Khác biệt giữa bản sửa đổi của “Tinh thể thời gian”

Bách khoa toàn thư mở Wikipedia
Duyệt lịch sử tương tác
← Thay đổi trướcThay đổi sau →
Nội dung được xóa Nội dung được thêm vào
Trực quanMã wiki
Dòng 7: Dòng 7:
==Tham khảo==
==Tham khảo==
{{tham khảo}}
{{tham khảo}}

===Tạp chí khoa học===
{{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|url=https://arxiv.org/pdf/astro-ph/0406504v2.pdf|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|url=https://arxiv.org/pdf/1407.5876v2.pdf|arxiv=1407.5876v2|bibcode=2016PhRvL.116a5503B|ref={{harvid|Boyle et al.|2016}} }}
: {{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|url=https://arxiv.org/pdf/1210.4128v1.pdf|ref=harv}}
: {{cite journal|last1=Bruno|first1=Patrick|title=Comment on "Space-Time Crystals of Trapped Ions"|journal=Physical Review Letters|volume=111|issue=2|year=2013b|issn=0031-9007|doi=10.1103/PhysRevLett.111.029301|arxiv=1211.4792v1 |url=https://arxiv.org/pdf/1211.4792v1.pdf|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|url=https://arxiv.org/pdf/1012.2268v5.pdf|arxiv=1012.2268v5|bibcode=2011RvMP...83..771C|ref={{harvid|Campisi et al.|2011}} }}
: {{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|url=https://arxiv.org/pdf/1610.08057v1.pdf|arxiv=1610.08057v1|bibcode=2016arXiv161008057C|journal=Nature|volume=543|issue=7644|year=2017|pages=221–225|issn=0028-0836|doi=10.1038/nature21426|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|url=https://arxiv.org/pdf/1203.6588v1.pdf|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|url=https://arxiv.org/pdf/1302.0462v1.pdf|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|year=2013b|issn=1550-7998|doi=10.1103/PhysRevD.87.025021|url=https://arxiv.org/pdf/1207.3052v2.pdf|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|url=https://arxiv.org/pdf/hep-th/0603057v3.pdf|ref={{harvid|Copeland et al.|2006}} }}
: {{cite journal|last1=Dillenschneider|first1=R.|last2=Lutz|first2=E.|title=Energetics of quantum correlations|journal=EPL (Europhysics Letters)|volume=88|issue=5|year=2009|pages=50003|issn=0295-5075|doi=10.1209/0295-5075/88/50003|url=https://arxiv.org/pdf/0803.4067.pdf|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|url=https://arxiv.org/pdf/1603.08001v4.pdf|ref={{harvid|Else et al.|2016}} }}
: {{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|url=https://arxiv.org/pdf/0811.3717v2.pdf|arxiv=0811.3717v2|bibcode=2009RvMP...81.1665E|ref={{harvid|Esposito et al.|2009}} }}
: {{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}}
: {{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|year=2013|issn=0031-9007|doi=10.1103/PhysRevLett.111.205303|arxiv=1305.1800v3|url=https://arxiv.org/pdf/1305.1800v3.pdf|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|url=https://arxiv.org/pdf/1002.3895v2.pdf|arxiv=1002.3895v2|bibcode=2010RvMP...82.3045H|ref=harv}}
: {{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|url=https://arxiv.org/pdf/quant-ph/0702225v2.pdf|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|url=https://arxiv.org/pdf/hep-th/0503158v1.pdf|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|url=https://arxiv.org/pdf/astro-ph/0604522v1.pdf|bibcode=2006PhLB..639...57J|ref=harv}}
: {{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|year=2016|issn=0031-9007|doi=10.1103/PhysRevLett.116.250401|bibcode=2016PhRvL.116y0401K|arxiv=1508.03344v3|url=https://arxiv.org/pdf/1508.03344v3.pdf|ref={{harvid|Khemani et al.|2016}} }}
: {{cite journal|last1=Lees|first1=J. P.|title=Observation of Time-Reversal Violation in the ''B''<sup>0</sup> Meson System|journal=Physical Review Letters|volume=109|issue=21|year=2012|issn=0031-9007|doi=10.1103/PhysRevLett.109.211801|arxiv=1207.5832v4|url=https://arxiv.org/pdf/1207.5832v4.pdf|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|year=2012a|issn=0031-9007|doi=10.1103/PhysRevLett.109.163001|url=https://arxiv.org/pdf/1206.4772v2.pdf|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|url=https://arxiv.org/pdf/1212.6959v2.pdf|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|url=https://arxiv.org/pdf/1008.1792v2.pdf|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|url=https://arxiv.org/pdf/1410.0682v1.pdf|bibcode=2014Sci...346..602N|ref={{harvid|Nadi-Perge et al.|2014}} }}
