# A quantum relaxation-time approximation for finite fermion systems

## Abstract

We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on time-dependent density functional theory at the level of the local density approximation. This mean-field picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semi-classical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semi-classical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly non-linear reactions. We observe a strong effect of dissipation on sensitive observables such as net ionization and angular distributions of emitted electrons. The effect is especially large for moderate excitations where typical relaxation/dissipation time scales efficiently compete with ionization for dissipating the available excitation energy. Technical details on the actual procedure to implement a working recipe of such a quantum relaxation approximation are givenmore »

- Authors:

- Institut für Theoretische Physik, Universität Erlangen, D-91058 Erlangen (Germany)
- Université de Toulouse, UPS, Laboratoire de Physique Théorique, IRSAMC, F-31062 Toulouse Cedex (France)
- (France)
- (United States)

- Publication Date:

- OSTI Identifier:
- 22447601

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 354; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR DISTRIBUTION; APPROXIMATIONS; DENSITY FUNCTIONAL METHOD; ELECTRON EMISSION; ELECTRON-ELECTRON INTERACTIONS; FERMIONS; MEAN-FIELD THEORY; QUANTUM SYSTEMS; RELAXATION TIME; TIME DEPENDENCE

### Citation Formats

```
Reinhard, P.-G., E-mail: paul-gerhard.reinhard@fau.de, Suraud, E., Laboratoire de Physique Théorique, Université Paul Sabatier, CNRS, F-31062 Toulouse Cédex, and Physics Department, University at Buffalo, The State University New York, Buffalo, NY 14260.
```*A quantum relaxation-time approximation for finite fermion systems*. United States: N. p., 2015.
Web. doi:10.1016/J.AOP.2014.12.011.

```
Reinhard, P.-G., E-mail: paul-gerhard.reinhard@fau.de, Suraud, E., Laboratoire de Physique Théorique, Université Paul Sabatier, CNRS, F-31062 Toulouse Cédex, & Physics Department, University at Buffalo, The State University New York, Buffalo, NY 14260.
```*A quantum relaxation-time approximation for finite fermion systems*. United States. doi:10.1016/J.AOP.2014.12.011.

```
Reinhard, P.-G., E-mail: paul-gerhard.reinhard@fau.de, Suraud, E., Laboratoire de Physique Théorique, Université Paul Sabatier, CNRS, F-31062 Toulouse Cédex, and Physics Department, University at Buffalo, The State University New York, Buffalo, NY 14260. Sun .
"A quantum relaxation-time approximation for finite fermion systems". United States.
doi:10.1016/J.AOP.2014.12.011.
```

```
@article{osti_22447601,
```

title = {A quantum relaxation-time approximation for finite fermion systems},

author = {Reinhard, P.-G., E-mail: paul-gerhard.reinhard@fau.de and Suraud, E. and Laboratoire de Physique Théorique, Université Paul Sabatier, CNRS, F-31062 Toulouse Cédex and Physics Department, University at Buffalo, The State University New York, Buffalo, NY 14260},

abstractNote = {We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on time-dependent density functional theory at the level of the local density approximation. This mean-field picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semi-classical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semi-classical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly non-linear reactions. We observe a strong effect of dissipation on sensitive observables such as net ionization and angular distributions of emitted electrons. The effect is especially large for moderate excitations where typical relaxation/dissipation time scales efficiently compete with ionization for dissipating the available excitation energy. Technical details on the actual procedure to implement a working recipe of such a quantum relaxation approximation are given in appendices for completeness.},

doi = {10.1016/J.AOP.2014.12.011},

journal = {Annals of Physics},

number = ,

volume = 354,

place = {United States},

year = {Sun Mar 15 00:00:00 EDT 2015},

month = {Sun Mar 15 00:00:00 EDT 2015}

}