Quantum microscopic dynamical approaches

TL;DR

This paper reviews quantum microscopic dynamical methods in nuclear physics, focusing on mean-field approaches like TDHF and RPA, and discusses extensions including correlations, fluctuations, and pairing effects.

Contribution

It introduces and compares various variational principles and methods for describing quantum many-body dynamics, highlighting recent developments and applications in nuclear physics.

Findings

Predictions of vibrational spectra using RPA.

Discussion of beyond mean-field correlations.

Inclusion of pairing correlations at BCS and Bogoliubov levels.

Abstract

Nuclear physics is ideal to test and develop techniques to describe the microscopic dynamics of quantum many-body systems. At low energy, nuclear dynamics is described with non-relativistic approaches based on the mean-field approximation and its extensions. Variational principles based on the stationarity of the action are introduced to build theoretical models with different levels of approximation. In particular, the time-dependent Hartree-Fock (TDHF) equation for mean-field dynamics and its linear approximation, also known as the Random Phase Approximation (RPA), are derived. Predictions of vibrational spectra at the RPA level are presented as an application. The inclusion of beyond TDHF correlations and fluctuations are then discussed. In particular, pairing correlations are treated at the BCS and Bogoliubov levels. The Balian-Veneroni variational principle is finally introduced. In addition to provide some insight into mean-field limitations, it offers a possibility to incorporate quantum fluctuations of one-body observables with the time-dependent RPA formalism.