请输入您要查询的百科知识：

　

词条 Time crystal
释义

  1. History

  2. Time translation symmetry

     Broken symmetry in normal crystals  Broken symmetry in time crystals 

  3. Thermodynamics

  4. Experiments

  5. Related concepts

  6. References

     Academic papers  Books  Press 

  7. External links

{{short description|structure that repeats in time, as well as space; a kind of non-equilibrium matter}}{{technical|date=August 2018}}{{Condensed matter physics}}{{Time sidebar |science}}

A time crystal or space-time crystal is a structure that repeats in time, as well as in space. Normal three-dimensional crystals have a repeating pattern in space, but remain unchanged as time passes. Time crystals repeat themselves in time as well, leading the crystal to change from moment to moment. A time crystal never reaches thermal equilibrium, as it is a type of non-equilibrium matter, a form of matter proposed in 2012, and first observed in 2017. This state of matter cannot be isolated from its environment{{citation needed|date=April 2018}}—it is an open system in non-equilibrium.

The idea of a time crystal was first described by Nobel laureate Frank Wilczek in 2012. Later work developed a more precise definition for time crystals. It was proven that they cannot exist in equilibrium.[1] Then, in 2014 Krzysztof Sacha predicted the behaviour of discrete time crystals in a periodically-driven many-body system.[2] and in 2016, Norman Yao et al. proposed a different way to create time crystals in spin systems. From there, Christopher Monroe and Mikhail Lukin independently confirmed this in their labs. Both experiments were published in Nature in 2017.

History

The idea of a space-time crystal was first put forward by Frank Wilczek, a professor at MIT and Nobel laureate, in 2012.[3]

In 2013, Xiang Zhang, a nanoengineer at University of California, Berkeley, and his team proposed creating a time crystal in the form of a constantly rotating ring of charged ions.[4]

In response to Wilczek and Zhang, Patrick Bruno, a theorist at the European Synchrotron Radiation Facility in Grenoble, France, published several papers in 2013 claiming to show that space-time crystals were impossible. Also later Masaki Oshikawa from the University of Tokyo showed that time crystals would be impossible at their ground state; moreover, he implied that any matter cannot exist in non-equilibrium in its ground state.[5][6]

Subsequent work developed more precise definitions of time translation symmetry-breaking which ultimately led to a 'no-go' proof that quantum time crystals in equilibrium are not possible.[7][1]

Several realizations of time crystals, which avoid the equilibrium no-go arguments, were later proposed.[8] Krzysztof Sacha at Jagiellonian University in Krakow predicted the behaviour of discrete time crystals in a periodically driven system of ultracold atoms.[9] Later works[10] suggested periodically driven quantum spin systems could show similar behaviour.

Norman Yao at Berkeley studied a different model of time crystals.[11] His blueprint was successfully used by two teams: a group led by Harvard's Mikhail Lukin[12] and a group led by Christopher Monroe at University of Maryland.[13]

Time translation symmetry

{{main|Time translation symmetry}}

Symmetries in nature lead directly to conservation laws, something which is precisely formulated by the Noether theorem.{{sfn|Cao|2004|p=151}}

The basic idea of time-translation symmetry is that a translation in time has no effect on physical laws, i.e. that the laws of nature that apply today were the same in the past and will be the same in the future.{{sfn|Wilczek|2015|loc=chpt. 3}} This symmetry implies the conservation of energy.{{sfn|Feng|Jin|2005|p=18}}

Broken symmetry in normal crystals

{{main|Crystal symmetry|spontaneous symmetry breaking}}

Time crystals shows a broken symmetry analogous to a discrete space-translation symmetry breaking. For example, the molecules of a liquid freezing on the surface of a crystal can align with the molecules of the crystal, but with a pattern less symmetric than the crystal : it breaks the initial symmetry. This broken symmetry exhibits three important characteristics :

  • the system has a lower symmetry than the underlying arrangement of the crystal
  • the system exhibits spatial and temporal long-range order (unlike a local and intermittent order in a liquid near the surface of a crystal)
  • it is the result of interactions between the constituents of the system, which aligns themselves relative to each other

Broken symmetry in time crystals

Time crystals seem to break time-translation symmetry, and have repeated patterns in time even if the laws of the system are invariant by translation of time. Actually, studied time crystals shows discrete time-translation symmetry breaking : they are periodically driven systems which oscillate at a fraction of the frequency of the driving force. The initial symmetry is already a discrete time-translation symmetry (), not a continuous one ().

Many systems can show behaviors of spontaneous time translation symmetry breaking : convection cells, oscillating chemical reactions, aerodynamic flutter, and subharmonic response to a periodic driving force such as the Faraday instability, NMR spin echos, parametric down-conversion, and period-doubled nonlinear dynamical systems.

However, Floquet time crystals are unique in that they follow a strict definition of discrete time-translation symmetry breaking[14] :

  • it is a broken symmetry : the system shows oscillations with a period longer than the driving force
  • the system is in crypto-equilibrium : these oscillations generate no entropy, and a time-dependant frame can be found in which the system is indistinguishable from an equilibrium when measured stroboscopically (which is not the case of convection cells, oscillating chemical reactions and aerodynamic flutter)
  • the system exhibits long-range order : the oscillations are in phase (synchronized) over arbitrarily long distances and time

Moreover, the broken symmetry in time crystals is the result of many-body interactions : the order is the consequence of a collective process, just like in spacial crystals. This is not the case for NMR spin echos.

Fields or particles may change their energy by interacting with a time crystal, just as they can change their momentum by interacting with a spatial crystal.

These characteristics makes time crystals analogous to spacial crystals as described above.

Thermodynamics

Time crystals do not violate the laws of thermodynamics: energy in the overall system is conserved, such a crystal does not spontaneously convert thermal energy into mechanical work, and it cannot serve as a perpetual store of work. But it may change perpetually in a fixed pattern in time for as long as the system can be maintained. They possess "motion without energy"[15]—their apparent motion does not represent conventional kinetic energy.[16]

It has been proven that a time crystal cannot exist in thermal equilibrium. Recent years have seen more studies of non-equilibrium quantum fluctuations.[17]

Experiments

In October 2016, Christopher Monroe at the University of Maryland claimed to have created the world's first discrete time crystal. Using the idea from Yao's proposal, his team trapped a chain of 171Yb+ (ytterbium) ions in a Paul trap, confined by radio frequency electromagnetic fields. One of the two spin states was selected by a pair of laser beams. The lasers were pulsed, with the shape of the pulse controlled by an acousto-optic modulator, using the Tukey window to avoid too much energy at the wrong optical frequency. The hyperfine electron states in that setup, 2S1/2 |F=0, mF = 0⟩ and |F = 1, mF = 0⟩, have very close energy levels, separated by 12.642831 GHz. Ten Doppler-cooled ions were placed in a line 0.025 mm long and coupled together.

