2018/08/23 by Tomoya Hayata, Hayata, Tomoya, Yoshimasa Hidaka +1 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Nonlinear Photonic Systems #Quantum Gases (cond-mat.quant-gas) #Quantum optics and atomic interactions #cond-mat.mes-hall #cond-mat.quant-gas #hep-ph #hep-th
paper · pdf · doi:10.48550/arxiv.1808.07636
5+4 pages, 4+1 figures
arxiv created 2018/08/23 · openalex publication_date 2018/08/23 · arxiv updated 2018/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ω=-iC\bm p2. We also show that noncommutative breaking of the time-translation and U(1) symmetries results in mixing of the NG modes, and the (typically) propagating NG mode appears, whose dispersion relation becomes ω=(± C1-iC2)\bm p2.