: {{cite journal|last1=Nozières|first1=Philippe|title=Time crystals: Can diamagnetic currents drive a charge density wave into rotation?|journal=EPL (Europhysics Letters)|volume=103|issue=5|year=2013|pages=57008|issn=0295-5075|doi=10.1209/0295-5075/103/57008|arxiv=1306.6229v1|url=https://arxiv.org/pdf/1306.6229v1.pdf|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|year=2015|issn=1050-2947|doi=10.1103/PhysRevA.91.033617|bibcode=2015PhRvA..91c3617S|arxiv=1410.3638v3|url=https://arxiv.org/pdf/1410.3638v3.pdf|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}}
: {{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|url=https://arxiv.org/pdf/1205.4176.pdf|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|year=2012|issn=0031-9007|doi=10.1103/PhysRevLett.109.160402|bibcode=2012PhRvL.109p0402S|arxiv=1202.2537v2|url=https://arxiv.org/pdf/1202.2537v2.pdf|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|url=https://arxiv.org/pdf/1508.07026v1.pdf|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|url=https://arxiv.org/pdf/0707.3400.pdf|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/profile/J_Mendonca/publication/272040551_Time_Crystals_in_Ultracold_Matter/links/54f6ea340cf2ca5eff007953.pdf|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|url=https://arxiv.org/pdf/1112.6238.pdf|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|url=https://arxiv.org/pdf/1408.3133v1.pdf|ref={{harvid|Ray et al.|2014}} }}
: {{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|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=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|url=https://arxiv.org/pdf/1308.5935.pdf|arxiv=1308.5935|bibcode=2014PhRvL.112c0602R|ref={{harvid|Roßnagel et al.|2014}} }}
: {{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|url=https://arxiv.org/pdf/1510.03681.pdf|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|url=https://arxiv.org/pdf/cond-mat/9711045.pdf|arxiv=cond-mat/9711045|ref={{harvid|Tatara et al.|1998}} }}
: {{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 |url=https://arxiv.org/pdf/1309.1845v2.pdf|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|year=2016|issn=2469-9950|doi=10.1103/PhysRevB.94.085112|arxiv=1605.00639v3|bibcode=2016PhRvB..94h5112V|url=https://arxiv.org/pdf/1605.00639v3.pdf|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|arxiv=1310.7563v1|bibcode=2013Sci...342..453W|url=https://arxiv.org/pdf/1310.7563v1.pdf|ref={{harvid|Wang et al.|2013}} }}
: {{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=2015|issn=0031-9007|doi=10.1103/PhysRevLett.114.251603|bibcode=2015PhRvL.114y1603W|arxiv=1410.2143v3|url=https://arxiv.org/pdf/1410.2143v3.pdf|ref=harv}}
: {{cite journal|last1=Wilczek|first1=Frank|title=Quantum Time Crystals|journal=Physical Review Letters|volume=109|issue=16|year=2012|issn=0031-9007|doi=10.1103/PhysRevLett.109.160401|arxiv=1202.2539v2|url=https://arxiv.org/pdf/1202.2539v2.pdf|bibcode=2012PhRvL.109p0401W|ref=harv}}
: {{cite journal|last1=Wilczek|first1=Frank|title=Wilczek Reply:|journal=Physical Review Letters|volume=110|issue=11|year=2013a|issn=0031-9007|doi=10.1103/PhysRevLett.110.118902|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|year=2013b|issn=0031-9007|doi=10.1103/PhysRevLett.111.250402|bibcode=2013PhRvL.111y0402W|arxiv=1308.5949v1|url=https://arxiv.org/pdf/1308.5949v1.pdf|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|year=2013|issn=0031-9007|doi=10.1103/PhysRevLett.111.186401|bibcode=2013PhRvL.111r6401W|arxiv=1301.2639v1|url=https://arxiv.org/pdf/1301.2639v1.pdf|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|year=2017|issn=0031-9007|doi=10.1103/PhysRevLett.118.030401|arxiv=1608.02589v2|url=https://arxiv.org/pdf/1608.02589v2.pdf|bibcode=2016arXiv160802589Y|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|year=2015|issn=1098-0121|doi=10.1103/PhysRevB.92.224512|arxiv=1404.3519v2|url=https://arxiv.org/pdf/1404.3519v2.pdf|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|url=https://arxiv.org/pdf/cond-mat/9706222.pdf|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|url=https://arxiv.org/pdf/cond-mat/0007456.pdf|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|url=https://arxiv.org/pdf/1609.08684v1.pdf|arxiv=1609.08684v1|bibcode=2016arXiv160908684Z|journal=Nature|volume=543|issue=7644|year=2017|pages=217–220|issn=0028-0836|doi=10.1038/nature21413|ref={{harvid|Zhang et al.|2017}} }}
{{refend}}

