123 research outputs found
A faster algorithm for computing a longest common increasing subsequence
Let and be two sequences with , whose elements are drawn from a totally ordered set. We present an algorithm that finds a longest common increasing subsequence of and in time and space, where is the length of the output. A previous algorithm by Yang et al. needs time and space, so ours is faster for a wide range of values of and
Group Theoretical Approach To Squeezed States Using Generalized Bose Operators
Generalized, k-boson Holstein-Primakoff realizations of SU(2) and SU(1,1) are introduced In terms of generalized bose operators. The corresponding group theoretical coherent states are studied with respect to their squeezing properties relative to k-boson dynamical variables
Generalized Holstein-Primakoff Squeezed States for SU(n)
We show how to define multi-photon, many-mode squeezed states for SU(n), using a generalized Holstein-Primakoff realization. We prove that for the class of realizations given, the resulting squeezing reduces to that of SU(2), and exemplify with a specific calculation for SU(3)
DobiĆski relations and ordering of boson operators
We introduce a generalization of the DobiĆski relation, through which we define a family of Bell-type numbers and polynomials. Such generalized DobiĆski 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
Exponential Operators, Dobinski Relations and Summability
We investigate properties of exponential operators preserving the particle
number using combinatorial methods developed in order to solve the boson normal
ordering problem. In particular, we apply generalized Dobinski relations and
methods of multivariate Bell polynomials which enable us to understand the
meaning of perturbation-like expansions of exponential operators. Such
expansions, obtained as formal power series, are everywhere divergent but the
Pade summation method is shown to give results which very well agree with exact
solutions got for simplified quantum models of the one mode bosonic systems.Comment: Presented at XIIth Central European Workshop on Quantum Optics,
Bilkent University, Ankara, Turkey, 6-10 June 2005. 4 figures, 6 pages, 10
reference
Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator
In this paper, we investigate the relation between the curvature of the
physical space and the deformation function of the deformed oscillator algebra
using non-linear coherent states approach. For this purpose, we study
two-dimensional harmonic oscillators on the flat surface and on a sphere by
applying the Higgs modell. With the use of their algebras, we show that the
two-dimensional oscillator algebra on a surface can be considered as a deformed
one-dimensional oscillator algebra where the effect of the curvature of the
surface is appeared as a deformation function. We also show that the curvature
of the physical space plays the role of deformation parameter. Then we
construct the associated coherent states on the flat surface and on a sphere
and compare their quantum statistical properties, including quadrature
squeezing and antibunching effect.Comment: 12 pages, 7 figs. To be appeared in J. Phys.
Combinatorial Solutions to Normal Ordering of Bosons
We present a combinatorial method of constructing solutions to the normal
ordering of boson operators. Generalizations of standard combinatorial notions
- the Stirling and Bell numbers, Bell polynomials and Dobinski relations - lead
to calculational tools which allow to find explicitly normally ordered forms
for a large class of operator functions.Comment: Presented at 14th Int. Colloquium on Integrable Systems, Prague,
Czech Republic, 16-18 June 2005. 6 pages, 11 reference
Hierarchical Dobinski-type relations via substitution and the moment problem
We consider the transformation properties of integer sequences arising from
the normal ordering of exponentiated boson ([a,a*]=1) monomials of the form
exp(x (a*)^r a), r=1,2,..., under the composition of their exponential
generating functions (egf). They turn out to be of Sheffer-type. We demonstrate
that two key properties of these sequences remain preserved under
substitutional composition: (a)the property of being the solution of the
Stieltjes moment problem; and (b) the representation of these sequences through
infinite series (Dobinski-type relations). We present a number of examples of
such composition satisfying properties (a) and (b). We obtain new Dobinski-type
formulas and solve the associated moment problem for several hierarchically
defined combinatorial families of sequences.Comment: 14 pages, 31 reference
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