74 research outputs found
The wonderful compactification for quantum groups
In this paper, we introduce a quantum version of the wonderful compactification of a group as a certain noncommutative projective scheme. Our approach stems from the fact that the wonderful compactification encodes the asymptotics of matrix coefficients, and from its realization as a GIT quotient of the Vinberg semigroup. In order to define the wonderful compactification for a quantum group, we adopt a generalized formalism of Proj categories in the spirit of Artin and Zhang. Key to our construction is a quantum version of the Vinberg semigroup, which we define as a q-deformation of a certain Rees algebra, compatible with a standard Poisson structure. Furthermore, we discuss quantum analogues of the stratification of the wonderful compactification by orbits for a certain group action, and provide explicit computations in the case of SL2
Analytic Formulae for the Matrix Elements of the Transition Operators in the Symplectic Extension of the Interacting Vector Boson Model
The tensor properties of all the generators of Sp(12,R) - the group of
dynamical symmetry of the Interacting Vector Boson Model (IVBM), are given with
respect to the reduction chain Sp(12,R) U(6) U(3) x U(2)
O(3) x U(1). Matrix elements of the basic building blocks of the
model are evaluated in symmetry adapted basis along the considered chain. As a
result of this, the analytic form of the matrix elements of any operator in the
enveloping algebra of the Sp(12,R), defining a certain transition operator, can
be calculated. The procedure allows further applications of the symplectic IVBM
for the description of transition probabilities between nuclear collective
states.Comment: 6 page
Phase Structure of the Interacting Vector Boson Model
The two-fluid Interacting Vector Boson Model (IVBM) with the U(6) as a
dynamical group possesses a rich algebraic structure of physical interesting
subgroups that define its distinct exactly solvable dynamical limits. The
classical images corresponding to different dynamical symmetries are obtained
by means of the coherent state method. The phase structure of the IVBM is
investigated and the following basic phase shapes, connected to a specific
geometric configurations of the ground state, are determined: spherical,
, unstable, O(6), and axially deformed
shape, . The ground state quantum phase transitions
between different phase shapes, corresponding to the different dynamical
symmetries and mixed symmetry case, are investigated.Comment: 9 pages, 10 figure
Collective states of the odd-mass nuclei within the framework of the Interacting Vector Boson Model
A supersymmetric extension of the dynamical symmetry group of
the Interacting Vector Boson Model (IVBM), to the orthosymplectic group
is developed in order to incorporate fermion degrees of
freedom into the nuclear dynamics and to encompass the treatment of odd mass
nuclei. The bosonic sector of the supergroup is used to describe the complex
collective spectra of the neighboring even-even nuclei and is considered as a
core structure of the odd nucleus. The fermionic sector is represented by the
fermion spin group .
The so obtained, new exactly solvable limiting case is applied for the
description of the nuclear collective spectra of odd mass nuclei. The
theoretical predictions for different collective bands in three odd mass
nuclei, namely , and from rare earth region are
compared with the experiment. The transition probabilities for the
and between the states of the ground band are also
studied. The important role of the symplectic structure of the model for the
proper reproduction of the behavior is revealed. The obtained results
reveal the applicability of the models extension.Comment: 18 pages, 8 figure
Structure of the doublet bands in doubly odd nuclei: The case of
The structure of the doublet bands in is
investigated within the framework of the Interacting Vector Boson Fermion Model
(IVBFM). A new, purely collective interpretation of these bands is given on the
basis of the used boson-fermion dynamical symmetry of the model. The energy
levels of the doublet bands as well as the absolute and
transition probabilities between the states of both yrast and yrare bands are
described quite well. The observed odd-even staggering of both and
values is reproduced by the introduction of an appropriate interaction
term of quadrupole type, which produces such a staggering effect in the
transition strengths. The calculations show that the appearance of doublet
bands in certain odd-odd nuclei could be a consequence of the realization of a
larger dynamical symmetry based on the non-compact supersymmetry group
.Comment: 12 pages, 8 figure
New Description of the Doublet Bands in Doubly Odd Nuclei
The experimentally observed doublet bands in some odd-odd
nuclei are analyzed within the orthosymplectic extension of the Interacting
Vector Boson Model (IVBM). A new, purely collective interpretation of these
bands is given on the basis of the obtained boson-fermion dynamical symmetry of
the model. It is illustrated by its application to three odd-odd nuclei from
the region, namely , and . The
theoretical predictions for the energy levels of the doublet bands as well as
and transition probabilities between the states of the yrast band in
the last two nuclei are compared with experiment and the results of other
theoretical approaches. The obtained results reveal the applicability of the
orthosymplectic extension of the IVBM.Comment: 15 pages, 13 figure
Unified dynamical symmetries in the symplectic extension of the interacting vector boson model
The algebraic Interacting Vector Boson Model (IVBM) is extended by exploiting three new subgroup chains in the reduction of its highest symplectic dynamical symmetry group Sp(12, R) to the physical angular momentum subgroup SO(3). The corresponding exactly solvable limiting cases are applied to achieve a description of complex nuclear collective spectra of even-even nuclei in the rare earth and actinide regions up to states of very high angular momentum. First we exploit two reductions in which collective modes can be mixed, and obtain successful descriptions of both positive and negative parity band conflgurations. The structure of band-head conflgurations, whose importance is established in the flrst two limits, is examined in a third reduction, that also provides important links between the subgroups of the other limits. © 2008 IOP Publishing Ltd
Symplectic dynamical symmetries in algebraic models of nuclear structure
Based on a generalized reduction scheme for boson representations of symplectic algebras of the type Sp(4k,R), we consider the symplectic extension of a boson realization of compact unitary algebras for the k 1, k 3 and k 6 cases, which have relevance in nuclear structure theory. First we review an application of the k 1 case for the creation of a Sp(4, R) classification scheme, which is used for obtaining a generalized phenomenological description of important nuclear characteristics in terms of the classification quantum numbers for large sets of nuclei. Then for the k 3 and k 6 cases we outline some of the new possibilities that appear in the symplectic extensions of the Interacting Vector Boson Model (IVBM) and the Interacting Boson Model (IBM-2), respectively. The examples presented are used to describe the collective modes of the nuclear spectra in individual nuclei as well as in sequences of nuclei. © Published under licence by IOP Publishing Ltd
Six-dimensional Davidson potential as a dynamical symmetry of the symplectic Interacting Vector Boson Model
A six-dimensional Davidson potential, introduced within the framework of the
Interacting Vector Boson Model (IVBM), is used to describe nuclei that exhibit
transitional spectra between the purely rotational and vibrational limits of
the theory. The results are shown to relate to a new dynamical symmetry that
starts with the reduction. Exact
solutions for the eigenstates of the model Hamiltonian in the basis defined by
a convenient subgroup chain of SO(6) are obtained. A comparison of the
theoretical results with experimental data for heavy nuclei with transitional
spectra illustrates the applicability of the theory.Comment: 9 pages, 4 figure
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