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Progress of Theoretical Physics

Application of the Canonical Theory of Mixed State to the Description of Bound States of the Nucleus. I: Reformulation of the Theory of Mixed State

A. K. J. daProvidencia, Masao Yamamura

Published Aug 1, 1991• 0 citations
Publisher

Abstract

In order to apply the prescription based on the concept of mixed state as a canonical formulation of the thermal field theory for the description of a system with incompletely occupied shells, we reformulate this prescription. We show the equivalence between both results in spite of difference in their formulations. In the present approach, the initial occupation number in each single-particle state can be taken into account as a dynamical variable.

DOI
10.1143/ptp/86.2.419

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In order to apply the prescription based on the concept of mixed state as a canonical formulation of the thermal field theory for the description of a system with incompletely occupied shells, we reformulate this prescription. We show the equivalence between both results in spite of difference in their formulations. In the present approach, the initial occupation number in each single-particle state can be taken into account as a dynamical variable.
A classical microscopic theory of mixed states has recently been formulated in order to deal with the theoretical description of nuclear phenomena observed in highly excited states. In this theory, which is here briefly reviewed, the degrees of freedom of real fermions are doubled by fictitious fermions, in the context of the formalism of thermofield dynamics. The requirement of static stability of the thermal state of equilibrium plays, in the theory, a relevant role. The possibility of constraining the dynamics of the fictitious degrees of freedom, in such a way as to eliminate spurious thermal excitations, is discussed. The concept of canonical collective variables for mixed states is analyzed. Boson expansions appropriate to describe collective excitations of hot quantal systems are introduced and their properties investigated. It is shown that thermal boson expansions based on the formalism of thermofield dynamics are free from formal inconsistencies which may be present in boson expansions derived by an ad hoc quantization of conventional thermal mean field theories. The formalism is applied to the Lipkin model, and the correlation energy of a hot system is discussed.
We develop a statistical mean-field theory of finite quantum systems in thermal equilibrium. Our formulation employs the canonical ensemble of statistical mechanics, and it enables us to analytically determine the occupation number distributions of interacting particles obeying Bose–Einstein or Fermi–Dirac statistics. We have also developed a numerical procedure that enables us to obtain a universal scaled occupation number distribution that, for a given total number of interacting particles in a finite system, makes it possible to determine the occupation number distribution for any temperature. The developed mean-field theory is applicable to a wide range of atomic, nuclear and condensed matter systems for which finite-size effects can play an important role. In particular, the present approach makes it possible to formulate a finite temperature mean-field theory for a specific ion in a dense plasma.