时间晶体
时间晶体(英语:time crystal)乃一开放系统,其与周围环境保持非平衡态,呈现时间平移对称破缺(英语:time translation symmetry breaking)的特性。2017年3月的科学报导指出,此一理论概念已在实验上获得证实;随着时间演进,时间晶体仍无法与环境达到热平衡。[1][2]
时间晶体的概念首先由诺贝尔物理学奖得主弗朗克·韦尔切克于2012年提出。相对于寻常晶体在空间上呈周期性重复,时间晶体则在时间上呈周期性重复而呈现永动状态。时间晶体在时间平移对称上具有自发对称破缺现象。时间晶体也与零点能量和动态卡西米尔效应有关。
2016年,姚颖(英语:Norman Y. Yao)与加州大学柏克莱分校物理系的同僚提出在实验室建构时间晶体的蓝图[3];随后此蓝图经两组人马采用,包括马里兰大学的Christopher Monroe以及哈佛大学的Mikhail Lukin,两团队皆成功创造出时间晶体,实验成果于2017年3月发表在《自然》期刊。[4][5]
常规晶体是一个三维物体,它们的内部原子按照有规则的顺序重复排列而构成。时间晶体是一种四维以上晶体,在时空中拥有一种周期性结构。 一个时间晶体能自发破坏时间平移的对称性,做空间的非平移运动,时间晶体的构成以‘空间’非定域的粒子交叉存在做相互关联运动,是能效粒子的‘额外维’超出‘定域空间’的能动量,时间晶体的存在同样揭示了‘超额外维度’的存在意义。
它可以随着时间改变,但是会持续回到它开始时的相同形态,就如一个钟的移动的指针周期性的回到它的原始位置。与普通的钟或者其他周期性的过程不同的是,时间晶体和空间晶体一样会是最低限度的能量的一种状态。可以将它看作是一只可以永远保持走时精确无误的钟,即便是在宇宙达到热寂之后也是如此。
主要特点
编辑设计方法
编辑2012年7月,来自美国加州大学伯克利分校的李统藏博士以及他来自密歇根大学和清华大学的同事们提出了一种新的方案,有可能实现时间晶体的设想。
首先需要一个离子阱,这是一种利用电场来将某一带电粒子固定在某一位置上的装置。这样做将可以让这些离子形成一个环状的晶体,这是因为当离子在极低温度条件下被捕获时,它们会相互排斥。随后科学家施加一个微弱的静磁场,它将驱动电子自旋。
量子力学指出,离子的自旋能量必须大于0,即便是在这个电子环已经被冷冻至最低能级的情况下也是如此。在这种状态下,已经不需要电场和磁场来帮助维持这一晶体的形状以及组成它的各个离子的自旋。这样做的结果就是获得一个时间晶体,或者更准确的说是一个时空晶体,因为这个离子环不但在时间上,在空间上也是不断重复着自身。
研究人员从理论上推理认为,这种时间晶体可以被用作计算机,它可以用不同的自旋状态当做传统计算法中的0和1。利用该系统方案,这一设想将是可能的[6]
该方案是基于电场离子阱和粒子之间的库伦斥力构建的。离子阱的电场将带电粒子固定住,而库伦斥力让它们自发地形成一个空间环状晶体。在一个微弱的静态磁场作用下,这一环状离子晶体将开始永无止境的转动。由于这一时空晶体已经位于最低量子能态,其时间序列,从理论上说将会永远持续,即便是当宇宙达到熵的极大值,也就是达到“热寂”状态时,情况也是一样。
制造方法:将10个镱原子排成一列,然后用两束激光交替轰击它们,使得这些原子进入一种稳定且重复的自旋翻转模式,符合“时间晶体”的定义。另一个来自哈佛大学的研究团队则通过向钻石中密集充入氮气的方式,也制造出了“时间晶体”。
意义
编辑构建一个时空晶体,存在着实际和重要的科学理由:有了这种4维晶体,科学家们将拥有一种全新的,更加有效的手段对复杂的物理属性和大量粒子的复杂相互作用行为进行研究,或者是研究物理学中所谓的“多体问题”。这种时空晶体同样可以被用来对量子世界进行研究,如量子纠缠现象,在这种状态中,当对其中一个粒子进行操作时,另外一个粒子也会相应地发生变化,即便这两个粒子之间隔开着巨大的距离。
参考文献
编辑- ^ Ghose, Tia. Time Crystals Created, Suspending Laws of Physics. Live Science (Purch). 2017-03-08 [2017-03-16]. (原始内容存档于2021-03-18).
- ^ Researcher unveils time crystal as new form of matter. Xinhua English news. [2021-11-15]. (原始内容存档于2021-05-24).
- ^ "时间晶体"不再是科幻_ 中国青年网. [2021-11-15]. (原始内容存档于2021-11-17).
- ^ “时间晶体”不再是科幻 人民网. [2021-11-15]. (原始内容存档于2021-11-15).
