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Civil War Book Review

On the Physical Significance of q-deformation in Many-body Physics

Jerry Paul Draayer, K. D. Sviratcheva, C. Bahri, A. I. Georgieva

Published Dec 1, 2006• 0 citations
Publisher

Abstract

A quantum extension of an algebraic sp(4) model is applied to a study of pairing correlations in nuclei with mass 40 ≤ A ≤ 100. While a reasonable overall description of certain nuclear properties is achieved in the nondeformed limit of the theory, the (/-deformation brings forward superior results and plays a significant role in understanding nonlinear effects in many-body physics.

DOI
10.1142/9789812772527_0012

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A quantum extension of an algebraic sp(4) model is applied to a study of pairing correlations in nuclei with mass 40 ≤ A ≤ 100. While a reasonable overall description of certain nuclear properties is achieved in the nondeformed limit of the theory, the (/-deformation brings forward superior results and plays a significant role in understanding nonlinear effects in many-body physics.
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In this article we consider the physical importance of q deformation in nuclear physics [ 1 ] by considering a q deformed generalization of a classical nuclear theory. The role of the deformation parameter is explored by comparing the non-deformed and deformed results with experimental data. This is accomplished by relating physical quantities, other than the Hamiltonian itself, with generators of the Cartan subalgebra of the principal symmetry group. This is important because the latter do not change as a function of the deformation while the other generators do. In this way the effects of the deformation on the underlying physics are isolated from other changes.
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical tools (qqq-numbers, qqq-analysis, qqq-oscillators, qqq-algebras), the suq_qq​(2) rotator model and its extensions, the construction of deformed exactly soluble models (Interacting Boson Model, Moszkowski model), the use of deformed bosons in the description of pairing correlations, and the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, are discussed in some detail. A brief description of similar applications to molecular structure and an outlook are also given.
Confined quantum many-body systems of a given particle number exhibit a variety of intrinsic shape characteristics as a function of increasing external field and internal thermal excitation. The shell model is an important tool for the theoretical description of these various structures and transitions in nuclei. Another system in which correlations beyond the mean field may play an important role is semiconductor quantum dots. In this Proceedings, the author compares nuclei and quantum dots and their various deformation properties. The author reports on shell-model calculations in nuclei and some recent mean-field calculations of the thermal properties of quantum dots.
Confined quantum many-body systems of a given particle number exhibit a variety of intrinsic shape characteristics as a function of increasing external field and internal thermal excitation. The shell model is an important tool for the theoretical description of these various structures and transitions in nuclei. Another system in which correlations beyond the mean field may play an important role is semiconductor quantum dots. In this Proceedings, the author compares nuclei and quantum dots and their various deformation properties. The author reports on shell-model calculations in nuclei and some recent mean-field calculations of the thermal properties of quantum dots.