The researchers observed a subharmonic oscillation of the drive. The experiment showed "rigidity" of the time crystal, where the oscillation frequency remained unchanged even when the time crystal was perturbed, and that it gained a frequency of its own and vibrated according to it (rather than only the frequency of the drive). However, once the perturbation or frequency of vibration grew too strong, the time crystal "melted" and lost this subharmonic oscillation, and it returned to the same state as before where it moved only with the induced frequency.[13]

Later in 2016, Mikhail Lukin at Harvard also reported the creation of a driven time crystal. His group used a diamond crystal doped with a high concentration of nitrogen-vacancy centers, which have strong dipole-dipole coupling and relatively long-lived spin coherence. This strongly-interacting dipolar spin system was driven with microwave fields, and the ensemble spin state was determined with an optical (laser) field. It was observed that the spin polarization evolved at half the frequency of the microwave drive. The oscillations persisted for over 100 cycles. This subharmonic response to the drive frequency is seen as a signature of time-crystalline order.[12]

Related concepts

A similar idea called a choreographic crystal has been proposed.[18]

{{Portal bar|Physics|Science|Mathematics}}

References

1. ^1 See {{harvp|Watanabe|Oshikawa|2015}}
2. ^See {{harvp|Sacha|2015}}
3. ^See {{harvp|Wilczek|2012}} and {{harvp|Shapere|Wilczek|2012}}
4. ^See {{harvs|txt|last1=Li et al.|year1=2012a|year2=2012b}}, Wolchover 2013
5. ^See {{harvp|Bruno|2013a}} and {{harvp|Bruno|2013b}}
6. ^{{Harvp|Thomas|2013}}
7. ^See {{harvp|Nozières|2013}}, {{harvp|Yao et al.|2017|p=1}} and {{harvp|Volovik|2013}}
8. ^See {{harvp|Wilczek|2013b}} and {{harvp|Yoshii et al.|2015}}
9. ^See {{harvp|Sacha|2015}}
10. ^See {{harvp|Khemani et al.|2016}} and {{harvp|Else et al.|2016}}
11. ^See {{harvp|Yao et al.|2017}}, {{Harvp|Richerme|2017}}
12. ^1 See {{harvp|Choi et al.|2017}}
13. ^1 See {{harvp|Zhang et al.|2017}}
14. ^{{cite journal|last1=Yao|last2=Nayak|title=Time crystals in periodically driven systems|journal=Physics Today|volume=71|issue=9|year=2018|pages=40–47|issn=0031-9228|doi=10.1063/PT.3.4020}}
15. ^{{Cite news|url=https://www.sciencealert.com/time-crystals-might-exist-after-all-and-they-could-break-the-symmetry-of-space-and-time|title=Time Crystals Might Exist After All - And They Could Break Space-Time Symmetry|last=Crew|first=Bec|work=ScienceAlert|access-date=2017-09-21|language=en-gb}}
16. ^{{Cite news|url=https://www.scientificamerican.com/article/time-crystals-could-be-legitimate-form-perpetual-motion/|title="Time Crystals" Could Be a Legitimate Form of Perpetual Motion - Scie…|date=2017-02-02|work=archive.is|access-date=2017-09-21|deadurl=bot: unknown|archiveurl=https://archive.today/20170202101455/https://www.scientificamerican.com/article/time-crystals-could-be-legitimate-form-perpetual-motion/|archivedate=2017-02-02|df=}}
17. ^See {{harvp|Esposito et al.|2009}} and {{harvp|Campisi et al.|2011}} for academic review articles on non-equilibrium quantum fluctuations
18. ^See {{harvp|Boyle et al.|2016}}

Academic papers

{{Refbegin|30em|indent=yes}}

{{cite journal|last1=Beck|first1=Christian|last2=Mackey|first2=Michael C.|title=Could dark energy be measured in the lab?|journal=Physics Letters B|volume=605|issue=3–4|year=2005|pages=295–300|issn=0370-2693|doi=10.1016/j.physletb.2004.11.060|arxiv=astro-ph/0406504v2|bibcode=2005PhLB..605..295B|ref=harv}}

{{cite journal|last1=Boyle|first1=Latham|last2=Khoo|first2=Jun Yong|last3=Smith|first3=Kendrick|title=Symmetric Satellite Swarms and Choreographic Crystals|journal=Physical Review Letters|volume=116|issue=1|year=2016|issn=0031-9007|doi=10.1103/PhysRevLett.116.015503|arxiv=1407.5876v2|bibcode=2016PhRvL.116a5503B|ref={{harvid|Boyle et al.|2016}}|pmid=26799028|page=015503}}

{{cite journal|last1=Bruno|first1=Patrick|title=Comment on "Quantum Time Crystals"|journal=Physical Review Letters|volume=110|issue=11|year=2013a|issn=0031-9007|doi=10.1103/PhysRevLett.110.118901|arxiv=1210.4128v1 |bibcode=2013PhRvL.110k8901B|ref=harv|pmid=25166585|page=118901|url=https://zenodo.org/record/1184403}}

{{cite journal|last1=Bruno|first1=Patrick|title=Comment on "Space-Time Crystals of Trapped Ions"|journal=Physical Review Letters|volume=111|issue=2|pages=029301|year=2013b|issn=0031-9007|doi=10.1103/PhysRevLett.111.029301|pmid=23889455|arxiv=1211.4792v1 |bibcode=2013PhRvL.111b9301B|ref=harv}}

{{cite journal|last1=Campisi|first1=Michele|last2=Hänggi|first2=Peter|last3=Talkner|first3=Peter|title=Colloquium: Quantum fluctuation relations: Foundations and applications|journal=Reviews of Modern Physics|volume=83|issue=3|year=2011|pages=771–791|issn=0034-6861|doi=10.1103/RevModPhys.83.771|arxiv=1012.2268v5|bibcode=2011RvMP...83..771C|ref={{harvid|Campisi et al.|2011}} |citeseerx=10.1.1.760.2265}}

{{cite journal|last1=Choi|first1=Soonwon|last2=Choi|first2=Joonhee|last3=Landig|first3=Renate|last4=Kucsko|first4=Georg|last5=Zhou|first5=Hengyun|last6=Isoya|first6=Junichi|last7=Jelezko|first7=Fedor|last8=Onoda|first8=Shinobu|last9=Sumiya|first9=Hitoshi|last10=Khemani|first10=Vedika|last11=von Keyserlingk|first11=Curt|last12=Yao|first12=Norman Y.|last13=Demler|first13=Eugene|last14=Lukin|first14=Mikhail D.|title=Observation of discrete time-crystalline order in a disordered dipolar many-body system|arxiv=1610.08057v1|bibcode=2017Natur.543..221C|journal=Nature|volume=543|issue=7644|year=2017|pages=221–225|issn=0028-0836|doi=10.1038/nature21426|pmid=28277511|pmc=5349499|ref={{harvid|Choi et al.|2017}} }}

{{cite journal|last1=Chernodub|first1=M. N.|title=Permanently rotating devices: extracting rotation from quantum vacuum fluctuations?|date=2012|bibcode=2012arXiv1203.6588C|arxiv=1203.6588v1|ref=harv}}

{{cite journal|last1=Chernodub|first1=M. N.|title=Zero-point fluctuations in rotation: Perpetuum mobile of the fourth kind without energy transfer|journal=Nuovo Cimento C|date=2013a|volume=5|issue=36|pages=53–63|doi=10.1393/ncc/i2013-11523-5|arxiv=1302.0462v1|bibcode=2013arXiv1302.0462C|ref=harv}}

{{cite journal|last1=Chernodub|first1=M. N.|title=Rotating Casimir systems: Magnetic-field-enhanced perpetual motion, possible realization in doped nanotubes, and laws of thermodynamics|journal=Physical Review D|volume=87|issue=2|pages=025021|year=2013b|issn=1550-7998|doi=10.1103/PhysRevD.87.025021|arxiv=1207.3052v2|bibcode=2013PhRvD..87b5021C|ref=harv}}

{{cite journal|last1=Copeland|first1=Edmund J.|last2=Sami|first2=M.|last3=Tsujikawa|first3=Shinji|title=Dynamics of dark energy|journal=International Journal of Modern Physics D|volume=15|issue=11|year=2006|pages=1753–1935|issn=0218-2718|doi=10.1142/S021827180600942X|arxiv=hep-th/0603057|bibcode=2006IJMPD..15.1753C|ref={{harvid|Copeland et al.|2006}} }}

{{cite journal|last1=Dillenschneider|first1=R.|last2=Lutz|first2=E.|title=Energetics of quantum correlations|journal=EPL|volume=88|issue=5|year=2009|pages=50003|issn=0295-5075|doi=10.1209/0295-5075/88/50003|arxiv=0803.4067|bibcode=2009EL.....8850003D|ref=harv}}

{{cite journal|last1=Else|first1=Dominic V.|last2=Bauer|first2=Bela|last3=Nayak|first3=Chetan|title=Floquet Time Crystals|journal=Physical Review Letters|volume=117|issue=9|year=2016|issn=0031-9007|doi=10.1103/PhysRevLett.117.090402|arxiv=1603.08001v4|bibcode=2016PhRvL.117i0402E|ref={{harvid|Else et al.|2016}}|pmid=27610834|page=090402}}