- ^ Choi, Soonwon; Choi, Joonhee; Landig, Renate; Kucsko, Georg; Zhou, Hengyun; Isoya, Junichi; Jelezko, Fedor; Onoda, Shinobu; Sumiya, Hitoshi; Khemani, Vedika; von Keyserlingk, Curt; Yao, Norman Y.; Demler, Eugene; Lukin, Mikhail D. Observation of discrete time-crystalline order in a disordered dipolar many-body system (PDF). Nature. 2017, 543 (7644): 221–225 [2017-03-23]. Bibcode:2016arXiv161008057C. ISSN 0028-0836. arXiv:1610.08057v1 . doi:10.1038/nature21426. (原始内容存档 (PDF)于2019-05-10).
- ^ 科学家打造超宇宙寿命“时空晶体”. 科学探索_科技时代:新浪网. [2019-04-20]. (原始内容存档于2019-06-04).
延伸阅读
编辑学术论文
编辑- Beck, Christian; Mackey, Michael C. Could dark energy be measured in the lab? (PDF). Physics Letters B. 2005, 605 (3–4): 295–300 [2021-03-28]. Bibcode:2005PhLB..605..295B. ISSN 0370-2693. arXiv:astro-ph/0406504v2 . doi:10.1016/j.physletb.2004.11.060. (原始内容存档 (PDF)于2019-10-15).
- Boyle, Latham; Khoo, Jun Yong; Smith, Kendrick. Symmetric Satellite Swarms and Choreographic Crystals (PDF). Physical Review Letters. 2016, 116 (1): 015503 [2021-03-28]. Bibcode:2016PhRvL.116a5503B. ISSN 0031-9007. PMID 26799028. arXiv:1407.5876v2 . doi:10.1103/PhysRevLett.116.015503. (原始内容存档 (PDF)于2017-02-11).
- Bruno, Patrick. Comment on "Quantum Time Crystals" (PDF). Physical Review Letters. 2013a, 110 (11): 118901 [2021-03-28]. Bibcode:2013PhRvL.110k8901B. ISSN 0031-9007. PMID 25166585. arXiv:1210.4128v1 . doi:10.1103/PhysRevLett.110.118901. (原始内容存档 (PDF)于2017-02-11).
- Bruno, Patrick. Comment on "Space-Time Crystals of Trapped Ions" (PDF). Physical Review Letters. 2013b, 111 (2) [2021-03-28]. Bibcode:2013PhRvL.111b9301B. ISSN 0031-9007. arXiv:1211.4792v1 . doi:10.1103/PhysRevLett.111.029301. (原始内容存档 (PDF)于2017-02-11).
- Campisi, Michele; Hänggi, Peter; Talkner, Peter. Colloquium: Quantum fluctuation relations: Foundations and applications (PDF). Reviews of Modern Physics. 2011, 83 (3): 771–791 [2021-03-28]. Bibcode:2011RvMP...83..771C. ISSN 0034-6861. arXiv:1012.2268v5 . doi:10.1103/RevModPhys.83.771. (原始内容存档 (PDF)于2019-01-27).
- Choi, Soonwon; Choi, Joonhee; Landig, Renate; Kucsko, Georg; Zhou, Hengyun; Isoya, Junichi; Jelezko, Fedor; Onoda, Shinobu; Sumiya, Hitoshi; Khemani, Vedika; von Keyserlingk, Curt; Yao, Norman Y.; Demler, Eugene; Lukin, Mikhail D. Observation of discrete time-crystalline order in a disordered dipolar many-body system (PDF). Nature. 2017, 543 (7644): 221–225 [2017-03-23]. Bibcode:2017Natur.543..221C. ISSN 0028-0836. arXiv:1610.08057v1 . doi:10.1038/nature21426. (原始内容存档 (PDF)于2019-05-10).
- Chernodub, M. N. Permanently rotating devices: extracting rotation from quantum vacuum fluctuations? (PDF). 2012 [2021-03-28]. Bibcode:2012arXiv1203.6588C. arXiv:1203.6588v1 . (原始内容存档 (PDF)于2019-10-24).
- Chernodub, M. N. Zero-point fluctuations in rotation: Perpetuum mobile of the fourth kind without energy transfer (PDF). Nuovo Cimento C. 2013a, 5 (36): 53–63 [2021-03-28]. Bibcode:2013arXiv1302.0462C. arXiv:1302.0462v1 . doi:10.1393/ncc/i2013-11523-5. (原始内容存档 (PDF)于2019-08-14).
- Chernodub, M. N. Rotating Casimir systems: Magnetic-field-enhanced perpetual motion, possible realization in doped nanotubes, and laws of thermodynamics (PDF). Physical Review D. 2013b, 87 (2) [2021-03-28]. Bibcode:2013PhRvD..87b5021C. ISSN 1550-7998. arXiv:1207.3052v2 . doi:10.1103/PhysRevD.87.025021. (原始内容存档 (PDF)于2019-10-23).
- Copeland, Edmund J.; Sami, M.; Tsujikawa, Shinji. Dynamics of dark energy (PDF). International Journal of Modern Physics D. 2006, 15 (11): 1753–1935 [2021-03-28]. Bibcode:2006IJMPD..15.1753C. ISSN 0218-2718. arXiv:hep-th/0603057 . doi:10.1142/S021827180600942X. (原始内容存档 (PDF)于2017-02-11).
- Dillenschneider, R.; Lutz, E. Energetics of quantum correlations (PDF). EPL. 2009, 88 (5): 50003 [2021-03-28]. Bibcode:2009EL.....8850003D. ISSN 0295-5075. arXiv:0803.4067 . doi:10.1209/0295-5075/88/50003. (原始内容存档 (PDF)于2019-10-01).
