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Journal of Mathematical Physics

A simple derivation of a closed formula for Bogoliubov boson transformations

Apolodor Aristotel Raduta, M. Badea, E. Badralexe

Published Apr 1, 1977• 7 citations
Publisher

Abstract

Considering the states with an arbitrary number of bosons and their transformed states under Bogoliubov transformations as wavefunctions of an oscillator type, a very simple derivation for the matrix elements of the Bogoliubov transformations is given.
DOI
10.1063/1.523320

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The paper considers quantal many-boson systems that are described by a rotationally invariant and boson-number conserving Hamiltonian. The properties of a generic model are studied which treats N bosons of p different kinds with non-zero angular momenta l_1,l_2,...,l_p, possibly augmented with a (number of) scalar s boson(s). The order k of the interaction between the bosons is arbitrary and closed formulas are given for matrix elements between N-boson states for any k if p=1 and p=2. A recursive procedure is defined for arbitrary k and p. With the expressions derived in the paper it is possible to express symbolically a Hamiltonian matrix element between N-boson states as a linear combination of k-body interaction matrix elements. More generally, the formulas allow the evaluation of matrix elements of tensor operators that are not necessarily scalar nor boson-number conserving. The numerical implementation of the formalism is discussed and illustrated with a few examples.