{{cite journal|last1=Esposito|first1=Massimiliano|last2=Harbola|first2=Upendra|last3=Mukamel|first3=Shaul|title=Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems|journal=Reviews of Modern Physics|volume=81|issue=4|year=2009|pages=1665–1702|issn=0034-6861|doi=10.1103/RevModPhys.81.1665|arxiv=0811.3717v2|bibcode=2009RvMP...81.1665E|ref={{harvid|Esposito et al.|2009}} |url=http://orbilu.uni.lu/handle/10993/12322}}

{{cite journal|last1=Grifoni|first1=Milena|last2=Hänggi|first2=Peter|title=Driven quantum tunneling|journal=Physics Reports|volume=304|issue=5–6|year=1998|pages=229–354|issn=0370-1573|doi=10.1016/S0370-1573(98)00022-2|url=https://pdfs.semanticscholar.org/9477/590bf9c4bc44f0aadf036bd6ab45ce76ebc8.pdf|bibcode=1998PhR...304..229G|ref=harv|citeseerx=10.1.1.65.9479}}

{{cite journal|last1=Guo|first1=Lingzhen|last2=Marthaler|first2=Michael|last3=Schön|first3=Gerd|title=Phase Space Crystals: A New Way to Create a Quasienergy Band Structure|journal=Physical Review Letters|volume=111|issue=20|pages=205303|year=2053|issn=0031-9007|doi=10.1103/PhysRevLett.111.205303|pmid=24289695|arxiv=1305.1800v3|bibcode=2013PhRvL.111t5303G|ref={{harvid|Guo et al.|2013}} }}

{{cite journal|last1=Hasan|first1=M. Z.|last2=Kane|first2=C. L.|title=Colloquium: Topological insulators|journal=Reviews of Modern Physics|volume=82|issue=4|year=2010|pages=3045–3067|issn=0034-6861|doi=10.1103/RevModPhys.82.3045|arxiv=1002.3895v2|bibcode=2010RvMP...82.3045H|ref=harv|url=https://repository.upenn.edu/physics_papers/39}}

{{cite journal|last1=Horodecki|first1=Ryszard|last2=Horodecki|first2=Paweł|last3=Horodecki|first3=Michał|last4=Horodecki|first4=Karol|title=Quantum entanglement|journal=Reviews of Modern Physics|volume=81|issue=2|year=2009|pages=865–942|issn=0034-6861|doi=10.1103/RevModPhys.81.865|arxiv=quant-ph/0702225v2|bibcode=2009RvMP...81..865H|ref={{harvid|Horodecki et al.|2009}} }}

{{cite journal|last=Jaffe |first=R. L.|year=2005|title=Casimir effect and the quantum vacuum|journal=Physical Review D|volume=72 |issue=2 |page=021301|arxiv= hep-th/0503158|bibcode= 2005PhRvD..72b1301J|doi=10.1103/PhysRevD.72.021301|ref=harv}}

{{cite journal|last1=Jarzynski|first1=Christopher|title=Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale|journal=Annual Review of Condensed Matter Physics|volume=2|issue=1|year=2011|pages=329–351|issn=1947-5454|doi=10.1146/annurev-conmatphys-062910-140506|url=http://newton.kias.re.kr/~brane/wc2012/download/Jarzynski_annurev-conmatphys-062910-140506.pdf|bibcode=2011ARCMP...2..329J|ref=harv}}

{{cite journal|last1=Jetzer|first1=Philippe|last2=Straumann|first2=Norbert|title=Josephson junctions and dark energy|journal=Physics Letters B|volume=639|issue=2|year=2006|pages=57–58|issn=0370-2693|doi=10.1016/j.physletb.2006.06.020|arxiv=astro-ph/0604522|bibcode=2006PhLB..639...57J|ref=harv|citeseerx=10.1.1.257.2245}}

{{cite journal|last1=Khemani|first1=Vedika|last2=Lazarides|first2=Achilleas|last3=Moessner|first3=Roderich|last4=Sondhi|first4=S. L.|title=Phase Structure of Driven Quantum Systems|journal=Physical Review Letters|volume=116|issue=25|pages=250401|year=2504|issn=0031-9007|doi=10.1103/PhysRevLett.116.250401|pmid=27391704|bibcode=2016PhRvL.116y0401K|arxiv=1508.03344v3|ref={{harvid|Khemani et al.|2016}} }}

{{cite journal|last1=Lees|first1=J. P.|title=Observation of Time-Reversal Violation in the B0 Meson System|journal=Physical Review Letters|volume=109|issue=21|pages=211801|year=2118|issn=0031-9007|doi=10.1103/PhysRevLett.109.211801|pmid=23215586|arxiv=1207.5832v4|bibcode=2012PhRvL.109u1801L|ref={{harvid|Lees et al.|2012}} }}

{{cite journal|last1=Li|first1=Tongcang|last2=Gong|first2=Zhe-Xuan|last3=Yin|first3=Zhang-Qi|last4=Quan|first4=H. T.|last5=Yin|first5=Xiaobo|last6=Zhang|first6=Peng|last7=Duan|first7=L.-M.|last8=Zhang|first8=Xiang|title=Space-Time Crystals of Trapped Ions|journal=Physical Review Letters|volume=109|issue=16|pages=163001|year=2012a|issn=0031-9007|doi=10.1103/PhysRevLett.109.163001|pmid=23215073|arxiv=1206.4772v2|bibcode=2012PhRvL.109p3001L|ref={{harvid|Li et al.|2012a}} }}

{{cite journal|last1=Li|first1=Tongcang|last2=Gong|first2=Zhe-Xuan|last3=Yin|first3=Zhang-Qi|last4=Quan|first4=H. T.|last5=Yin|first5=Xiaobo|last6=Zhang|first6=Peng|last7=Duan|first7=L.-M.|last8=Zhang|first8=Xiang|title=Reply to Comment on "Space-Time Crystals of Trapped Ions"|date=2012b|arxiv=1212.6959v2|bibcode= 2012arXiv1212.6959L


|ref={{harvid|Li et al.|2012b}} }}

{{cite journal|last1=Lindner|first1=Netanel H.|last2=Refael|first2=Gil|last3=Galitski|first3=Victor|title=Floquet topological insulator in semiconductor quantum wells|journal=Nature Physics|volume=7|issue=6|year=2011|pages=490–495|issn=1745-2473|doi=10.1038/nphys1926|arxiv=1008.1792v2|bibcode=2011NatPh...7..490L|ref={{harvid|Lindner et al.|2011}} }}

{{cite journal|last1=Nadj-Perge|first1=S.|last2=Drozdov|first2=I. K.|last3=Li|first3=J.|last4=Chen|first4=H.|last5=Jeon|first5=S.|last6=Seo|first6=J.|last7=MacDonald|first7=A. H.|last8=Bernevig|first8=B. A.|last9=Yazdani|first9=A.|title=Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor|journal=Science|volume=346|issue=6209|year=2014|pages=602–607|issn=0036-8075|doi=10.1126/science.1259327|arxiv=1410.0682v1|bibcode=2014Sci...346..602N|ref={{harvid|Nadi-Perge et al.|2014}}|pmid=25278507}}

{{cite journal|last1=Nozières|first1=Philippe|title=Time crystals: Can diamagnetic currents drive a charge density wave into rotation?|journal=EPL|volume=103|issue=5|year=2013|pages=57008|issn=0295-5075|doi=10.1209/0295-5075/103/57008|arxiv=1306.6229v1|bibcode=2013EL....10357008N|ref=harv}}

{{cite journal|last1=Sacha|first1=Krzysztof|title=Modeling spontaneous breaking of time-translation symmetry|journal=Physical Review A|volume=91|issue=3|pages=033617|year=2015|issn=1050-2947|doi=10.1103/PhysRevA.91.033617|bibcode=2015PhRvA..91c3617S|arxiv=1410.3638v3|ref=harv}}

