14,484 research outputs found
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
Combinatorial Physics, Normal Order and Model Feynman Graphs
The general normal ordering problem for boson strings is a combinatorial
problem. In this note we restrict ourselves to single-mode boson monomials.
This problem leads to elegant generalisations of well-known combinatorial
numbers, such as Bell and Stirling numbers. We explicitly give the generating
functions for some classes of these numbers. Finally we show that a graphical
representation of these combinatorial numbers leads to sets of model field
theories, for which the graphs may be interpreted as Feynman diagrams
corresponding to the bosons of the theory. The generating functions are the
generators of the classes of Feynman diagrams.Comment: 9 pages, 4 figures. 12 references. Presented at the Symposium
'Symmetries in Science XIII', Bregenz, Austria, 200
Predictions of spray combustion interactions
Mean and fluctuating phase velocities; mean particle mass flux; particle size; and mean gas-phase Reynolds stress, composition and temperature were measured in stationary, turbulent, axisymmetric, and flows which conform to the boundary layer approximations while having well-defined initial and boundary conditions in dilute particle-laden jets, nonevaporating sprays, and evaporating sprays injected into a still air environment. Three models of the processes, typical of current practice, were evaluated. The local homogeneous flow and deterministic separated flow models did not provide very satisfactory predictions over the present data base. In contrast, the stochastic separated flow model generally provided good predictions and appears to be an attractive approach for treating nonlinear interphase transport processes in turbulent flows containing particles (drops)
Structure of Evaporating and Combusting Sprays: Measurements and Predictions
Complete measurements of the structure of nonevaporating, evaporating and combusting sprays for sufficiently well defined boundary conditions to allow evaluation of models of these processes were obtained. The development of rational design methods for aircraft combustion chambers and other devices involving spray combustion were investigated. Three methods for treating the discrete phase are being considered: a locally homogeneous flow (LHF) model, a deterministic separated flow (DSF) model, and a stochastic separated flow (SSF) model. The main properties of these models are summarized
Hopf Algebras in General and in Combinatorial Physics: a practical introduction
This tutorial is intended to give an accessible introduction to Hopf
algebras. The mathematical context is that of representation theory, and we
also illustrate the structures with examples taken from combinatorics and
quantum physics, showing that in this latter case the axioms of Hopf algebra
arise naturally. The text contains many exercises, some taken from physics,
aimed at expanding and exemplifying the concepts introduced
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
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
Laguerre-type derivatives: Dobinski relations and combinatorial identities
We consider properties of the operators D(r,M)=a^r(a^\dag a)^M (which we call
generalized Laguerre-type derivatives), with r=1,2,..., M=0,1,..., where a and
a^\dag are boson annihilation and creation operators respectively, satisfying
[a,a^\dag]=1. We obtain explicit formulas for the normally ordered form of
arbitrary Taylor-expandable functions of D(r,M) with the help of an operator
relation which generalizes the Dobinski formula. Coherent state expectation
values of certain operator functions of D(r,M) turn out to be generating
functions of combinatorial numbers. In many cases the corresponding
combinatorial structures can be explicitly identified.Comment: 14 pages, 1 figur
- …