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2018

Diffusive Nambu-Goldstone modes in quantum time-crystals

Hayata, Tomoya, Hidaka, Yoshimasa

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We study the Nambu-Goldstone (NG) modes associated with spontaneous breaking of the continuous time-translation symmetry.

To discuss a quantum time-crystal with the spontaneously-broken continuous time-translation symmetry, we introduce the van der Pol type nonlinear-friction to open quantum systems.
By considering small fluctuations around a time-periodic mean-field solution, we show that a gapless collective mode necessarily appears; this is nothing but the NG mode associated with a time crystal.
We show that its dispersion relation becomes $\omega=-iC\bm p^2$.

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