{{cite journal|last1=Schwinger|first1=Julian|title=Casimir effect in source theory|journal=Letters in Mathematical Physics|date=1975|volume=1|issue=1|pages=43–47|doi=10.1007/BF00405585|bibcode=1975LMaPh...1...43S|ref=harv}}

{{cite journal|last1=Schwinger|first1=Julian|last2=DeRaad|first2=Lester L.|last3=Milton|first3=Kimball A.|title=Casimir effect in dielectrics|journal=Annals of Physics|date=1978|volume=115|issue=1|pages=1–23|doi=10.1016/0003-4916(78)90172-0|bibcode=1978AnPhy.115....1S|ref={{harvid|Schwinger et al.|1978}} }}

{{cite journal|last1=Scully|first1=Marlan O.|title=Extracting Work from a Single Thermal Bath via Quantum Negentropy|journal=Physical Review Letters|volume=87|issue=22|year=2001|issn=0031-9007|doi=10.1103/PhysRevLett.87.220601|bibcode=2001PhRvL..87v0601S|ref=harv|pmid=11736390|page=220601}}

{{cite journal|last1=Scully|first1=Marlan O.|last2=Zubairy|first2=M. Suhail|last3=Agarwal|first3=Girish S.|last4=Walther|first4=Herbert.|title=Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence|journal=Science|volume=299|issue=5608|year=2003|pages=862–864|issn=0036-8075|doi=10.1126/science.1078955|bibcode=2003Sci...299..862S|pmid=12511655|ref={{harvid|Scully et al.|2003}} }}

{{cite journal|last1=Seifert|first1=Udo|title=Stochastic thermodynamics, fluctuation theorems and molecular machines|journal=Reports on Progress in Physics|volume=75|issue=12|year=2012|pages=126001|issn=0034-4885|doi=10.1088/0034-4885/75/12/126001|pmid=23168354|arxiv=1205.4176v1|bibcode=2012RPPh...75l6001S|ref=harv}}

{{cite journal|last1=Senitzky|first1=I. R.|title=Dissipation in Quantum Mechanics. The Harmonic Oscillator|journal=Physical Review|volume=119|issue=2|year=1960|pages=670–679|issn=0031-899X|doi=10.1103/PhysRev.119.670|bibcode=1960PhRv..119..670S|ref=harv}}

{{cite journal|last1=Shapere|first1=Alfred|last2=Wilczek|first2=Frank|title=Classical Time Crystals|journal=Physical Review Letters|volume=109|issue=16|pages=160402|year=2012|issn=0031-9007|doi=10.1103/PhysRevLett.109.160402|pmid=23215057|bibcode=2012PhRvL.109p0402S|arxiv=1202.2537v2|ref=harv}}

{{cite journal|last1=Shirley|first1=Jon H.|title=Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time|journal=Physical Review|volume=138|issue=4B|year=1965|pages=B979–B987|issn=0031-899X|doi=10.1103/PhysRev.138.B979|bibcode=1965PhRv..138..979S|ref=harv}}

{{cite journal|last1=Smith|first1=J.|last2=Lee|first2=A.|last3=Richerme|first3=P.|last4=Neyenhuis|first4=B.|last5=Hess|first5=P. W.|last6=Hauke|first6=P.|last7=Heyl|first7=M.|last8=Huse|first8=D. A.|last9=Monroe|first9=C.|title=Many-body localization in a quantum simulator with programmable random disorder|journal=Nature Physics|volume=12|issue=10|year=2016|pages=907–911|issn=1745-2473|doi=10.1038/nphys3783|arxiv=1508.07026v1|bibcode=2016NatPh..12..907S|ref={{harvid|Smith et al.|2016}} }}

{{cite journal|last1=Maruyama|first1=Koji|last2=Nori|first2=Franco|last3=Vedral|first3=Vlatko|title=Colloquium: The physics of Maxwell's demon and information|journal=Reviews of Modern Physics|volume=81|issue=1|year=2009|pages=1–23|issn=0034-6861|doi=10.1103/RevModPhys.81.1|arxiv=0707.3400|bibcode=2009RvMP...81....1M|ref={{harvid|Maruyama et al.|2009}} }}

{{cite journal|last1=Mendonça|first1=J. T.|last2=Dodonov|first2=V. V.|title=Time Crystals in Ultracold Matter|journal=Journal of Russian Laser Research|volume=35|issue=1|year=2014|pages=93–100|issn=1071-2836|doi=10.1007/s10946-014-9404-9|url=https://www.researchgate.net/publication/272040551|ref=harv}}

{{cite journal|last1=Modi|first1=Kavan|last2=Brodutch|first2=Aharon|last3=Cable|first3=Hugo|last4=Paterek|first4=Tomasz|last5=Vedral|first5=Vlatko|title=The classical-quantum boundary for correlations: Discord and related measures|journal=Reviews of Modern Physics|volume=84|issue=4|year=2012|pages=1655–1707|issn=0034-6861|doi=10.1103/RevModPhys.84.1655|arxiv=1112.6238|bibcode=2012RvMP...84.1655M|ref={{harvid|Modi et al.|2012}} }}

{{cite journal|last1=Ray|first1=M. W.|last2=Ruokokoski|first2=E.|last3=Kandel|first3=S.|last4=Möttönen|first4=M.|last5=Hall|first5=D. S.|title=Observation of Dirac monopoles in a synthetic magnetic field|journal=Nature|volume=505|issue=7485|year=2014|pages=657–660|issn=0028-0836|doi=10.1038/nature12954|bibcode=2014Natur.505..657R|arxiv=1408.3133v1|ref={{harvid|Ray et al.|2014}}|pmid=24476889}}

{{cite journal|last1=Ray|first1=M. W.|last2=Ruokokoski|first2=E.|last3=Tiurev|first3=K.|last4=Mottonen|first4=M.|last5=Hall|first5=D. S.|title=Observation of isolated monopoles in a quantum field|journal=Science|volume=348|issue=6234|year=2015|pages=544–547|issn=0036-8075|doi=10.1126/science.1258289|pmid=25931553|bibcode=2015Sci...348..544R|url=https://aaltodoc.aalto.fi/bitstream/handle/123456789/16541/article5.pdf?sequence=8|ref={{harvid|Ray et al.|2015}} }}

{{cite journal|last1=Reimann|first1=Peter|last2=Grifoni|first2=Milena|last3=Hänggi|first3=Peter|title=Quantum Ratchets|journal=Physical Review Letters|volume=79|issue=1|year=1997|pages=10–13|issn=0031-9007|doi=10.1103/PhysRevLett.79.10|url=https://pdfs.semanticscholar.org/eb04/b17564b443e5bcb7d9b8f579bbfb501db507.pdf|bibcode=1997PhRvL..79...10R|ref={{harvid|Reimann et al.|1997}} }}

{{cite journal|last1=Robicheaux|first1=F.|last2=Niffenegger|first2=K.|title=Quantum simulations of a freely rotating ring of ultracold and identical bosonic ions|journal=Physical Review A|volume=91|issue=6|year=2015|pages=063618|issn=2469-9926|doi=10.1103/PhysRevA.91.063618|bibcode=2015PhRvA.91063618R|ref=harv}}

{{cite journal|last1=Roßnagel|first1=J.|last2=Abah|first2=O.|last3=Schmidt-Kaler|first3=F.|last4=Singer|first4=K.|last5=Lutz|first5=E.|title=Nanoscale Heat Engine Beyond the Carnot Limit|journal=Physical Review Letters|volume=112|issue=3|year=2014|issn=0031-9007|doi=10.1103/PhysRevLett.112.030602|arxiv=1308.5935|bibcode=2014PhRvL.112c0602R|ref={{harvid|Roßnagel et al.|2014}}|pmid=24484127|page=030602}}

