy is sufficiently large to allow $2p2h$ transitions. Limitations concerning low energy excitations and memory effects are also discussed.