Dynamics of spontaneous symmetry breaking in a space-time crystal

We present the theory of spontaneous symmetry breaking (SSB) of discrete time translations as recently realized in the space-time crystals of an atomic Bose-Einstein condensate. The non-equilibrium physics related to such a driven-dissipative system is discussed in both the Langevin as well as the F...

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Bibliographic Details
Published in:arXiv.org 2021-07
Main Authors: Stehouwer, J N, Smits, J, van der Straten, P, Stoof, H T C
Format: Article
Language:English
Subjects:
Bose-Einstein condensates
Broken symmetry
Crystals
Equilibrium
Fokker-Planck equation
Relativity
Spacetime
Symmetry
Translations
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Summary:We present the theory of spontaneous symmetry breaking (SSB) of discrete time translations as recently realized in the space-time crystals of an atomic Bose-Einstein condensate. The non-equilibrium physics related to such a driven-dissipative system is discussed in both the Langevin as well as the Fokker-Planck formulation. We consider a semi-classical and a fully quantum approach, depending on the dissipation being either frequency independent or linearly dependent on frequency, respectively. For both cases, the Langevin equation and Fokker-Planck equation are derived, and the resulting equilibrium distribution is studied. We also study the time evolution of the space-time crystal and focus in particular on its formation and the associated dynamics of the spontaneous breaking of a Z2 symmetry out of the symmetry unbroken phase, i.e., the equilibrium Bose-Einstein condensate before the periodic drive is turned on. Finally, we compare our results with experiments and conclude that our theory provides a solid foundation for the observations.
ISSN:2331-8422
DOI:10.48550/arxiv.2107.14505