{{cite journal|last1=Roßnagell|first1=J.|last2=Dawkins|first2=S. T.|last3=Tolazzi|first3=K. N.|last4=Abah|first4=O.|last5=Lutz|first5=E.|last6=Schmidt-Kaler|first6=F.|last7=Singer|first7=K.|title=A single-atom heat engine|journal=Science|volume=352|issue=6283|year=2016|pages=325–329|issn=0036-8075|doi=10.1126/science.aad6320|pmid=27081067|arxiv=1510.03681|bibcode=2016Sci...352..325R|ref={{harvid|Roßnagel et al.|2016}} }}

{{cite journal|last1=Tatara|first1=Gen|last2=Kikuchi|first2=Makoto|last3=Yukawa|first3=Satoshi|last4=Matsukawa|first4=Hiroshi|title=Dissipation Enhanced Asymmetric Transport in Quantum Ratchets|journal=Journal of the Physical Society of Japan|volume=67|issue=4|year=1998|pages=1090–1093|issn=0031-9015|doi=10.1143/JPSJ.67.1090|arxiv=cond-mat/9711045|ref={{harvid|Tatara et al.|1998}} |bibcode=1998JPSJ...67.1090T}}

{{cite journal|last1=Volovik|first1=G. E.|title=On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order|journal=JETP Letters|volume=98|issue=8|year=2013|pages=491–495|issn=0021-3640|doi=10.1134/S0021364013210133|arxiv=1309.1845v2 |bibcode=2013JETPL..98..491V|ref=harv}}

{{cite journal|last1=von Keyserlingk|first1=C. W.|last2=Khemani|first2=Vedika|last3=Sondhi|first3=S. L.|title=Absolute stability and spatiotemporal long-range order in Floquet systems|journal=Physical Review B|volume=94|issue=8|pages=085112|year=2016|issn=2469-9950|doi=10.1103/PhysRevB.94.085112|arxiv=1605.00639v3|bibcode=2016PhRvB..94h5112V|ref={{harvid|von Keyserlingk et al.|2016}} }}

{{cite journal|last1=Wang|first1=Y. H.|last2=Steinberg|first2=H.|last3=Jarillo-Herrero|first3=P.|last4=Gedik|first4=N.|title=Observation of Floquet-Bloch States on the Surface of a Topological Insulator|journal=Science|volume=342|issue=6157|year=2013|pages=453–457|issn=0036-8075|doi=10.1126/science.1239834|pmid=24159040|arxiv=1310.7563v1|bibcode=2013Sci...342..453W|ref={{harvid|Wang et al.|2013}} |hdl=1721.1/88434}}

{{cite journal|last1=Watanabe|first1=Haruki|last2=Oshikawa|first2=Masaki|title=Absence of Quantum Time Crystals|journal=Physical Review Letters|volume=114|issue=25|year=2516|issn=0031-9007|doi=10.1103/PhysRevLett.114.251603|bibcode=2015PhRvL.114y1603W|arxiv=1410.2143v3|ref=harv|pmid=26197119|page=251603}}

{{cite journal|last1=Wilczek|first1=Frank|title=Quantum Time Crystals|journal=Physical Review Letters|volume=109|issue=16|pages=160401|year=2012|issn=0031-9007|doi=10.1103/PhysRevLett.109.160401|pmid=23215056|arxiv=1202.2539v2|bibcode=2012PhRvL.109p0401W|ref=harv}}

{{cite journal|last1=Wilczek|first1=Frank|title=Wilczek Reply|journal=Physical Review Letters|volume=110|issue=11|pages=118902|year=2013a|issn=0031-9007|doi=10.1103/PhysRevLett.110.118902|pmid=25166586|url=http://xa.yimg.com/kq/groups/2385221/2027721577/name/WilzcekreplyPhysRevLett.110.118902-1.pdf|bibcode=2013PhRvL.110k8902W|ref=harv}}

{{cite journal|last1=Wilczek|first1=Frank|title=Superfluidity and Space-Time Translation Symmetry Breaking|journal=Physical Review Letters|volume=111|issue=25|pages=250402|year=2504|issn=0031-9007|doi=10.1103/PhysRevLett.111.250402|pmid=24483732|bibcode=2013PhRvL.111y0402W|arxiv=1308.5949v1|ref=harv}}

{{cite journal|last1=Willett|first1=R. L.|last2=Nayak|first2=C.|last3=Shtengel|first3=K.|last4=Pfeiffer|first4=L. N.|last5=West|first5=K. W.|title=Magnetic-Field-Tuned Aharonov-Bohm Oscillations and Evidence for Non-Abelian Anyons atν=5/2|journal=Physical Review Letters|volume=111|issue=18|pages=186401|year=2013|issn=0031-9007|doi=10.1103/PhysRevLett.111.186401|pmid=24237543|bibcode=2013PhRvL.111r6401W|arxiv=1301.2639v1|ref={{harvid|Willett et al.|2013}} }}

{{cite journal|last1=Yao|first1=N. Y.|last2=Potter|first2=A. C.|last3=Potirniche|first3=I.-D.|last4=Vishwanath|first4=A.|title=Discrete Time Crystals: Rigidity, Criticality, and Realizations|journal=Physical Review Letters|volume=118|issue=3|pages=030401|year=2017|issn=0031-9007|doi=10.1103/PhysRevLett.118.030401|pmid=28157355|arxiv=1608.02589v2|bibcode=2017PhRvL.118c0401Y|ref={{harvid|Yao et al.|2017}} }}

{{cite journal|last1=Yoshii|first1=Ryosuke|last2=Takada|first2=Satoshi|last3=Tsuchiya|first3=Shunji|last4=Marmorini|first4=Giacomo|last5=Hayakawa|first5=Hisao|last6=Nitta|first6=Muneto|title=Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions|journal=Physical Review B|volume=92|issue=22|pages=224512|year=2015|issn=1098-0121|doi=10.1103/PhysRevB.92.224512|arxiv=1404.3519v2|bibcode=2015PhRvB..92v4512Y|ref={{harvid|Yoshii et al.|2015}} }}

{{cite journal|last1=Yukawa|first1=Satoshi|last2=Kikuchi|first2=Macoto|last3=Tatara|first3=Gen|last4=Matsukawa|first4=Hiroshi|title=Quantum Ratchets|journal=Journal of the Physical Society of Japan|volume=66|issue=10|year=1997|pages=2953–2956|issn=0031-9015|doi=10.1143/JPSJ.66.2953|arxiv=cond-mat/9706222|bibcode=1997JPSJ...66.2953Y|ref={{harvid|Yukawa et al.|1997}} }}

{{cite journal|last1=Yukawa|first1=Satoshi|title=A Quantum Analogue of the Jarzynski Equality|journal=Journal of the Physical Society of Japan|volume=69|issue=8|year=2000|pages=2367–2370|issn=0031-9015|doi=10.1143/JPSJ.69.2367|arxiv=cond-mat/0007456|bibcode=2000JPSJ...69.2367Y|ref=harv}}

{{cite journal|last1=Zel'Dovich|first1=Y. B.|title=The quasienergy of a quantum-mechanical system subjected to a periodic action|journal=Soviet Physics JETP|date=1967|volume=24|issue=5|pages=1006–1008|url=http://jetp.ac.ru/cgi-bin/dn/e_024_05_1006.pdf|bibcode=1967JETP...24.1006Z|ref=harv}}

{{cite journal|last1=Zhang|first1=J.|last2=Hess|first2=P. W.|last3=Kyprianidis|first3=A.|last4=Becker|first4=P.|last5=Lee|first5=A.|last6=Smith|first6=J.|last7=Pagano|first7=G.|last8=Potirniche|first8=I.-D.|last9=Potter|first9=A. C.|last10=Vishwanath|first10=A.|last11=Yao|first11=N. Y.|last12=Monroe|first12=C.|title=Observation of a Discrete Time Crystal|arxiv=1609.08684v1|bibcode=2017Natur.543..217Z|journal=Nature|volume=543|issue=7644|year=2017|pages=217–220|issn=0028-0836|doi=10.1038/nature21413|pmid=28277505|ref={{harvid|Zhang et al.|2017}} }}