- Else, Dominic V.; Bauer, Bela; Nayak, Chetan. Floquet Time Crystals (PDF). Physical Review Letters. 2016, 117 (9): 090402 [2021-03-28]. Bibcode:2016PhRvL.117i0402E. ISSN 0031-9007. PMID 27610834. arXiv:1603.08001v4 . doi:10.1103/PhysRevLett.117.090402. (原始内容存档 (PDF)于2019-10-16).
- Esposito, Massimiliano; Harbola, Upendra; Mukamel, Shaul. Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems (PDF). Reviews of Modern Physics. 2009, 81 (4): 1665–1702 [2021-03-28]. Bibcode:2009RvMP...81.1665E. ISSN 0034-6861. arXiv:0811.3717v2 . doi:10.1103/RevModPhys.81.1665. (原始内容存档 (PDF)于2017-02-11).
- Grifoni, Milena; Hänggi, Peter. Driven quantum tunneling (PDF). Physics Reports. 1998, 304 (5–6): 229–354 [2021-03-28]. Bibcode:1998PhR...304..229G. ISSN 0370-1573. doi:10.1016/S0370-1573(98)00022-2. (原始内容 (PDF)存档于2017-02-11).
- Guo, Lingzhen; Marthaler, Michael; Schön, Gerd. Phase Space Crystals: A New Way to Create a Quasienergy Band Structure (PDF). Physical Review Letters. 2013, 111 (20) [2021-03-28]. Bibcode:2013PhRvL.111t5303G. ISSN 0031-9007. arXiv:1305.1800v3 . doi:10.1103/PhysRevLett.111.205303. (原始内容存档 (PDF)于2017-02-11).
- Hasan, M. Z.; Kane, C. L. Colloquium: Topological insulators (PDF). Reviews of Modern Physics. 2010, 82 (4): 3045–3067 [2021-03-28]. Bibcode:2010RvMP...82.3045H. ISSN 0034-6861. arXiv:1002.3895v2 . doi:10.1103/RevModPhys.82.3045. (原始内容存档 (PDF)于2017-02-11).
- Horodecki, Ryszard; Horodecki, Paweł; Horodecki, Michał; Horodecki, Karol. Quantum entanglement (PDF). Reviews of Modern Physics. 2009, 81 (2): 865–942 [2021-03-28]. Bibcode:2009RvMP...81..865H. ISSN 0034-6861. arXiv:quant-ph/0702225v2 . doi:10.1103/RevModPhys.81.865. (原始内容存档 (PDF)于2017-02-11).
- Jaffe, R. L. Casimir effect and the quantum vacuum (PDF). Physical Review D. 2005, 72 (2): 021301 [2021-03-28]. Bibcode:2005PhRvD..72b1301J. arXiv:hep-th/0503158 . doi:10.1103/PhysRevD.72.021301. (原始内容存档 (PDF)于2017-11-05).
- Jarzynski, Christopher. Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale (PDF). Annual Review of Condensed Matter Physics. 2011, 2 (1): 329–351 [2021-03-28]. Bibcode:2011ARCMP...2..329J. ISSN 1947-5454. doi:10.1146/annurev-conmatphys-062910-140506. (原始内容存档 (PDF)于2017-02-11).
- Jetzer, Philippe; Straumann, Norbert. Josephson junctions and dark energy (PDF). Physics Letters B. 2006, 639 (2): 57–58 [2021-03-28]. Bibcode:2006PhLB..639...57J. ISSN 0370-2693. arXiv:astro-ph/0604522 . doi:10.1016/j.physletb.2006.06.020. (原始内容存档 (PDF)于2019-01-27).
- Khemani, Vedika; Lazarides, Achilleas; Moessner, Roderich; Sondhi, S. L. Phase Structure of Driven Quantum Systems (PDF). Physical Review Letters. 2016, 116 (25) [2021-03-28]. Bibcode:2016PhRvL.116y0401K. ISSN 0031-9007. arXiv:1508.03344v3 . doi:10.1103/PhysRevLett.116.250401. (原始内容存档 (PDF)于2019-10-22).
- Lees, J. P. Observation of Time-Reversal Violation in the B0 Meson System (PDF). Physical Review Letters. 2012, 109 (21) [2021-03-28]. Bibcode:2012PhRvL.109u1801L. ISSN 0031-9007. arXiv:1207.5832v4 . doi:10.1103/PhysRevLett.109.211801. (原始内容存档 (PDF)于2019-01-27).
- Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang. Space-Time Crystals of Trapped Ions (PDF). Physical Review Letters. 2012a, 109 (16) [2021-03-28]. Bibcode:2012PhRvL.109p3001L. ISSN 0031-9007. arXiv:1206.4772v2 . doi:10.1103/PhysRevLett.109.163001. (原始内容存档 (PDF)于2017-02-11).
- Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang. Reply to Comment on "Space-Time Crystals of Trapped Ions" (PDF). 2012b [2021-03-28]. Bibcode:2012arXiv1212.6959L. arXiv:1212.6959v2 . (原始内容存档 (PDF)于2017-02-11).
