Some useful combinatorial formulas for bosonic operators

Blasiak, P.; Penson, K.A.; Solomon, A.I.; Horzela, A. and Duchamp, G.H.E. (2005). Some useful combinatorial formulas for bosonic operators. Journal of Mathematical Physics, 46(5)

DOI: https://doi.org/10.1063/1.1904161

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Abstract

We give a general expression for the normally ordered form of a function F[w(a,a⁺)] where w is a function of boson annihilation and creation operators satisfying [a,a⁺]=1. The expectation value of this expression in a coherent state becomes an exact generating function of Feynman-type graphs associated with the zero-dimensional Quantum Field Theory defined by F(w). This enables one to enumerate explicitly the graphs of given order in the realm of combinatorially defined sequences. We give several examples of the use of this technique, including the applications to Kerr-type and superfluidity-type Hamiltonians.

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• Item ORO ID
• 4826
• Item Type
• Journal Item
• ISSN
• 0022-2488
• Extra Information
• Copyright held by the American Institute of Physics.
• Keywords
• differential dynamical systems; differential operators; Hamilton-Jacobi equations; Hamiltonian systems; Stochastic processes; superfluidity
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Physical Sciences
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
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• Users 6042 not found.