{{refend}}

Books

{{Refbegin|30em|indent=yes}}

{{cite journal|last1=Bordag|first1=M.|last2=Mohideen|first2=U.|last3=Mostepanenko|first3=V.M.|title=New developments in the Casimir effect|journal=Physics Reports|volume=353|issue=1–3|year=2001|pages=1–205|issn=0370-1573|doi=10.1016/S0370-1573(01)00015-1|arxiv=quant-ph/0106045|ref=harv|bibcode=2001PhR...353....1B}}

{{cite book|last1=Bordag|first1=M.|last2=Mohideen|first2=U.|last3=Mostepanenko|first3=V.M.|last4=Klimchitskaya|first4=G. L|title=Advances in the Casimir Effect|url=https://books.google.com/books?id=CqE1f_s5PgYC|date=28 May 2009|publisher=Oxford University Press|location=Oxford|isbn=978-0-19-157988-2|ref=harv}}

{{cite book|last1=Cao|first1=Tian Yu|title=Conceptual Foundations of Quantum Field Theory|url=https://books.google.com/books?id=d0wS0EJHZ3MC&printsec=frontcover#v=onepage&q&f=falseC|date=25 March 2004|publisher=Cambridge University Press|isbn=978-0-521-60272-3|location=Cambridge|ref=harv}}

{{cite book|last1=Enz|first1=Charles P.|editor1-last=Enz|editor1-first=C. P.|editor2-last=Mehra|editor2-first=J.|title=Physical Reality and Mathematical Description|chapter=Is the Zero-Point Energy Real?|date=1974|publisher=D. Reidel Publishing Company|location=Dordrecht|isbn=978-94-010-2274-3|pages=124–132|doi=10.1007/978-94-010-2274-3_8|ref=harv}}

{{cite book|last1=Greiner|first1=Walter|last2=Müller|first2=B.|last3=Rafelski|first3=J.|title=Quantum Electrodynamics of Strong Fields: With an Introduction into Modern Relativistic Quantum Mechanics|date=2012|publisher=Springer|isbn=978-3-642-82274-2|doi=10.1007/978-3-642-82272-8|url=https://books.google.com/books?id=Wh3-CAAAQBAJ&printsec=frontcover#v=onepage&q&f=false|ref={{harvid|Greiner et al.|2012}} }}

{{cite book|last1=Lee|first1=T. D.|title=Particle Physics|url=https://books.google.com/books?id=sZxBBAAAQBAJ&printsec=frontcover&vq=unobservable#v=onepage&q&f=false|date=15 August 1981|publisher=CRC Press|isbn=978-3-7186-0033-5|ref=harv}}

{{cite book|last1=Feng|first1=Duan|last2=Jin|first2=Guojun|title=Introduction to Condensed Matter Physics|url=https://books.google.com/books?id=-iuYN5arHwoC&printsec=frontcover#v=onepage&q&f=false|year=2005|publisher=World Scientific|location=singapore|isbn=978-981-238-711-0|ref=harv}}

{{cite book|last1=Milonni|first1=Peter W.|authorlink1=Peter W. Milonni|title=The Quantum Vacuum: An Introduction to Quantum Electrodynamics|date=1994|publisher=Academic Press|location=London|isbn=978-0-124-98080-8|url=https://books.google.com/books?id=uPHJCgAAQBAJ&lpg=PP1&dq=inauthor%3A%22Peter%20W.%20Milonni%22&pg=PP1#v=onepage&q&f=false|ref=harv}}

{{cite book|title=Quantum Mechanics for Pedestrians 2: Applications and Extensions|url=https://books.google.com/books?id=KOy5BAAAQBAJ&printsec=frontcover#v=onepage&q&f=false|publisher=Springer|isbn=978-3-319-00813-4|last1=Pade|first1=Jochen|year=2014|issn=2192-4791|doi=10.1007/978-3-319-00813-4|location=Dordrecht|ref=harv|series=Undergraduate Lecture Notes in Physics}}

{{cite book|last1=Schwinger|first1=Julian|title=Particles, Sources, And Fields, Volume 1: v. 1 (Advanced Books Classics)|date=1998a|publisher=Perseus|isbn=978-0-738-20053-8|ref=harv}}

{{cite book|last1=Schwinger|first1=Julian|title=Particles, Sources, And Fields, Volume 2: v. 2 (Advanced Books Classics)|date=1998b|publisher=Perseus|isbn=978-0-738-20054-5|ref=harv}}

{{cite book|last1=Schwinger|first1=Julian|title=Particles, Sources, And Fields, Volume 3: v. 3 (Advanced Books Classics)|date=1998c|publisher=Perseus|isbn=978-0-738-20055-2|ref=harv}}

{{cite book|last1=Sólyom|first1=Jenö|title=Fundamentals of the Physics of Solids: Volume 1: Structure and Dynamics|url=https://books.google.com/books?id=zn-se2TKv3QC|date=19 September 2007|publisher=Springer|isbn=978-3-540-72600-5|ref=harv}}

{{cite book|last1=Wilczek|first1=Frank|title=A Beautiful Question: Finding Nature's Deep Design|url=https://books.google.com/books?id=Oh3ICAAAQBAJ&printsec=frontcover#v=onepage&q&f=false|date=16 July 2015|publisher=Penguin Books Limited|isbn=978-1-84614-702-9|ref=harv}}

{{refend}}

Press

{{Refbegin|30em|indent=yes}}

{{cite web|author1=Aalto University|title=Physicists discover quantum-mechanical monopoles|url=https://phys.org/news/2015-04-physicists-quantum-mechanical-monopoles.html|website=phys.org|publisher=Science X|archiveurl=https://archive.today/20150430211147/http://phys.org/news/2015-04-physicists-quantum-mechanical-monopoles.html|archivedate=30 April 2015|date=30 April 2015|ref=harv|deadurl=yes|df=}}

{{cite journal|last1=Aitchison|first1=Ian|title=Observing the Unobservable|journal=New Scientist|date=19 November 1981|volume=92|issue=1280|pages=540–541|url=https://books.google.com/books?id=riW31Fy4kpkC&printsec=frontcover#v=onepage&q&f=false|issn=0262-4079|ref=harv}}

{{cite web|author1=Amherst College|title=Physicists create synthetic magnetic monopole predicted more than 80 years ago|url=https://phys.org/news/2014-01-physicists-synthetic-magnetic-monopole-years.html|archiveurl=https://archive.today/20140129235555/http://phys.org/news/2014-01-physicists-synthetic-magnetic-monopole-years.html|archivedate=29 January 2014|date=29 January 2014|website=phys.org|publisher=Science X|ref=harv|deadurl=yes|df=}}

{{cite web|last1=Aron|first1=Jacob|title=Computer that could outlive the universe a step closer|url=https://www.newscientist.com/article/dn22028-computer-that-could-outlive-the-universe-a-step-closer/|website=newscientist.com|publisher=New Scientist|archiveurl=https://archive.today/20170202104051/https://www.newscientist.com/article/dn22028-computer-that-could-outlive-the-universe-a-step-closer/|archivedate=2 February 2017|date=6 July 2012|ref=harv|deadurl=yes|df=}}

{{cite web|last1=Ball|first1=Philip|title=Focus: New Crystal Type is Always in Motion|url=http://physics.aps.org/articles/v9/4|website=physics.aps.org|publisher=APS Physics|archiveurl=https://archive.today/20170203141844/http://physics.aps.org/articles/v9/4|archivedate=3 February 2017|date=8 January 2016|ref=harv|deadurl=yes|df=}}

{{cite journal|last1=Ball|first1=Philip|title=Scepticism greets pitch to detect dark energy in the lab|journal=Nature|volume=430|issue=6996|date=8 July 2004|pages=126|issn=0028-0836|doi=10.1038/430126b|pmid=15241374|bibcode=2004Natur.430..126B|ref=harv}}