- Lindner, Netanel H.; Refael, Gil; Galitski, Victor. Floquet topological insulator in semiconductor quantum wells (PDF). Nature Physics. 2011, 7 (6): 490–495 [2021-03-28]. Bibcode:2011NatPh...7..490L. ISSN 1745-2473. arXiv:1008.1792v2 . doi:10.1038/nphys1926. (原始内容存档 (PDF)于2019-10-13).
- Nadj-Perge, S.; Drozdov, I. K.; Li, J.; Chen, H.; Jeon, S.; Seo, J.; MacDonald, A. H.; Bernevig, B. A.; Yazdani, A. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor (PDF). Science. 2014, 346 (6209): 602–607 [2021-03-28]. Bibcode:2014Sci...346..602N. ISSN 0036-8075. PMID 25278507. arXiv:1410.0682v1 . doi:10.1126/science.1259327. (原始内容存档 (PDF)于2017-02-11).
- Nozières, Philippe. Time crystals: Can diamagnetic currents drive a charge density wave into rotation? (PDF). EPL. 2013, 103 (5): 57008 [2021-03-28]. Bibcode:2013EL....10357008N. ISSN 0295-5075. arXiv:1306.6229v1 . doi:10.1209/0295-5075/103/57008. (原始内容存档 (PDF)于2019-10-21).
- Sacha, Krzysztof. Modeling spontaneous breaking of time-translation symmetry (PDF). Physical Review A. 2015, 91 (3) [2021-03-28]. Bibcode:2015PhRvA..91c3617S. ISSN 1050-2947. arXiv:1410.3638v3 . doi:10.1103/PhysRevA.91.033617. (原始内容存档 (PDF)于2017-02-11).
- Schwinger, Julian. Casimir effect in source theory. Letters in Mathematical Physics. 1975, 1 (1): 43–47. Bibcode:1975LMaPh...1...43S. doi:10.1007/BF00405585.
- Schwinger, Julian; DeRaad, Lester L.; Milton, Kimball A. Casimir effect in dielectrics. Annals of Physics. 1978, 115 (1): 1–23. Bibcode:1978AnPhy.115....1S. doi:10.1016/0003-4916(78)90172-0.
- Scully, Marlan O. Extracting Work from a Single Thermal Bath via Quantum Negentropy. Physical Review Letters. 2001, 87 (22): 220601. Bibcode:2001PhRvL..87v0601S. ISSN 0031-9007. PMID 11736390. doi:10.1103/PhysRevLett.87.220601.
- Scully, Marlan O.; Zubairy, M. Suhail; Agarwal, Girish S.; Walther, Herbert. Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence. Science. 2003, 299 (5608): 862–864. Bibcode:2003Sci...299..862S. ISSN 0036-8075. PMID 12511655. doi:10.1126/science.1078955.
- Seifert, Udo. Stochastic thermodynamics, fluctuation theorems and molecular machines (PDF). Reports on Progress in Physics. 2012, 75 (12): 126001 [2021-03-28]. Bibcode:2012RPPh...75l6001S. ISSN 0034-4885. arXiv:1205.4176v1 . doi:10.1088/0034-4885/75/12/126001. (原始内容存档 (PDF)于2017-02-11).
- Senitzky, I. R. Dissipation in Quantum Mechanics. The Harmonic Oscillator. Physical Review. 1960, 119 (2): 670–679. Bibcode:1960PhRv..119..670S. ISSN 0031-899X. doi:10.1103/PhysRev.119.670.
- Shapere, Alfred; Wilczek, Frank. Classical Time Crystals (PDF). Physical Review Letters. 2012, 109 (16) [2021-03-28]. Bibcode:2012PhRvL.109p0402S. ISSN 0031-9007. arXiv:1202.2537v2 . doi:10.1103/PhysRevLett.109.160402. (原始内容存档 (PDF)于2017-02-11).
- Shirley, Jon H. Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time. Physical Review. 1965, 138 (4B): B979–B987. Bibcode:1965PhRv..138..979S. ISSN 0031-899X. doi:10.1103/PhysRev.138.B979.
- Smith, J.; Lee, A.; Richerme, P.; Neyenhuis, B.; Hess, P. W.; Hauke, P.; Heyl, M.; Huse, D. A.; Monroe, C. Many-body localization in a quantum simulator with programmable random disorder (PDF). Nature Physics. 2016, 12 (10): 907–911 [2021-03-28]. Bibcode:2016NatPh..12..907S. ISSN 1745-2473. arXiv:1508.07026v1 . doi:10.1038/nphys3783. (原始内容存档 (PDF)于2017-02-11).
- Maruyama, Koji; Nori, Franco; Vedral, Vlatko. Colloquium* The physics of Maxwell’s demon and information (PDF). Reviews of Modern Physics. 2009, 81 (1): 1–23 [2021-03-28]. Bibcode:2009RvMP...81....1M. ISSN 0034-6861. arXiv:0707.3400 . doi:10.1103/RevModPhys.81.1. (原始内容存档 (PDF)于2017-02-11).
- Mendonça, J. T.; Dodonov, V. V. Time Crystals in Ultracold Matter (PDF). Journal of Russian Laser Research. 2014, 35 (1): 93–100 [2021-03-28]. ISSN 1071-2836. doi:10.1007/s10946-014-9404-9. (原始内容存档 (PDF)于2018-06-23).
