Generalized Bargmann functions, their growth and von Neumann lattices

Generalized Bargmann representations which are based on generalized coherent states are considered. The growth of the corresponding analytic functions in the complex plane is studied. Results about the overcompleteness or undercompleteness of discrete sets of these generalized coherent states are given. Several examples are discussed in detail.Comment: 9 pages, changes with respect to previous version: typos removed, improved presentatio

Coherent pairing states for the Hubbard model

We consider the Hubbard model and its extensions on bipartite lattices. We define a dynamical group based on the $\eta$-pairing operators introduced by C.N.Yang, and define coherent pairing states, which are combinations of eigenfunctions of $\eta$-operators. These states permit exact calculations of numerous physical properties of the system, including energy, various fluctuations and correlation functions, including pairing ODLRO to all orders. This approach is complementary to BCS, in that these are superconducting coherent states associated with the exact model, although they are not eigenstates of the Hamiltonian.Comment: 5 pages, RevTe

A product formula and combinatorial field theory

We treat the problem of normally ordering expressions involving the standard boson operators a, ay where [a; ay] = 1. We show that a simple product formula for formal power series | essentially an extension of the Taylor expansion | leads to a double exponential formula which enables a powerful graphical description of the generating functions of the combinatorial sequences associated with such functions | in essence, a combinatorial eld theory. We apply these techniques to some examples related to specic physical Hamiltonians

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

Chaotic diffusion of particles with finite mass in oscillating convection flows

Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor. The diffusion constants are numerically calculated for convection models with free and rigid boundary conditions.Comment: 5 figure

Hopf algebras: motivations and examples

This paper provides motivation as well as a method of construction for Hopf algebras, starting from an associative algebra. The dualization technique involved relies heavily on the use of Sweedler's dual

On certain non-unique solutions of the Stieltjes moment problem

We construct explicit solutions of a number of Stieltjes moment problems based on moments of the form (2rn)! and [(rn)!]2. It is shown using criteria for uniqueness and non-uniqueness (Carleman, Krein, Berg, Pakes, Stoyanov) that for r > 1 both forms give rise to non-unique solutions. Examples of such solutions are constructed using the technique of the inverse Mellin transform supplemented by a Mellin convolution. We outline a general method of generating non-unique solutions for moment problems

Dobinski-type relations: Some properties and physical applications

We introduce a generalization of the Dobinski relation through which we define a family of Bell-type numbers and polynomials. For all these sequences we find the weight function of the moment problem and give their generating functions. We provide a physical motivation of this extension in the context of the boson normal ordering problem and its relation to an extension of the Kerr Hamiltonian.Comment: 7 pages, 1 figur

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