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Exponential Operators, Dobiński Relations and Summability

Paweł Błasiak, A Gawron, A Horzela +2 more

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 Dobiński 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 Padé 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.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 Dobiński 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 Padé 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.

arXiv:quant-ph/0510080Journal of Physics Conference SeriesApr 1, 20061 citation

Order in Boson Systems

Alan Coleman, Vyacheslav I. Yukalov

Lecture notes in chemistryJan 1, 20000 citations

Normal and antinormal ordering of boson operator functions

B. L. Willis, Paul F. Zweifel

Physics Letters AApr 1, 19851 citation

Exponential Operators, Dobinski Relations and Summability

Paweł Błasiak, Agnieszka Gawron, A. Horzela +2 more

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.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.

Oct 12, 20051 citation

Combinatorics of Boson Normal Ordering: the Dobinski Formula Revisited

K. A. Penson, A. I. Solomon

We derive explicit formulas for the normal ordering of powers of arbitrary monomials of boson operators. These formulas lead to generalisations of conventional Bell and Stirling numbers and to appropriate generalisations of the Dobinski relations. These new combinatorial numbers are shown to be coherent state matrix elements of powers of the monomials in question. It is further demonstrated that such Bell-type numbers, when considered as power moments, give rise to positive measures on the positive half-axis, which in many cases can be written in terms of known functions.We derive explicit formulas for the normal ordering of powers of arbitrary monomials of boson operators. These formulas lead to generalisations of conventional Bell and Stirling numbers and to appropriate generalisations of the Dobinski relations. These new combinatorial numbers are shown to be coherent state matrix elements of powers of the monomials in question. It is further demonstrated that such Bell-type numbers, when considered as power moments, give rise to positive measures on the positive half-axis, which in many cases can be written in terms of known functions.

arXiv:quant-ph/0211028Nov 6, 20020 citations

Effective operator theory in boson mappings

P. Navrátil, H. B. Geyer

Nuclear Physics AMay 1, 199313 citations

Dobiński relations and ordering of boson operators

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