- Modi, Kavan; Brodutch, Aharon; Cable, Hugo; Paterek, Tomasz; Vedral, Vlatko. The classical-quantum boundary for correlations* Discord and related measures (PDF). Reviews of Modern Physics. 2012, 84 (4): 1655–1707 [2021-03-28]. Bibcode:2012RvMP...84.1655M. ISSN 0034-6861. arXiv:1112.6238 . doi:10.1103/RevModPhys.84.1655. (原始内容存档 (PDF)于2017-02-11).
- Ray, M. W.; Ruokokoski, E.; Kandel, S.; Möttönen, M.; Hall, D. S. Observation of Dirac monopoles in a synthetic magnetic field (PDF). Nature. 2014, 505 (7485): 657–660 [2021-03-28]. Bibcode:2014Natur.505..657R. ISSN 0028-0836. PMID 24476889. arXiv:1408.3133v1 . doi:10.1038/nature12954. (原始内容存档 (PDF)于2019-10-20).
- Ray, M. W.; Ruokokoski, E.; Tiurev, K.; Mottonen, M.; Hall, D. S. Observation of isolated monopoles in a quantum field (PDF). Science. 2015, 348 (6234): 544–547 [2021-03-28]. Bibcode:2015Sci...348..544R. ISSN 0036-8075. doi:10.1126/science.1258289. (原始内容存档 (PDF)于2017-08-08).
- Reimann, Peter; Grifoni, Milena; Hänggi, Peter. Quantum Ratchets (PDF). Physical Review Letters. 1997, 79 (1): 10–13 [2021-03-28]. Bibcode:1997PhRvL..79...10R. ISSN 0031-9007. doi:10.1103/PhysRevLett.79.10. (原始内容 (PDF)存档于2017-02-11).
- Roßnagel, J.; Abah, O.; Schmidt-Kaler, F.; Singer, K.; Lutz, E. Nanoscale Heat Engine Beyond the Carnot Limit (PDF). Physical Review Letters. 2014, 112 (3): 030602 [2021-03-28]. Bibcode:2014PhRvL.112c0602R. ISSN 0031-9007. PMID 24484127. arXiv:1308.5935 . doi:10.1103/PhysRevLett.112.030602. (原始内容存档 (PDF)于2016-06-16).
- Roßnagell, J.; Dawkins, S. T.; Tolazzi, K. N.; Abah, O.; Lutz, E.; Schmidt-Kaler, F.; Singer, K. A single-atom heat engine (PDF). Science. 2016, 352 (6283): 325–329 [2021-03-28]. Bibcode:2016Sci...352..325R. ISSN 0036-8075. arXiv:1510.03681 . doi:10.1126/science.aad6320. (原始内容存档 (PDF)于2017-02-11).
- Tatara, Gen; Kikuchi, Makoto; Yukawa, Satoshi; Matsukawa, Hiroshi. Dissipation Enhanced Asymmetric Transport in Quantum Ratchets (PDF). Journal of the Physical Society of Japan. 1998, 67 (4): 1090–1093 [2021-03-28]. Bibcode:1998JPSJ...67.1090T. ISSN 0031-9015. arXiv:cond-mat/9711045 . doi:10.1143/JPSJ.67.1090. (原始内容存档 (PDF)于2019-10-01).
- Volovik, G. E. On the broken time translation symmetry in macroscopic systems* Precessing states and off-diagonal long-range order (PDF). JETP Letters. 2013, 98 (8): 491–495 [2021-03-28]. Bibcode:2013JETPL..98..491V. ISSN 0021-3640. arXiv:1309.1845v2 . doi:10.1134/S0021364013210133. (原始内容存档 (PDF)于2019-01-27).
- von Keyserlingk, C. W.; Khemani, Vedika; Sondhi, S. L. Absolute stability and spatiotemporal long-range order in Floquet systems (PDF). Physical Review B. 2016, 94 (8) [2021-03-28]. Bibcode:2016PhRvB..94h5112V. ISSN 2469-9950. arXiv:1605.00639v3 . doi:10.1103/PhysRevB.94.085112. (原始内容存档 (PDF)于2019-10-21).
- Wang, Y. H.; Steinberg, H.; Jarillo-Herrero, P.; Gedik, N. Observation of Floquet-Bloch States on the Surface of a Topological Insulator (PDF). Science. 2013, 342 (6157): 453–457 [2021-03-28]. Bibcode:2013Sci...342..453W. ISSN 0036-8075. arXiv:1310.7563v1 . doi:10.1126/science.1239834. (原始内容存档 (PDF)于2019-10-19).
- Watanabe, Haruki; Oshikawa, Masaki. Absence of Quantum Time Crystals (PDF). Physical Review Letters. 2015, 114 (25): 251603 [2021-03-28]. Bibcode:2015PhRvL.114y1603W. ISSN 0031-9007. PMID 26197119. arXiv:1410.2143v3 . doi:10.1103/PhysRevLett.114.251603. (原始内容存档 (PDF)于2019-10-12).
- Wilczek, Frank. Quantum Time Crystals (PDF). Physical Review Letters. 2012, 109 (16) [2021-03-28]. Bibcode:2012PhRvL.109p0401W. ISSN 0031-9007. arXiv:1202.2539v2 . doi:10.1103/PhysRevLett.109.160401. (原始内容存档 (PDF)于2019-10-16).
