Selected Aspects of Collective Motions in Nuclei: Order and Disorder

This article is devoted to a compilation of recent results about collective vibrations in nuclei. We will describe different approaches to study mesoscopic systems such as nuclei which are at the limit between quantum mechanics of small systems and statistical mechanics of large systems. We will focus on solutions of the many-body problem such as the time dependent mean-field methods, the small amplitude response and its extensions. In particular we will discuss the quantification of periodic orbits, the boson mappings and the variational approximations in the boson space and the stochastic mean-field approaches. We will then discuss how a nucleus may self-organize in collective motion. We will discuss the nature, the structure, the dynamics and the properties of collective vibrations in cold or hot nuclei and in stable or unstable situations. For stable vibrations, we will study their energy and their damping. Then we will discuss multiphonon excitations, their properties and their excitations stressing that these states are a direct demonstration of the vibrational nature of giant resonances. As far as hot resonances are concerned, we will show how their characteristics are deeply related to the properties of the nuclei at high temperature. Finally in the presence of instabilities, we will discuss the relation between unstable modes and the phase diagram of nuclear matter. We will underline their role in the dynamics of first order phase transition such as in the spinodal decomposition of infinite as well as finite systems. All these points will be illustrated considering experimental results obtained in heavy ion reactions.