Group theory and collective degrees of freedom in nuclear many body systems

Takuji Ishikawa

Nuclei are rather classical systems in a sense. In the old days, their phenomena were roughly explained in classical rules such as the liquid drop model. This fact may be understood that when we see an finite quantum many body system like nucleus, though which is a group of quantum mechanical particles, its any collective degree of freedom has any classicality. Getting a classicality does not depend on spatial scales of objects. It is made by a phenomenon called Quantum Decoherence. We have studied about Quantum Decoherence in a finite system as nucleus. In this paper, at the harmonic three body problem (3 Schroedinger cats), it is shown that one degree of freedom as a sub-system would get classicality because of the other two degrees of freedom. Therefore we can assume that a nuclear collective degree of freedom would get classicality when it couples with any other internal degrees of freedom. In this paper, we also note that there is some relationship between the Quantum Decoherence and Crossing of classical orbits in 3 Schroedinger cats model.

J.P. Jeukenne, A Lejeune, Claude Mahaux

Pavel Cejnar, Pavel Stránský

Abstract Quantum phase transitions (QPTs) represent a quickly developing subject of theoretical and experimental research. Nuclear physics contributed to the formation of the QPT concept in the 1970s and remains an area where new viewpoints and original approaches to criticality in many-body systems can be created. In this review, we present a comprehensible introduction to the subject, with an emphasis on the role of nuclear physics, and point out some specific features of QPTs in the systems that exhibit an effective separation of some collective degrees of freedom. The focus on collectivity, which stems from the nuclear context, is an essential ingredient of our treatise. It leads to some consequences that find application in nuclei as well as in a wide spectrum of non-nuclear systems.

V. M. Kolomietz, Sven Åberg, S. V. Radionov

The general problem of dissipation in macroscopic large-amplitude collective motion and its relation to energy diffusion of intrinsic degrees of freedom of a nucleus is studied. By applying the cranking approach to the nuclear many-body system, a set of coupled dynamical equations for the collective classical variable and the quantum mechanical occupancies of the intrinsic nuclear states is derived in the limit of weak coupling of the collective and intrinsic subsystems. Different dynamical regimes of the intrinsic nuclear motion and its consequences on time properties of collective dissipation are discussed.