- Wilczek, Frank. Wilczek Reply* (PDF). Physical Review Letters. 2013a, 110 (11) [2021-03-28]. Bibcode:2013PhRvL.110k8902W. ISSN 0031-9007. doi:10.1103/PhysRevLett.110.118902. (原始内容存档 (PDF)于2017-02-11).
- Wilczek, Frank. Superfluidity and Space-Time Translation Symmetry Breaking (PDF). Physical Review Letters. 2013b, 111 (25) [2021-03-28]. Bibcode:2013PhRvL.111y0402W. ISSN 0031-9007. arXiv:1308.5949v1 . doi:10.1103/PhysRevLett.111.250402. (原始内容存档 (PDF)于2019-10-18).
- Willett, R. L.; Nayak, C.; Shtengel, K.; Pfeiffer, L. N.; West, K. W. Magnetic-Field-Tuned Aharonov-Bohm Oscillations and Evidence for Non-Abelian Anyons atν=5/2 (PDF). Physical Review Letters. 2013, 111 (18) [2021-03-28]. Bibcode:2013PhRvL.111r6401W. ISSN 0031-9007. arXiv:1301.2639v1 . doi:10.1103/PhysRevLett.111.186401. (原始内容存档 (PDF)于2016-06-02).
- Yao, N. Y.; Potter, A. C.; Potirniche, I.-D.; Vishwanath, A. Discrete Time Crystals* Rigidity, Criticality, and Realizations (PDF). Physical Review Letters. 2017, 118 (3) [2021-03-28]. Bibcode:2017PhRvL.118c0401Y. ISSN 0031-9007. arXiv:1608.02589v2 . doi:10.1103/PhysRevLett.118.030401. (原始内容存档 (PDF)于2019-01-27).
- Yoshii, Ryosuke; Takada, Satoshi; Tsuchiya, Shunji; Marmorini, Giacomo; Hayakawa, Hisao; Nitta, Muneto. Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields* Phase diagram and the first-order phase transitions (PDF). Physical Review B. 2015, 92 (22) [2021-03-28]. Bibcode:2015PhRvB..92v4512Y. ISSN 1098-0121. arXiv:1404.3519v2 . doi:10.1103/PhysRevB.92.224512. (原始内容存档 (PDF)于2017-02-11).
- Yukawa, Satoshi; Kikuchi, Macoto; Tatara, Gen; Matsukawa, Hiroshi. Quantum Ratchets (PDF). Journal of the Physical Society of Japan. 1997, 66 (10): 2953–2956 [2021-03-28]. Bibcode:1997JPSJ...66.2953Y. ISSN 0031-9015. arXiv:cond-mat/9706222 . doi:10.1143/JPSJ.66.2953. (原始内容存档 (PDF)于2017-02-11).
- Yukawa, Satoshi. A Quantum Analogue of the Jarzynski Equality (PDF). Journal of the Physical Society of Japan. 2000, 69 (8): 2367–2370 [2021-03-28]. Bibcode:2000JPSJ...69.2367Y. ISSN 0031-9015. arXiv:cond-mat/0007456 . doi:10.1143/JPSJ.69.2367. (原始内容存档 (PDF)于2019-01-27).
- Zel'Dovich, Y. B. The quasienergy of a quantum-mechanical system subjected to a periodic action (PDF). Soviet Physics JETP. 1967, 24 (5): 1006–1008 [2021-03-28]. Bibcode:1967JETP...24.1006Z. (原始内容存档 (PDF)于2017-02-11).
- Zhang, J.; Hess, P. W.; Kyprianidis, A.; Becker, P.; Lee, A.; Smith, J.; Pagano, G.; Potirniche, I.-D.; Potter, A. C.; Vishwanath, A.; Yao, N. Y.; Monroe, C. Observation of a Discrete Time Crystal (PDF). Nature. 2017, 543 (7644): 217–220 [2021-03-28]. Bibcode:2017Natur.543..217Z. ISSN 0028-0836. arXiv:1609.08684v1 . doi:10.1038/nature21413. (原始内容存档 (PDF)于2019-10-20).
书籍
编辑- Bordag, M.; Mohideen, U.; Mostepanenko, V.M. New developments in the Casimir effect (PDF). Physics Reports. 2001, 353 (1–3): 1–205 [2021-03-28]. Bibcode:2001PhR...353....1B. ISSN 0370-1573. arXiv:quant-ph/0106045 . doi:10.1016/S0370-1573(01)00015-1. (原始内容存档 (PDF)于2017-02-11).
- Bordag, M.; Mohideen, U.; Mostepanenko, V.M.; Klimchitskaya, G. L. Advances in the Casimir Effect. Oxford: Oxford University Press. 28 May 2009 [2021-03-28]. ISBN 978-0-19-157988-2. (原始内容存档于2019-03-31).
- Cao, Tian Yu. Conceptual Foundations of Quantum Field Theory. Cambridge: Cambridge University Press. 25 March 2004 [2021-03-28]. ISBN 978-0-521-60272-3. (原始内容存档于2019-12-15).
- Enz, Charles P. Is the Zero-Point Energy Real?. Enz, C. P.; Mehra, J. (编). Physical Reality and Mathematical Description. Dordrecht: D. Reidel Publishing Company. 1974: 124–132. ISBN 978-94-010-2274-3. doi:10.1007/978-94-010-2274-3_8.
