Quantum microscopic dynamical approaches
arXiv:2207.13290 · doi:10.1007/978-981-15-8818-1_19-1
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.
Book chapter to be published in Handbook of Nuclear Physics. 35 pages, 4 figures
References in corpus (5)
- Heavy-ions collisions and fission dynamics with the time-dependent Hartree-Fock theory and its extensions
- Heavy-ion interaction potential deduced from density-constrained TDHF calculation
- TDHF Theory and Its Extensions for the Multinucleon Transfer Reaction: a Mini Review
- Low-Energy Heavy-Ion Reactions and the Skyrme Effective Interaction
- Examining empirical evidence of the effect of superfluidity on the fusion barrier