{{sơ khai vật lý}}
{{sơ khai vật lý}}

Phiên bản lúc 09:06, ngày 16 tháng 3 năm 2017

Tinh thể thời gian hoặc tinh thể thời gian-không gian là một hệ thống mở không cân bằng với môi trường của nó thể hiện sự phá vỡ đối xứng thời gian dịch (TTSB). Không thể cho một tinh thể thời gian được trong sự cân bằng với môi trường của nó. Ý tưởng về pha lê thời gian lần đầu tiên được Nobel đoạt giải và giáo sư Frank Wilczek của MIT vào năm 2012[a]. Một tinh thể không gian thời gian mở rộng sự đối xứng ba chiều thường thấy trong tinh thể để bao gồm chiều thứ tư của thời gian; Một tinh thể thời gian tự nhiên phá vỡ tính đối xứng của bản dịch thời gian. Kiểu của tinh thể không lặp lại trong không gian, nhưng theo thời gian cho phép tinh thể được chuyển động vĩnh viễn [2]. Các tinh thể thời gian có liên quan mật thiết đến khái niệm năng lượng không điểm và hiệu ứng Casimir động[b]

Vào năm 2016, Norman Yao và các đồng nghiệp của ông từ Đại học California, Berkeley, đưa ra một đề xuất cụ thể cho phép tạo ra các tinh thể thời gian trong môi trường phòng thí nghiệm.[c] Kế hoạch chi tiết của Yao sau đó được sử dụng bởi hai đội, nhóm do Christopher Monroe thuộc Đại học Maryland[d] và một nhóm do Mikhail Lukin làm việc tại Đại học Harvard[e] , đã thành công trong việc tạo ra một tinh thể thời gian. Cả hai thí nghiệm đã được công bố trên tạp chí Nature tháng 3 năm 2017[5].

Các tinh thể thời gian được cho là có thứ tự topo[6], hiện tượng nổi lên, trong đó các mối tương quan không liên quan đến mật mã hóa trong toàn bộ chức năng sóng của một hệ thống cho phép dung sai lỗi đối với các nhiễu loạn, do đó cho phép các trạng thái lượng tử ổn định so với các hiệu ứng không liên kết thường giới hạn Tuổi thọ hữu ích. Ngăn chặn sự mất kiên nhẫn có nhiều hàm ý: Hiệu quả của một số lý thuyết thông tin và nhiệm vụ động lực học lượng tử có thể được tăng cường đáng kể khi sử dụng các trạng thái tương quan lượng tử. Người ta cũng cho rằng các tinh thể thời gian cũng có thể hiểu sâu hơn lý thuyết về thời gian[7].

Tham khảo

  1. ^ a b Powell 2013.
  2. ^ a b Sacha 2015, tr. 1.
  3. ^ Richerme 2017.
  4. ^ Richerme 2017; Wood 2017; Ouellette 2017.
  5. ^ Gibney 2017.
  6. ^ Richermen 2017.
  7. ^ Wolchover 2013.

