Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2005-12-14
Annals Phys. 321 (2006) 1892-1917
Physics
Condensed Matter
Strongly Correlated Electrons
Accepted for publication in Ann. Phys., 33pages
Scientific paper
10.1016/j.aop.2005.12.009
We construct an approximate scheme based on the concept of the spontaneous symmetry breakdown, satisfying the Goldstone theorem, for finite volume Bose-Einstein condensed gases in both zero and finite temperature cases. In this paper, we discuss the Bose-Einstein condensation in a box with periodic boundary condition and do not assume the thermodynamic limit. When energy spectrum is discrete, we found that it is necessary to deal with the Nambu-Goldstone mode explicitly without the Bogoliubov's prescription, in which zero-mode creation- and annihilation-operators are replaced with a {\it c}-number by hand, for satisfying the Goldstone theorem. Furthermore, we confirm that the unitary inequivalence of vacua in the spontaneous symmetry breakdown is true for the finite volume system.
Enomoto Hiroaki
Okumura Masahiko
Yamanaka Yoshiya
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