3,421 research outputs found
Boson-fermion mapping of collective fermion-pair algebras
We construct finite Dyson boson-fermion mappings of general collective
algebras extended by single-fermion operators. A key element in the
construction is the implementation of a similarity transformation which
transforms boson-fermion images obtained directly from the supercoherent state
method. In addition to the general construction, we give detailed applications
to SO(2N), SU(l+1), SO(5), and SO(8) algebras.Comment: 22 pages, latex, no figure
SDG fermion-pair algebraic SO(12) and Sp(10) models and their boson realizations
It is shown how the boson mapping formalism may be applied as a useful
many-body tool to solve a fermion problem. This is done in the context of
generalized Ginocchio models for which we introduce S-, D-, and G-pairs of
fermions and subsequently construct the sdg-boson realizations of the
generalized Dyson type. The constructed SO(12) and Sp(10) fermion models are
solved beyond the explicit symmetry limits. Phase transitions to rotational
structures are obtained, also in situations where there is no underlying SU(3)
symmetry.Comment: 25 LaTeX pages, 4 uuencoded postscript figures included, Preprint
IFT/8/94 & STPHY-TH/94-
Fermion-Boson Interactions and Quantum Algebras
Quantum Algebras (q-algebras) are used to describe interactions between
fermions and bosons. Particularly, the concept of a su_q(2) dynamical symmetry
is invoked in order to reproduce the ground state properties of systems of
fermions and bosons interacting via schematic forces. The structure of the
proposed su_q(2) Hamiltonians, and the meaning of the corresponding deformation
parameters, are discussed.Comment: 20 pages, 10 figures. Physical Review C (in press
Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations
The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl
J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian
augmented by a non-Hermitian -symmetric part, is re-examined in the
light of an su(1,1) approach. An alternative derivation, only relying on
properties of su(1,1) generators, is proposed. Being independent of the
realization considered for the latter, it opens the way towards the
construction of generalized non-Hermitian (not necessarily -symmetric)
oscillator Hamiltonians related by similarity to Hermitian ones. Some examples
of them are reviewed.Comment: 11 pages, no figure; changes in title and in paragraphs 3 and 5;
final published versio
Analysis of the Strong Coupling Limit of the Richardson Hamiltonian using the Dyson Mapping
The Richardson Hamiltonian describes superconducting correlations in a
metallic nanograin. We do a perturbative analysis of this and related
Hamiltonians, around the strong pairing limit, without having to invoke Bethe
Ansatz solvability. Rather we make use of a boson expansion method known as the
Dyson mapping. Thus we uncover a selection rule that facilitates both
time-independent and time-dependent perturbation expansions. In principle the
model we analise is realised in a very small metalic grain of a very regular
shape. The results we obtain point to subtleties sometimes neglected when
thinking of the superconducting state as a Bose-Einstein condensate. An
appendix contains a general presentation of time-independent perturbation
theory for operators with degenerate spectra, with recursive formulas for
corrections of arbitrarily high orders.Comment: New final version accepted for publication in PRB. 17 two-column
pages, no figure
Moyal products -- a new perspective on quasi-hermitian quantum mechanics
The rationale for introducing non-hermitian Hamiltonians and other
observables is reviewed and open issues identified. We present a new approach
based on Moyal products to compute the metric for quasi-hermitian systems. This
approach is not only an efficient method of computation, but also suggests a
new perspective on quasi-hermitian quantum mechanics which invites further
exploration. In particular, we present some first results which link the Berry
connection and curvature to non-perturbative properties and the metric.Comment: 14 pages. Submitted to J Phys A special issue on The Physics of
Non-Hermitian Operator
On Pseudo-Hermitian Hamiltonians and Their Hermitian Counterparts
In the context of two particularly interesting non-Hermitian models in
quantum mechanics we explore the relationship between the original Hamiltonian
H and its Hermitian counterpart h, obtained from H by a similarity
transformation, as pointed out by Mostafazadeh. In the first model, due to
Swanson, h turns out to be just a scaled harmonic oscillator, which explains
the form of its spectrum. However, the transformation is not unique, which also
means that the observables of the original theory are not uniquely determined
by H alone. The second model we consider is the original PT-invariant
Hamiltonian, with potential V=igx^3. In this case the corresponding h, which we
are only able to construct in perturbation theory, corresponds to a complicated
velocity-dependent potential. We again explore the relationship between the
canonical variables x and p and the observables X and P.Comment: 9 pages, no figure
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