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Intrinsic and collective structure in the interacting boson model
ANNALS
OF PHYSICS
178, 330 (1987)
Abstracts
of Papers
to Appear
in Future
Issues
and Collective Structure in the Interacting Boson Model. AMIRAM LEVIATAN. Department of Nuclear Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
Intrinsic
A general non-spherical boson basis is introduced to study the excitation modes in the interacting boson model (IBM). A prescription for construction of intrinsic states is presented. The general IBM Hamiltonian is resolved exactly into intrinsic and collective parts. The limit of large boson number is discussed analytically for spectrum and transitions. The method of analysis reveals an underlying intrinsic and collective structure closely linked with symmetry considerations. The suggested new approach seems to be adequate as a tool to obtain the physical content and normal modes in any number conserving algebraic bosonic system.
Geometrical
Phase
Factors
and
Higher-Order
Adiabatic
Approximations.
NOR~O NAKAGAWA. Ames
Laboratory, Iowa State University, Ames, Iowa 50011. A detailed study of Schrodinger equations having several components with a time-dependent Hamiltonian is carried out, paying particular attention to the geometrical nature of these equations. Two features of such a study will be presented: (i) It is shown that the diagonalization process of such equations possessesa certain arbitrariness which can be interpreted precisely as a local gauge degree of freedom. For a two-component problem, this gauge symmetry structure is determined completely in terms of the corresponding geometrical structure, i.e., a differentiable principal fibre bundle equipped with a connection form. This geometrical structure, and particularly the notion of parallelism provided by it, is used subsequently to show that the wavefunction factorizes into two parts, one of which is thereby given a purely geometrical interpretation. (ii) Second, it is shown that the adiabatic theorem, well-known to hold in the extreme adiabatic limit, can be generalized in such a way that higher-order terms with respect to the adiabatic approximation can be calculated systematically. This part of the study is carried out for a reduced Schrodinger equation given subsequently after the aforementioned geometrical factorization. Clarification on how the combination of these two results allows one to study the now popular subject of “Berry’s phase” for a wider class of systems than those in the earlier literature is given. Applications of the present result to certain systems, including the neutrino propagation in matter, are also discussed.
330 0003-4916/87 $7.50 Copyright 0 1987 by Academic Press. Inc. All rights of reproduction in any form reserved.
OF PHYSICS
178, 330 (1987)
Abstracts
of Papers
to Appear
in Future
Issues
and Collective Structure in the Interacting Boson Model. AMIRAM LEVIATAN. Department of Nuclear Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
Intrinsic
A general non-spherical boson basis is introduced to study the excitation modes in the interacting boson model (IBM). A prescription for construction of intrinsic states is presented. The general IBM Hamiltonian is resolved exactly into intrinsic and collective parts. The limit of large boson number is discussed analytically for spectrum and transitions. The method of analysis reveals an underlying intrinsic and collective structure closely linked with symmetry considerations. The suggested new approach seems to be adequate as a tool to obtain the physical content and normal modes in any number conserving algebraic bosonic system.
Geometrical
Phase
Factors
and
Higher-Order
Adiabatic
Approximations.
NOR~O NAKAGAWA. Ames
Laboratory, Iowa State University, Ames, Iowa 50011. A detailed study of Schrodinger equations having several components with a time-dependent Hamiltonian is carried out, paying particular attention to the geometrical nature of these equations. Two features of such a study will be presented: (i) It is shown that the diagonalization process of such equations possessesa certain arbitrariness which can be interpreted precisely as a local gauge degree of freedom. For a two-component problem, this gauge symmetry structure is determined completely in terms of the corresponding geometrical structure, i.e., a differentiable principal fibre bundle equipped with a connection form. This geometrical structure, and particularly the notion of parallelism provided by it, is used subsequently to show that the wavefunction factorizes into two parts, one of which is thereby given a purely geometrical interpretation. (ii) Second, it is shown that the adiabatic theorem, well-known to hold in the extreme adiabatic limit, can be generalized in such a way that higher-order terms with respect to the adiabatic approximation can be calculated systematically. This part of the study is carried out for a reduced Schrodinger equation given subsequently after the aforementioned geometrical factorization. Clarification on how the combination of these two results allows one to study the now popular subject of “Berry’s phase” for a wider class of systems than those in the earlier literature is given. Applications of the present result to certain systems, including the neutrino propagation in matter, are also discussed.
330 0003-4916/87 $7.50 Copyright 0 1987 by Academic Press. Inc. All rights of reproduction in any form reserved.