Some useful combinatorial formulae for bosonic operators

Details Some useful combinatorial formulae for bosonic operators Some useful combinatorial formulae for bosonic operators

2004-05-18

arxiv.org/abs/quant-ph/0405103v2

Journal of Mathematical Physics 46: 052110 (2005)

Physics

Quantum Physics

8 pages, 3 figures, 17 references

Scientific paper

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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