1,363 research outputs found
Coherent States from Combinatorial Sequences
We construct coherent states using sequences of combinatorial numbers such as
various binomial and trinomial numbers, and Bell and Catalan numbers. We show
that these states satisfy the condition of the resolution of unity in a natural
way. In each case the positive weight functions are given as solutions of
associated Stieltjes or Hausdorff moment problems, where the moments are the
combinatorial numbers.Comment: 4 pages, Latex; Conference 'Quantum Theory and Symmetries 2', Krakow,
Poland, July 200
Combinatorial coherent states via normal ordering of bosons
We construct and analyze a family of coherent states built on sequences of
integers originating from the solution of the boson normal ordering problem.
These sequences generalize the conventional combinatorial Bell numbers and are
shown to be moments of positive functions. Consequently, the resulting coherent
states automatically satisfy the resolution of unity condition. In addition
they display such non-classical fluctuation properties as super-Poissonian
statistics and squeezing.Comment: 12 pages, 7 figures. 20 references. To be published in Letters in
Mathematical Physic
Densities of the Raney distributions
We prove that if and then the sequence
, , is positive definite, more
precisely, is the moment sequence of a probability measure with
compact support contained in . This family of measures encompasses
the multiplicative free powers of the Marchenko-Pastur distribution as well as
the Wigner's semicircle distribution centered at . We show that if
is a rational number, , then is absolutely continuous and
its density can be expressed in terms of the Meijer and the
generalized hypergeometric functions. In some cases, including the
multiplicative free square and the multiplicative free square root of the
Marchenko-Pastur measure, turns out to be an elementary function
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