{{cite web|last1=Cartlidge|first1=Edwin|title=Scientists build heat engine from a single atom|url=http://www.sciencemag.org/news/2015/10/scientists-build-heat-engine-single-atom|website=sciencemag.org|publisher=Science Magazine|archiveurl=https://archive.today/20170201155641/http://www.sciencemag.org/news/2015/10/scientists-build-heat-engine-single-atom|archivedate=1 February 2017|date=21 October 2015|ref=harv|deadurl=yes|df=}}

{{cite web|last1=Chandler|first1=David|title=Topological insulators: Persuading light to mix it up with matter|url=https://phys.org/news/2013-10-topological-insulators.html|website=phys.org|publisher=Science X|archiveurl=https://archive.today/20170208171631/https://phys.org/news/2013-10-topological-insulators.html|archivedate=8 February 2017|date=24 October 2014|ref=harv|deadurl=yes|df=}}

{{cite journal|last1=Coleman|first1=Piers|title=Quantum physics: Time crystals|journal=Nature|volume=493|issue=7431|date=9 January 2013|pages=166–167|issn=0028-0836|doi=10.1038/493166a|pmid=23302852|bibcode=2013Natur.493..166C|ref=harv}}

{{cite web|last1=Cowen|first1=Ron|title="Time Crystals" Could Be a Legitimate Form of Perpetual Motion|url=https://www.scientificamerican.com/article/time-crystals-could-be-legitimate-form-perpetual-motion/|website=scientificamerican.com|publisher=Scientific American|archiveurl=https://archive.is/20170202101455/https://www.scientificamerican.com/article/time-crystals-could-be-legitimate-form-perpetual-motion/|archivedate=2 February 2017|date=27 February 2012|ref=harv}}

{{cite web|last1=Daghofer|first1=Maria|title=Viewpoint: Toward Fractional Quantum Hall Physics with Cold Atoms|url=http://physics.aps.org/articles/v6/49#c2|website=physics.aps.org|publisher=APS Physics|archiveurl=https://archive.today/20170207153409/http://physics.aps.org/articles/v6/49%23c2#c2|archivedate=7 February 2017|date=29 April 2013|ref=harv|deadurl=yes|df=}}

{{cite journal|last1=Gibney|first1=Elizabeth|title=The quest to crystallize time|journal=Nature|volume=543|issue=7644|year=2017|pages=164–166|issn=0028-0836|doi=10.1038/543164a|pmid=28277535|ref=harv|bibcode=2017Natur.543..164G}}

{{cite web|last1=Grossman|first1=Lisa|title=Death-defying time crystal could outlast the universe|url=https://www.newscientist.com/article/mg21328484-000-death-defying-time-crystal-could-outlast-the-universe/|website=newscientist.com|publisher=New Scientist|archiveurl=https://archive.is/20170202104619/https://www.newscientist.com/article/mg21328484-000-death-defying-time-crystal-could-outlast-the-universe/|archivedate=2 February 2017|date=18 January 2012}}

{{cite web|last1=Hackett|first1=Jennifer|title=Curious Crystal Dances for Its Symmetry|url=https://www.scientificamerican.com/article/curious-crystal-dances-for-its-symmetry/|website=scientificamerican.com|publisher=Scientific American|archiveurl=https://archive.today/20170203152135/https://www.scientificamerican.com/article/curious-crystal-dances-for-its-symmetry/|archivedate=3 February 2017|date=22 February 2016|ref=harv|deadurl=yes|df=}}

{{cite web|last1=Hewitt|first1=John|title=Creating time crystals with a rotating ion ring|url=https://phys.org/news/2013-05-crystals-rotating-ion.html|website=phys.org|publisher=Science X|archiveurl=https://archive.today/20130704232506/http://phys.org/news/2013-05-crystals-rotating-ion.html|archivedate=4 July 2013|date=3 May 2013|deadurl=yes|df=}}

{{cite web|last1=Johnston|first1=Hamish|title='Choreographic crystals' have all the right moves|url=http://physicsworld.com/cws/article/news/2016/jan/18/choreographic-crystals-have-all-the-right-moves|website=physicsworld.com|publisher=Institute of Physics|archiveurl=https://archive.today/20170203142329/http://physicsworld.com/cws/article/news/2016/jan/18/choreographic-crystals-have-all-the-right-moves|archivedate=3 February 2017|date=18 January 2016|ref=harv|deadurl=yes|df=}}

{{cite web|author1=Johannes Gutenberg Universitaet Mainz|title=Prototype of single ion heat engine created|url=https://www.sciencedaily.com/releases/2014/02/140203101031.htm|website=sciencedaily.com|publisher=ScienceDaily|archiveurl=https://archive.today/20170201102542/https://www.sciencedaily.com/releases/2014/02/140203101031.htm|archivedate=1 February 2017|date=3 February 2014|ref={{harvid|Johannes Gutenberg Universitaet Mainz|2014}}|deadurl=yes|df=}}

{{cite web|author1=Joint Quantum Institute|title=Floquet Topological Insulators|url=http://jqi.umd.edu/news/floquet-topological-insulators|website=jqi.umd.edu|publisher=Joint Quantum Institute|date=22 March 2011|ref=harv}}

{{cite web|last1=Morgan|first1=James|title=Elusive magnetic 'monopole' seen in quantum system|url=https://www.bbc.co.uk/news/science-environment-25946734|website=bbc.co.uk|publisher=BBC|archiveurl=https://archive.today/20140130075042/http://www.bbc.co.uk/news/science-environment-25946734|archivedate=30 January 2014|date=30 January 2014|ref=harv|deadurl=yes|df=}}

{{cite web|last1=Moskowitz|first1=Clara|title=New Particle Is Both Matter and Antimatter|url=https://www.scientificamerican.com/article/majorana-particle-matter-and-antimatter/|website=scientificamerican.com|publisher=Scientific American|archiveurl=https://archive.is/20141009014336/http://www.scientificamerican.com/article/majorana-particle-matter-and-antimatter/|archivedate=9 October 2014|date=2 October 2014|ref=harv}}

{{cite web|last1=Ouellette|first1=Jennifer|title=World's first time crystals cooked up using new recipe|url=https://www.newscientist.com/article/2119804-worlds-first-time-crystals-cooked-up-using-new-recipe/|website=newscientist.com|publisher=New Scientist|archiveurl=https://archive.today/20170201185926/https://www.newscientist.com/article/2119804-worlds-first-time-crystals-cooked-up-using-new-recipe/|archivedate=1 February 2017|date=31 January 2017|ref=harv|deadurl=yes|df=}}

{{cite news|last1=Pilkington|first1=Mark|title=Zero point energy|url=https://www.theguardian.com/education/2003/jul/17/research.highereducation|publisher=The Guardian|date=17 July 2003|archiveurl=https://archive.is/20170207125201/https://www.theguardian.com/education/2003/jul/17/research.highereducation|archivedate=7 February 2017|website=theguardian.com|ref=harv}}

{{cite journal|last1=Powell|first1=Devin|title=Can matter cycle through shapes eternally?|journal=Nature|year=2013|issn=1476-4687|doi=10.1038/nature.2013.13657|url=http://www.nature.com/news/can-matter-cycle-through-shapes-eternally-1.13657|archiveurl=https://archive.is/20170203080014/http://www.nature.com/news/can-matter-cycle-through-shapes-eternally-1.13657|archivedate=3 February 2017|ref=harv}}

{{cite web|last1=Rao|first1=Achintya|title=BaBar makes first direct measurement of time-reversal violation|url=http://physicsworld.com/cws/article/news/2012/nov/21/babar-makes-first-direct-measurement-of-time-reversal-violation|website=physicsworld.com|publisher=Institute of Physics|archiveurl=https://archive.today/20150324082309/http://physicsworld.com/cws/article/news/2012/nov/21/babar-makes-first-direct-measurement-of-time-reversal-violation|archivedate=24 March 2015|date=21 November 2012|ref=harv|deadurl=yes|df=}}

