In this work we introduce {\it boundary time-crystals}. Here {\it continuous} time-translation symmetry breaking occurs only in a macroscopic fraction of a many-body quantum system. After introducing their definition and properties, we analyse in detail a solvable model where an accurate scaling analysis can be performed. The existence of the boundary time crystals is intimately connected to the emergence of a time-periodic steady state in the thermodynamic limit of a many-body open quantum system. We also discuss connections to quantum synchronisation.
Non-Resonant Boundary Time Crystals from Quantum Synchronization Breakdown
Shenzhen Technology University（深圳理工大学）；RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学中心）；Quantum Science Center of Guangdong-Hongkong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；Renmin University of China（中国人民大学）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Boundary Time Crystals Induced by Local Dissipation and Long-Range Interactions
Tsinghua University（清华大学）；State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University（清华大学物理系低维量子物理国家重点实验室）；Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；LPTMS（理论与统计物理实验室）；Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所尼尔斯·玻尔国际学院）；University of Copenhagen（哥本哈根大学）；Clarendon Laboratory, University of Oxford（牛津大学克拉伦登实验室）；University of Oxford（牛津大学）；Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）；University of Innsbruck（因斯布鲁克大学）；Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences（奥地利科学院量子光学和量子信息研究所）
The Boundary Time Crystal as a light source for collectively enhanced sensing
Universität Tübingen（蒂宾根大学）；The University of Nottingham（诺丁汉大学）；Institute for Cross-Disciplinary Physics and Complex Systems (IFISC) UIB-CSIC（跨学科物理与复杂系统研究所（IFISC）巴伊利亚大学-西班牙国家科研委员会）