Tạp chí khoa học

Beck, Christian; Mackey, Michael C. (2005). “Could dark energy be measured in the lab?” (PDF). Physics Letters B. 605 (3–4): 295–300. arXiv:astro-ph/0406504v2. Bibcode:2005PhLB..605..295B. doi:10.1016/j.physletb.2004.11.060. ISSN 0370-2693.Quản lý CS1: ref=harv (liên kết)
Boyle, Latham; Khoo, Jun Yong; Smith, Kendrick (2016). “Symmetric Satellite Swarms and Choreographic Crystals” (PDF). Physical Review Letters. 116 (1). arXiv:1407.5876v2. Bibcode:2016PhRvL.116a5503B. doi:10.1103/PhysRevLett.116.015503. ISSN 0031-9007.
Bruno, Patrick (2013a). “Comment on "Quantum Time Crystals"” (PDF). Physical Review Letters. 110 (11). arXiv:1210.4128v1. Bibcode:2013PhRvL.110k8901B. doi:10.1103/PhysRevLett.110.118901. ISSN 0031-9007.Quản lý CS1: ref=harv (liên kết)
Bruno, Patrick (2013b). “Comment on "Space-Time Crystals of Trapped Ions"” (PDF). Physical Review Letters. 111 (2). arXiv:1211.4792v1. Bibcode:2013PhRvL.111b9301B. doi:10.1103/PhysRevLett.111.029301. ISSN 0031-9007.Quản lý CS1: ref=harv (liên kết)
Campisi, Michele; Hänggi, Peter; Talkner, Peter (2011). “Colloquium: Quantum fluctuation relations: Foundations and applications” (PDF). Reviews of Modern Physics. 83 (3): 771–791. arXiv:1012.2268v5. Bibcode:2011RvMP...83..771C. doi:10.1103/RevModPhys.83.771. ISSN 0034-6861.
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. (2017). “Observation of discrete time-crystalline order in a disordered dipolar many-body system” (PDF). Nature. 543 (7644): 221–225. arXiv:1610.08057v1. Bibcode:2016arXiv161008057C. doi:10.1038/nature21426. ISSN 0028-0836.
Chernodub, M. N. (2012). “Permanently rotating devices: extracting rotation from quantum vacuum fluctuations?” (PDF). arXiv:1203.6588v1. Bibcode:2012arXiv1203.6588C. Chú thích journal cần |journal= (trợ giúp)Quản lý CS1: ref=harv (liên kết)
Chernodub, M. N. (2013a). “Zero-point fluctuations in rotation: Perpetuum mobile of the fourth kind without energy transfer” (PDF). Nuovo Cimento C. 5 (36): 53–63. arXiv:1302.0462v1. Bibcode:2013arXiv1302.0462C. doi:10.1393/ncc/i2013-11523-5.Quản lý CS1: ref=harv (liên kết)
Chernodub, M. N. (2013b). “Rotating Casimir systems: Magnetic-field-enhanced perpetual motion, possible realization in doped nanotubes, and laws of thermodynamics” (PDF). Physical Review D. 87 (2). arXiv:1207.3052v2. Bibcode:2013PhRvD..87b5021C. doi:10.1103/PhysRevD.87.025021. ISSN 1550-7998.Quản lý CS1: ref=harv (liên kết)
Copeland, Edmund J.; Sami, M.; Tsujikawa, Shinji (2006). “Dynamics of dark energy” (PDF). International Journal of Modern Physics D. 15 (11): 1753–1935. arXiv:hep-th/0603057. Bibcode:2006IJMPD..15.1753C. doi:10.1142/S021827180600942X. ISSN 0218-2718.
Dillenschneider, R.; Lutz, E. (2009). “Energetics of quantum correlations” (PDF). EPL (Europhysics Letters). 88 (5): 50003. arXiv:0803.4067. Bibcode:2009EL.....8850003D. doi:10.1209/0295-5075/88/50003. ISSN 0295-5075.Quản lý CS1: ref=harv (liên kết)
Else, Dominic V.; Bauer, Bela; Nayak, Chetan (2016). “Floquet Time Crystals” (PDF). Physical Review Letters. 117 (9). arXiv:1603.08001v4. Bibcode:2016PhRvL.117i0402E. doi:10.1103/PhysRevLett.117.090402. ISSN 0031-9007.
Esposito, Massimiliano; Harbola, Upendra; Mukamel, Shaul (2009). “Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems” (PDF). Reviews of Modern Physics. 81 (4): 1665–1702. arXiv:0811.3717v2. Bibcode:2009RvMP...81.1665E. doi:10.1103/RevModPhys.81.1665. ISSN 0034-6861.