- Greiner, Walter; Müller, B.; Rafelski, J. Quantum Electrodynamics of Strong Fields* With an Introduction into Modern Relativistic Quantum Mechanics. Springer. 2012 [2021-03-28]. ISBN 978-3-642-82274-2. doi:10.1007/978-3-642-82272-8. (原始内容存档于2020-08-20).
- Lee, T. D. Particle Physics. CRC Press. 15 August 1981 [2021-03-28]. ISBN 978-3-7186-0033-5. (原始内容存档于2020-08-19).
- Feng, Duan; Jin, Guojun. Introduction to Condensed Matter Physics. singapore: World Scientific. 2005 [2021-03-28]. ISBN 978-981-238-711-0. (原始内容存档于2019-03-31).
- Milonni, Peter W. The Quantum Vacuum* An Introduction to Quantum Electrodynamics. London: Academic Press. 1994 [2021-03-28]. ISBN 978-0-124-98080-8. (原始内容存档于2020-08-20).
- Pade, Jochen. Quantum Mechanics for Pedestrians 2* Applications and Extensions. Dordrecht: Springer. 2014 [2021-03-28]. ISBN 978-3-319-00813-4. ISSN 2192-4791. doi:10.1007/978-3-319-00813-4. (原始内容存档于2020-08-19).
- Schwinger, Julian. Particles, Sources, And Fields, Volume 1* v. 1 (Advanced Books Classics). Perseus. 1998a. ISBN 978-0-738-20053-8.
- Schwinger, Julian. Particles, Sources, And Fields, Volume 2* v. 2 (Advanced Books Classics). Perseus. 1998b. ISBN 978-0-738-20054-5.
- Schwinger, Julian. Particles, Sources, And Fields, Volume 3* v. 3 (Advanced Books Classics). Perseus. 1998c. ISBN 978-0-738-20055-2.
- Sólyom, Jenö. Fundamentals of the Physics of Solids* Volume 1* Structure and Dynamics. Springer. 19 September 2007 [2021-03-28]. ISBN 978-3-540-72600-5. (原始内容存档于2019-03-31).
- Wilczek, Frank. A Beautiful Question* Finding Nature's Deep Design. Penguin Books Limited. 16 July 2015 [2021-03-28]. ISBN 978-1-84614-702-9. (原始内容存档于2019-12-15).
出版物
编辑- Aalto University. Physicists discover quantum-mechanical monopoles. phys.org. Science X. 30 April 2015 [2019-01-14]. (原始内容存档于2015-04-30).
- Aitchison, Ian. Observing the Unobservable. New Scientist. 19 November 1981, 92 (1280): 540–541 [2021-03-28]. ISSN 0262-4079. (原始内容存档于2020-08-19).
- Amherst College. Physicists create synthetic magnetic monopole predicted more than 80 years ago. phys.org. Science X. 29 January 2014 [2019-01-14]. (原始内容存档于2014-01-29).
- Aron, Jacob. Computer that could outlive the universe a step closer. newscientist.com. New Scientist. 6 July 2012 [2019-01-14]. (原始内容存档于2017-02-02).
- Ball, Philip. Focus* New Crystal Type is Always in Motion. physics.aps.org. APS Physics. 8 January 2016 [2019-01-14]. (原始内容存档于2017-02-03).
- Ball, Philip. Scepticism greets pitch to detect dark energy in the lab. Nature. 8 July 2004, 430 (6996): 126–126 [2021-03-28]. Bibcode:2004Natur.430..126B. ISSN 0028-0836. doi:10.1038/430126b. (原始内容存档于2019-04-22).
- Cartlidge, Edwin. Scientists build heat engine from a single atom. sciencemag.org. Science Magazine. 21 October 2015 [2019-01-14]. (原始内容存档于2017-02-01).
- Chandler, David. Topological insulators* Persuading light to mix it up with matter. phys.org. Science X. 24 October 2014 [2019-01-14]. (原始内容存档于2017-02-08).
- Coleman, Piers. Quantum physics* Time crystals. Nature. 9 January 2013, 493 (7431): 166–167. Bibcode:2013Natur.493..166C. ISSN 0028-0836. doi:10.1038/493166a.
- Cowen, Ron. "Time Crystals" Could Be a Legitimate Form of Perpetual Motion. scientificamerican.com. Scientific American. 27 February 2012 [2019-01-14]. (原始内容存档于2017-02-02).
- Daghofer, Maria. Viewpoint* Toward Fractional Quantum Hall Physics with Cold Atoms. physics.aps.org. APS Physics. 29 April 2013 [2019-01-14]. (原始内容存档于2017-02-07).
- Gibney, Elizabeth. The quest to crystallize time. Nature. 2017, 543 (7644): 164–166 [2021-03-28]. Bibcode:2017Natur.543..164G. ISSN 0028-0836. doi:10.1038/543164a. (原始内容存档于2017-03-13).
- Grossman, Lisa. Death-defying time crystal could outlast the universe. newscientist.com. New Scientist. 18 January 2012 [2019-01-14]. (原始内容存档于2017-02-02).
- Hackett, Jennifer. Curious Crystal Dances for Its Symmetry. scientificamerican.com. Scientific American. 22 February 2016 [2019-01-14]. (原始内容存档于2017-02-03).
