304 research outputs found
Recursively minimally-deformed oscillators
A recursive deformation of the boson commutation relation is introduced. Each
step consists of a minimal deformation of a commutator
[a,\ad]=f_k(\cdots;\no) into [a,\ad]_{q_{k+1}}=f_k(\cdots;\no), where
stands for the set of deformation parameters that depends on,
followed by a transformation into the commutator [a,\ad]=f_{k+1}(\cdots,\,
q_{k+1};\no) to which the deformed commutator is equivalent within the Fock
space. Starting from the harmonic oscillator commutation relation [a,\ad]=1
we obtain the Arik-Coon and the Macfarlane-Biedenharn oscillators at the first
and second steps, respectively, followed by a sequence of multiparameter
generalizations. Several other types of deformed commutation relations related
to the treatment of integrable models and to parastatistics are also obtained.
The ``generic'' form consists of a linear combination of exponentials of the
number operator, and the various recursive families can be classified according
to the number of free linear parameters involved, that depends on the form of
the initial commutator.Comment: 19 pages, LateX, no figur
On an Alternative Parametrization for the Theory of Complex Spectra
The purpose of this letter is threefold : (i) to derive, in the framework of
a new parametrization, some compact formulas of energy averages for the
electrostatic interaction within an (nl)N configuration, (ii) to describe a new
generating function for obtaining the number of states with a given spin
angular momentum in an (nl)N configuration, and (iii) to report some apparently
new sum rules, actually a by-product of (i), for SU(2) > U(1) coupling
coefficients.Comment: Published in Physics Letters A 147, 417-422 (1990
Wick's theorem for q-deformed boson operators
In this paper combinatorial aspects of normal ordering arbitrary words in the
creation and annihilation operators of the q-deformed boson are discussed. In
particular, it is shown how by introducing appropriate q-weights for the
associated ``Feynman diagrams'' the normally ordered form of a general
expression in the creation and annihilation operators can be written as a sum
over all q-weighted Feynman diagrams, representing Wick's theorem in the
present context.Comment: 9 page
Quantum defect asymptotics at the critical charge: A study of the integrality conjecture
A single (n, ℓ) electron outside an (N −1)-electron atomic core is bound as long as Z > Zc = N − 1. A conjecture is examined, according to which the quantum defect of the outermost electron satisfies limZ!Zc δn,ℓ(Z) = Nℓ, where Nℓ is the number of occupied or partially occupied orbitals with angular momentum quantum number ℓ within the (N − 1)-electron core. Specifically, the 3s quantum defect is inspected for the different occupancies of the n = 1 and n = 2 shells. The conjecture is found to hold in all the cases considered
Number of states with fixed angular momentum for identical fermions and bosons
We present in this paper empirical formulas for the number of angular
momentum I states for three and four identical fermions or bosons. In the cases
with large I we prove that the number of states with the same and n
but different J is identical if for fermions
and for bosons, and that the number of states is also identical
for the same but different n and J if min(n, 2J+1 -
n) for fermions and for min(n, 2J) for bosons. Here , n is the particle number, and J refers to the angular momentum of
a single-particle orbit for fermions, or the spin L carried by bosons.Comment: 9 pages, no figure
Normal Ordering for Deformed Boson Operators and Operator-valued Deformed Stirling Numbers
The normal ordering formulae for powers of the boson number operator
are extended to deformed bosons. It is found that for the `M-type'
deformed bosons, which satisfy , the
extension involves a set of deformed Stirling numbers which replace the
Stirling numbers occurring in the conventional case. On the other hand, the
deformed Stirling numbers which have to be introduced in the case of the
`P-type' deformed bosons, which satisfy , are found to depend on the operator . This distinction
between the two types of deformed bosons is in harmony with earlier
observations made in the context of a study of the extended
Campbell-Baker-Hausdorff formula.Comment: 14 pages, Latex fil
Representation-theoretic derivation of the Temperley-Lieb-Martin algebras
Explicit expressions for the Temperley-Lieb-Martin algebras, i.e., the
quotients of the Hecke algebra that admit only representations corresponding to
Young diagrams with a given maximum number of columns (or rows), are obtained,
making explicit use of the Hecke algebra representation theory. Similar
techniques are used to construct the algebras whose representations do not
contain rectangular subdiagrams of a given size.Comment: 12 pages, LaTeX, to appear in J. Phys.
Negative Binomial States of the Radiation Field and their Excitations are Nonlinear Coherent States
We show that the well-known negative binomial states of the radiation field
and their excitations are nonlinear coherent states. Excited nonlinear coherent
state are still nonlinear coherent states with different nonlinear functions.
We finally give exponential form of the nonlinear coherent states and remark
that the binomial states are not nonlinear coherent states.Comment: 10 pages, no figure
Dobiński relations and ordering of boson operators
We introduce a generalization of the Dobiński relation, through which we define a family of Bell-type numbers and polynomials. Such generalized Dobiński relations are coherent state matrix elements of expressions involving boson ladder operators. This may be used in order to obtain normally ordered forms of polynomials in creation and annihilation operators, both if the latter satisfy canonical and deformed commutation relations
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