Projects per year
Abstract
The meanfield approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum manybody systems that are too large to be treated by ab initio methods. Some examples are strongly interacting medium and heavy mass atomic nuclei and mesoscopic condensed matter systems. In this approach, the linear Schrodinger equation for the exact manybody wave function is mapped onto a nonlinear densitydependent onebody potential problem. This approximation, not only provides computationally very simple solutions even for systems with many particles, but due to the nonlinearity, it also allows for obtaining solutions that break essential symmetries of the system, often connected with phase transitions. In this way, additional correlations are subsumed in the system. However, the meanfield approach suffers from the drawback that the corresponding wave functions do not have sharp quantum numbers and, therefore, many results cannot be compared directly with experimental data. In this article, we discuss general grouptheory techniques to restore the broken symmetries, and provide detailed expressions on the restoration of translational, rotational, spin, isospin, parity and gauge symmetries, where the latter corresponds to the restoration of the particle number. In order to avoid the numerical complexity of exact projection techniques, various approximation methods available in the literature are examined. Applications of the projection methods are presented for simple nuclear models, realistic calculations in relatively small configuration spaces, nuclear energy density functional theory, as well as in other mesoscopic systems. We also discuss applications of projection techniques to quantum statistics in order to treat the averaging over restricted ensembles with fixed quantum numbers. Further, unresolved problems in the application of the symmetry restoration methods to the energy density functional theories are highlighted in the present work.
Original language  English 

Article number  123001 
Journal  Journal of physics gNuclear and particle physics 
Volume  48 
Issue number  12 
DOIs  
Publication status  Published  1 Nov 2021 
Bibliographical note
© 2021 The Author(s). Published by IOP Publishing Ltd.Projects
 2 Finished

Nuclear Physics Consolidated Grant
Jenkins, D., Andreyev, A., Bentley, M., Diget, C. A., Dobaczewski, J. J., Fulton, B. R., Laird, A. M., Paschalis, S., Pastore, A., Petri, M. & Wadsworth, R.
SCIENCE AND TECHNOLOGY FACILITIES COUNCIL (STFC)
1/10/17 → 30/09/22
Project: Research project (funded) › Research

Nuclear Physics Theory
Dobaczewski, J. J. & Pastore, A.
SCIENCE AND TECHNOLOGY FACILITIES COUNCIL (STFC)
1/06/15 → 31/03/20
Project: Research project (funded) › Research