Spontaneous Symmetry Breaking and Higgs Mode: Comparing Gross-Pitaevskii and Nonlinear Klein-Gordon Equations

Year: 2018

Authors: Faccioli M., Salasnich L.

Autors Affiliation: Univ Padua, Dipartimento Fis & Astron Galileo Galilei, Via Marzolo 8, I-35131 Padua, Italy; CNR, INO, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy.

Abstract: We discuss the mechanism of spontaneous symmetry breaking and the elementary excitations for a weakly-interacting Bose gas at a finite temperature. We consider both the non-relativistic case, described by the Gross-Pitaevskii equation, and the relativistic one, described by the cubic nonlinear Klein-Gordon equation. We analyze similarities and differences in the two equations and, in particular, in the phase and amplitude modes (i.e., Goldstone and Higgs modes) of the bosonic matter field. We show that the coupling between phase and amplitude modes gives rise to a single gapless Bogoliubov spectrum in the non-relativistic case. Instead, in the relativistic case the spectrum has two branches: one is gapless and the other is gapped. In the non-relativistic limit we find that the relativistic spectrum reduces to the Bogoliubov one. Finally, as an application of the above analysis, we consider the Bose-Hubbard model close to the superfluid-Mott quantum phase transition and we investigate the elementary excitations of its effective action, which contains both non-relativistic and relativistic terms.

Journal/Review: Symmetry-Basel

Volume: 10 (4)      Pages from: 80-1  to: 80-15

More Information: Luca Salasnich acknowledges for partial support the 2016 BIRD project Superfluid properties of Fermi gases in optical potentials of the University of Padova.
KeyWords: superfluidity; Gross-Pitaevskii equation; nonlinear Klein-Gordon equation; Higgs mode; Bose-Hubbard model
DOI: 10.3390/sym10040080

Citations: 8
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