{{cite web|last1=Richerme|first1=Phil|title=Viewpoint: How to Create a Time Crystal|url=http://physics.aps.org/articles/v10/5|website=physics.aps.org|publisher=APS Physics|archiveurl=https://archive.today/20170202115727/http://physics.aps.org/articles/v10/5|archivedate=2 February 2017|date=18 January 2017|ref={{harvid|Richerme|2017}}|deadurl=yes|df=}}

{{cite web|last1=Thomas|first1=Jessica|title=Notes from the Editors: The Aftermath of a Controversial Idea|url=http://physics.aps.org/articles/v6/31|website=physics.aps.org|publisher=APS Physics|archiveurl=https://archive.today/20170202100552/http://physics.aps.org/articles/v6/31|archivedate=2 February 2017|date=15 March 2013|ref=harv|deadurl=yes|df=}}

{{cite journal|last1=Qi|first1=Xiao-Liang|last2=Zhang|first2=Shou-Cheng|title=The quantum spin Hall effect and topological insulators|journal=Physics Today|volume=63|issue=1|year=2010|pages=33–38|issn=0031-9228|doi=10.1063/1.3293411|url=http://web.physics.ucsb.edu/~phys123B/w2015/QiZhangReview-1.pdf|ref=harv|arxiv=1001.1602|bibcode=2010PhT....63a..33Q}}

{{cite web|author1=University of California, Berkeley|title=Physicists unveil new form of matter—time crystals|url=https://phys.org/news/2017-01-physicists-unveil-mattertime-crystals.html|website=phys.org|publisher=Science X|archiveurl=https://archive.today/20170128214118/https://phys.org/news/2017-01-physicists-unveil-mattertime-crystals.html|archivedate=28 January 2017|date=26 January 2017|deadurl=yes|df=}}

{{cite web|last1=Weiner|first1=Sophie|title=Scientists Create A New Kind Of Matter: Time Crystals|url=http://www.popularmechanics.com/science/a24957/time-crystals/|website=popularmechanics.com|publisher=Popular mechanics|archiveurl=https://archive.today/20170203161545/http://www.popularmechanics.com/science/a24957/time-crystals/|archivedate=3 February 2017|date=28 January 2017|ref=harv|deadurl=yes|df=}}

{{cite web|last1=Wolchover|first1=Natalie|title=Perpetual Motion Test Could Amend Theory of Time|url=https://www.quantamagazine.org/20130425-perpetual-motion-test-could-amend-theory-of-time/#|website=quantamagazine.org|publisher=Simons Foundation|archiveurl=https://archive.today/20170202105225/https://www.quantamagazine.org/20130425-perpetual-motion-test-could-amend-theory-of-time/|archivedate=2 February 2017|date=25 April 2013|ref=harv|deadurl=yes|df=}}

{{cite web|last1=Wolchover|first1=Natalie|title=Forging a Qubit to Rule Them All|url=https://www.quantamagazine.org/20140515-forging-a-qubit-to-rule-them-all/|website=quantamagazine.org|publisher=Simmons Foundation|archiveurl=https://archive.today/20160315170716/https://www.quantamagazine.org/20140515-forging-a-qubit-to-rule-them-all/|archivedate=15 March 2016|date=15 May 2014|ref=harv|deadurl=yes|df=}}

{{cite web|last1=Wood|first1=Charlie|title=Time crystals realize new order of space-time|url=http://www.csmonitor.com/Science/2017/0131/Time-crystals-realize-new-order-of-space-time|website=csmonitor.com|publisher=Christian Science Monitor|archiveurl=https://archive.today/20170202110602/http://www.csmonitor.com/Science/2017/0131/Time-crystals-realize-new-order-of-space-time|archivedate=2 February 2017|date=31 January 2017|ref=harv|deadurl=yes|df=}}

{{cite web|last1=Yirka|first1=Bob|title=Physics team proposes a way to create an actual space-time crystal|url=https://phys.org/news/2012-07-physics-team-actual-space-time-crystal.html|website=phys.org|publisher=Science X|archiveurl=https://archive.today/20130415190255/http://phys.org/news/2012-07-physics-team-actual-space-time-crystal.html|archivedate=15 April 2013|date=9 July 2012|deadurl=yes|df=}}

{{cite web|last1=Zakrzewski|first1=Jakub|title=Viewpoint: Crystals of Time|url=http://physics.aps.org/articles/v5/116|website=physics.aps.org|publisher=APS Physics|archiveurl=https://archive.today/20170202102150/http://physics.aps.org/articles/v5/116|archivedate=2 February 2017|date=15 October 2012|deadurl=yes|df=}}

{{cite web|last1=Zeller|first1=Michael|title=Viewpoint: Particle Decays Point to an Arrow of Time|url=http://physics.aps.org/articles/v5/129|website=physics.aps.org|publisher=APS Physics|archiveurl=https://archive.today/20170204141533/http://physics.aps.org/articles/v5/129|archivedate=4 February 2017|date=19 November 2012|ref=harv|deadurl=yes|df=}}

{{cite web|last1=Zyga|first1=Lisa|title=Time crystals could behave almost like perpetual motion machines|url=https://phys.org/news/2012-02-crystals-perpetual-motion-machines.html#nRlv|website=phys.org|publisher=Science X|archiveurl=https://archive.today/20170203082720/https://phys.org/news/2012-02-crystals-perpetual-motion-machines.html%23nRlv#nRlv|archivedate=3 February 2017|date=20 February 2012|deadurl=yes|df=}}

{{cite web|last1=Zyga|first1=Lisa|title=Physicist proves impossibility of quantum time crystals|url=https://phys.org/news/2013-08-physicist-impossibility-quantum-crystals.html|website=phys.org|publisher=Space X|archiveurl=https://archive.today/20170203084130/https://phys.org/news/2013-08-physicist-impossibility-quantum-crystals.html|archivedate=3 February 2017|date=22 August 2013|deadurl=yes|df=}}

{{cite web|last1=Zyga|first1=Lisa|title=Nanoscale heat engine exceeds standard efficiency limit|url=https://phys.org/news/2014-01-nanoscale-standard-efficiency-limit.html|website=phys.org|publisher=Science X|archiveurl=https://archive.today/20150404110141/http://phys.org/news/2014-01-nanoscale-standard-efficiency-limit.html|archivedate=4 April 2015|date=27 January 2014|ref=harv|deadurl=yes|df=}}

{{cite web|last1=Zyga|first1=Lisa|title=Physicists propose new definition of time crystals—then prove such things don't exist|url=https://phys.org/news/2015-07-physicists-definition-crystalsthen-dont.html|website=phys.org|publisher=Science X|archiveurl=https://archive.today/20150709134338/http://phys.org/news/2015-07-physicists-definition-crystalsthen-dont.html|archivedate=9 July 2015|date=9 July 2015|deadurl=yes|df=}}

{{cite web|last1=Zyga|first1=Lisa|title=Time crystals might exist after all (Update)|url=https://phys.org/news/2016-09-crystals.html|website=phys.org|publisher=Science X|archiveurl=https://archive.today/20160911165310/http://phys.org/news/2016-09-crystals.html|archivedate=11 September 2016|date=9 September 2016|deadurl=yes|df=}}

{{Refend}}

External links

  • [https://www.umdphysics.umd.edu/people/faculty/current/item/348-monroe.html Christopher Monroe] at University of Maryland
  • Frank Wilczek
  • Lukin Group at Harvard University
  • Norman Yao at Berkeley University
{{Condensed matter physics topics}}{{Quantum computing}}{{Statistical mechanics topics}}{{Physics-footer}}{{DEFAULTSORT:Condensed Matter Physics}}

12 : Branches of thermodynamics|Condensed matter physics|Concepts in physics|Crystallography|Non-equilibrium thermodynamics|Perpetual motion|Physical paradoxes|Quantum information theory|Quantum measurement|Quantum mechanics|Statistical mechanics|2012 in science
随便看

　

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。

　

Copyright © 2023 OENC.NET All Rights Reserved
京ICP备2021023879号 更新时间：2024/9/27 19:15:14