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arXiv:0706.2406 · Physical Review C

Collective motion in a quantum diffusive environment

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

Published Jan 9, 2008• 6 citations
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Abstract

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.

DOI
10.1103/physrevc.77.014305

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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.
We address the problem of the dissipative character of collective motion in finite Fermi systems. We study this problem from the point of view of chaotic features of the fermionic degrees of freedom of the many-body Fermi systems. Our main aim is of two kinds: first, we investigate how quantum chaos sets in in many-body systems and then, we try to relate quantum many-body chaos of the intrinsic fermionic degrees of freedom to the corresponding dissipative properties of the macroscopic collective motion. The main focus is on the role of two-body interaction between fermions in onset of the quantum many-body chaos and collective dissipation.
Within random matrix model, the response of a complex quantum system Ĥ(q[t]) on time variations in an external parameter q. In the limit of weak coupling of the external parameter to the quantum system, the different dynamical regimes of the diffusion in a space of the occupancies of eigenstates of Ĥ(q) are considered. The main focus is made on measuring the role of memory effects in the quantum diffusive dynamics. Possible macroscopic manifestations of the quantum mechanical diffusion are discussed in the context of the cranking approach, where the time variations in the classical parameter q provides the constancy of energy of the total system.
A theory based on the time•dependent Hartree•Fock theory is proposed with the aim of describing large amplitude collective motion and its coupling with intrinsic degrees of freedom.With the use of time•dependent canonical transformation, the whole system is separated into two types of degrees of freedom.Under the condition of unique separation, two kinds of equations of collective submanifold are obtained.One js for the collective motion and of the same form as that previously given by the present authors.The other is for the intrinsic degrees of freedom and consists of a set of linear partial differential equations.It is reduced to the old one, the form of which is non-linear.
In this article, I provide a simple review on conventional methods and models on the transport phenomenon of nuclear many-body systems. By exploiting the basic idea of time-dependent projection operator, I recommend a novel method to derive the transport equation for collective motion which is embedded on the microscopic dynamics of timedependent single-particle motion. It is emphasized that the microscopic dynamics of single-particle motion should play an important role for understanding the dynamics of nuclear reaction and the synthesis mechanisms of new superheavy elements. The numerical results of energy dissipation and entropy production indicate that the collective motion passes through three stages, such as dephasing/decoherence, statistical relaxation and stationary state. The statistical relaxation is a complex anomalous diffusion process in general. With the aid of above analysis and results, a possible way to define the collective and single-particle variables for the realistic nuclear many-body systems is proposed.