The Gaussian Approximation to Homogeneous Bose Gas
We study low-lying excitations of a spinless homogeneous Bose gas with repulsive interaction at zero temperature in terms of the Gaussian mean field approximation. The dynamical equations of this approximation have been derived for small displacements from the static Hartree-Fock-Bogoliubov solution. We obtain a gapped continuous band of excitations above a discrete branch with phonon behavior at long wavelength regime. We also discuss the available forms of excitations and conclude that there are constraints on the first order deviations of the Gaussian approximation parameters and they are generated by an infinitesimal unitary transformation.
KeywordsBose-Einstein condensation Quantum gases Mean field theories
The authors would like to thank A. F. R. de Toledo Piza for introducing the subject as well as discussion. This work was supported by the FAPESP and CNPq.
- 9.J.P. Blaizot, G. Ripka, Quantum Theory of Finite Systems (MIT Press, Cambridge, 1986) Google Scholar
- 11.H. Shi, A. Griffin, Phys. Rep. 304(1) (1998) Google Scholar
- 17.L.D. Landau, E.M. Lifshitz, Statistical Physics, Part 1, 3rd edn., vol. 5 (Butterworth-Heinemann, Oxford, 1980) Google Scholar
- 26.A.L. Fetter, J.D. Walecka, Quantum Theory of Many Particle Systems (Dover, New York, 2003) Google Scholar
- 31.L.D. Landau, E.M. Lifshitz, Quantum Mechanics Non-relativistic Theory, 3rd edn., vol. 3 (Butterworth-Heinemann, Oxford, 1981) Google Scholar
- 32.W.H. Press, B.P. Flannery, S.A. Teukolski, W.T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, Cambridge, 1992) Google Scholar