- Hewitt, John. Creating time crystals with a rotating ion ring. phys.org. Science X. 3 May 2013 [2019-01-14]. (原始内容存档于2013-07-04).
- Johnston, Hamish. 'Choreographic crystals' have all the right moves. physicsworld.com. Institute of Physics. 18 January 2016 [2019-01-14]. (原始内容存档于2017-02-03).
- Johannes Gutenberg Universitaet Mainz. Prototype of single ion heat engine created. sciencedaily.com. ScienceDaily. 3 February 2014 [2019-01-14]. (原始内容存档于2017-02-01).
- Joint Quantum Institute. Floquet Topological Insulators. jqi.umd.edu. Joint Quantum Institute. 22 March 2011 [2019-01-14]. (原始内容存档于2019-04-03).
- Morgan, James. Elusive magnetic 'monopole' seen in quantum system. bbc.co.uk. BBC. 30 January 2014 [2019-01-14]. (原始内容存档于2014-01-30).
- Moskowitz, Clara. New Particle Is Both Matter and Antimatter. scientificamerican.com. Scientific American. 2 October 2014 [2019-01-14]. (原始内容存档于2014-10-09).
- Ouellette, Jennifer. World’s first time crystals cooked up using new recipe. newscientist.com. New Scientist. 31 January 2017 [2019-01-14]. (原始内容存档于2017-02-01).
- Pilkington, Mark. Zero point energy. theguardian.com (The Guardian). 17 July 2003 [2019-01-14]. (原始内容存档于2017-02-07).
- Powell, Devin. Can matter cycle through shapes eternally?. Nature. 2013 [2021-03-28]. ISSN 1476-4687. doi:10.1038/nature.2013.13657. (原始内容存档于2017-02-03).
- Rao, Achintya. BaBar makes first direct measurement of time-reversal violation. physicsworld.com. Institute of Physics. 21 November 2012 [2019-01-14]. (原始内容存档于2015-03-24).
- Richerme, Phil. Viewpoint* How to Create a Time Crystal. physics.aps.org. APS Physics. 18 January 2017 [2019-01-14]. (原始内容存档于2017-02-02).
- Thomas, Jessica. Notes from the Editors* The Aftermath of a Controversial Idea. physics.aps.org. APS Physics. 15 March 2013 [2019-01-14]. (原始内容存档于2017-02-02).
- Qi, Xiao-Liang; Zhang, Shou-Cheng. The quantum spin Hall effect and topological insulators (PDF). Physics Today. 2010, 63 (1): 33–38 [2021-03-28]. Bibcode:2010PhT....63a..33Q. ISSN 0031-9228. arXiv:1001.1602 . doi:10.1063/1.3293411. (原始内容存档 (PDF)于2017-08-12).
- University of California, Berkeley. Physicists unveil new form of matter—time crystals. phys.org. Science X. 26 January 2017 [2019-01-14]. (原始内容存档于2017-01-28).
- Weiner, Sophie. Scientists Create A New Kind Of Matter* Time Crystals. popularmechanics.com. Popular mechanics. 28 January 2017 [2019-01-14]. (原始内容存档于2017-02-03).
- Wolchover, Natalie. Perpetual Motion Test Could Amend Theory of Time. quantamagazine.org. Simons Foundation. 25 April 2013 [2019-01-14]. (原始内容存档于2017-02-02).
- Wolchover, Natalie. Forging a Qubit to Rule Them All. quantamagazine.org. Simmons Foundation. 15 May 2014 [2019-01-14]. (原始内容存档于2016-03-15).
- Wood, Charlie. Time crystals realize new order of space-time. csmonitor.com. Christian Science Monitor. 31 January 2017 [2019-01-14]. (原始内容存档于2017-02-02).
- Yirka, Bob. Physics team proposes a way to create an actual space-time crystal. phys.org. Science X. 9 July 2012 [2019-01-14]. (原始内容存档于2013-04-15).
- Zakrzewski, Jakub. Viewpoint* Crystals of Time. physics.aps.org. APS Physics. 15 October 2012 [2019-01-14]. (原始内容存档于2017-02-02).
- Zeller, Michael. Viewpoint* Particle Decays Point to an Arrow of Time. physics.aps.org. APS Physics. 19 November 2012 [2019-01-14]. (原始内容存档于2017-02-04).
- Zyga, Lisa. Time crystals could behave almost like perpetual motion machines. phys.org. Science X. 20 February 2012 [2019-01-14]. (原始内容存档于2017-02-03).
- Zyga, Lisa. Physicist proves impossibility of quantum time crystals. phys.org. Space X. 22 August 2013 [2019-01-14]. (原始内容存档于2017-02-03).
- Zyga, Lisa. Nanoscale heat engine exceeds standard efficiency limit. phys.org. Science X. 27 January 2014 [2019-01-14]. (原始内容存档于2015-04-04).
- Zyga, Lisa. Physicists propose new definition of time crystals—then prove such things don't exist. phys.org. Science X. 9 July 2015 [2019-01-14]. (原始内容存档于2015-07-09).
- Zyga, Lisa. Time crystals might exist after all (Update). phys.org. Science X. 9 September 2016 [2019-01-14]. (原始内容存档于2016-09-11).