A modified Bogoliubov method applied to a simple boson model

O. Litt, W. H. Bassichis

Texas A&M University, College Station, Texas, United States of America

Abstract: We use a non-gauge-invariant modification of the exact Hamiltonian to obtain a new Hamiltonian-like operator for a simple exactly solvable boson model. The eigenvalues of the new operator are close to those of the original Hamiltonian. We make a one-body approximation of the new two-body operator in the spirit of the Bogoliubov approximation. Because only the number operator appears, the $c$-number approximation is not required individually for the creation or annihilation operators in the ground state. For the simple model, the results using the new approximation are closer to the exact results than the usual Bogoliubov results over a wide range of parameters. The improvement increases dramatically as the model interaction strength increases.

Keywords: modified Bogoliubov approximation.

Received: 23.10.2015
Revised: 19.04.2016

DOI: 10.4213/tmf9088

 English version: Theoretical and Mathematical Physics, 2017, 190:1, 109–119

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