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Many-body study of pair correlations and elementary excitations in the interacting bose system

Thaddeus V. Samulski

Published Jul 1, 1976• 0 citations
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Some properties of a two-dimensional charged Bose gas interacting with a ln(r) potential are investigated on the basis of a self-consistent-field formalism which includes the short-range correlations between bosons through a local-field correction depending on the pair correlation function. Numerical results for the static structure factor, pair correlation function, spectrum of elementary excitations, and the response of the system to a static impurity charge are presented. Our results show the same qualitative behavior as those of the three-dimensional analog but the correlation effects are somewhat more pronounced in two dimensions.
We expand the Hamiltonian of a weakly interacting Bose system to second order in the Bose operators of the elementary excitations and use the mean-field approximation to linearize it. It is found that the dynamical algebra of the ``pairing'' approximated Hamiltonian is SU(1,1) algebra. By using the generalized SU(1,1) coherent-state theory we show that both the condensate states and the weakly excited states are generalized SU(1,1) coherent states. Based on these states, the quantum fluctuations and the second-order correlation functions of the Bose system are calculated and discussed.
A variational method is developed for calculating the thermodynamic potential of quantum-mechanical many-body systems with pair-wise interactions. The method is based on Peierls' theorem and yields an upper bound to the thermodynamic potential density in the limit of an infinite system. Evaluation and minimization of the bound involves solution of a set of coupled nonlinear integral equations for the distribution function of elementary excitations and for functions defining a unitary transformation from bare particles to elementary excitations. Application of the theory to the BCS model of superconductivity reproduces the BCS results, and application to a degenerate imperfect Bose gas gives equations which are shown to be equivalent to those of Tolmachev and Wentzel.