Grifoni, Milena; Hänggi, Peter (1998). “Driven quantum tunneling” (PDF). Physics Reports. 304 (5–6): 229–354. Bibcode:1998PhR...304..229G. doi:10.1016/S0370-1573(98)00022-2. ISSN 0370-1573.Quản lý CS1: ref=harv (liên kết)
Guo, Lingzhen; Marthaler, Michael; Schön, Gerd (2013). “Phase Space Crystals: A New Way to Create a Quasienergy Band Structure” (PDF). Physical Review Letters. 111 (20). arXiv:1305.1800v3. Bibcode:2013PhRvL.111t5303G. doi:10.1103/PhysRevLett.111.205303. ISSN 0031-9007.
Hasan, M. Z.; Kane, C. L. (2010). “Colloquium: Topological insulators” (PDF). Reviews of Modern Physics. 82 (4): 3045–3067. arXiv:1002.3895v2. Bibcode:2010RvMP...82.3045H. doi:10.1103/RevModPhys.82.3045. ISSN 0034-6861.Quản lý CS1: ref=harv (liên kết)
Horodecki, Ryszard; Horodecki, Paweł; Horodecki, Michał; Horodecki, Karol (2009). “Quantum entanglement” (PDF). Reviews of Modern Physics. 81 (2): 865–942. arXiv:quant-ph/0702225v2. Bibcode:2009RvMP...81..865H. doi:10.1103/RevModPhys.81.865. ISSN 0034-6861.
Jaffe, R. L. (2005). “Casimir effect and the quantum vacuum” (PDF). Physical Review D. 72 (2): 021301. arXiv:hep-th/0503158. Bibcode:2005PhRvD..72b1301J. doi:10.1103/PhysRevD.72.021301.Quản lý CS1: ref=harv (liên kết)
Jarzynski, Christopher (2011). “Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale” (PDF). Annual Review of Condensed Matter Physics. 2 (1): 329–351. Bibcode:2011ARCMP...2..329J. doi:10.1146/annurev-conmatphys-062910-140506. ISSN 1947-5454.Quản lý CS1: ref=harv (liên kết)
Jetzer, Philippe; Straumann, Norbert (2006). “Josephson junctions and dark energy” (PDF). Physics Letters B. 639 (2): 57–58. arXiv:astro-ph/0604522. Bibcode:2006PhLB..639...57J. doi:10.1016/j.physletb.2006.06.020. ISSN 0370-2693.Quản lý CS1: ref=harv (liên kết)
Khemani, Vedika; Lazarides, Achilleas; Moessner, Roderich; Sondhi, S. L. (2016). “Phase Structure of Driven Quantum Systems” (PDF). Physical Review Letters. 116 (25). arXiv:1508.03344v3. Bibcode:2016PhRvL.116y0401K. doi:10.1103/PhysRevLett.116.250401. ISSN 0031-9007.
Lees, J. P. (2012). “Observation of Time-Reversal Violation in the B0 Meson System” (PDF). Physical Review Letters. 109 (21). arXiv:1207.5832v4. Bibcode:2012PhRvL.109u1801L. doi:10.1103/PhysRevLett.109.211801. ISSN 0031-9007.
Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang (2012a). “Space-Time Crystals of Trapped Ions” (PDF). Physical Review Letters. 109 (16). arXiv:1206.4772v2. Bibcode:2012PhRvL.109p3001L. doi:10.1103/PhysRevLett.109.163001. ISSN 0031-9007.
Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang (2012b). “Reply to Comment on "Space-Time Crystals of Trapped Ions"” (PDF). arXiv:1212.6959v2. Bibcode:2012arXiv1212.6959L. Chú thích journal cần |journal= (trợ giúp)
Lindner, Netanel H.; Refael, Gil; Galitski, Victor (2011). “Floquet topological insulator in semiconductor quantum wells” (PDF). Nature Physics. 7 (6): 490–495. arXiv:1008.1792v2. Bibcode:2011NatPh...7..490L. doi:10.1038/nphys1926. ISSN 1745-2473.
Nadj-Perge, S.; Drozdov, I. K.; Li, J.; Chen, H.; Jeon, S.; Seo, J.; MacDonald, A. H.; Bernevig, B. A.; Yazdani, A. (2014). “Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor” (PDF). Science. 346 (6209): 602–607. arXiv:1410.0682v1. Bibcode:2014Sci...346..602N. doi:10.1126/science.1259327. ISSN 0036-8075.
Nozières, Philippe (2013). “Time crystals: Can diamagnetic currents drive a charge density wave into rotation?” (PDF). EPL (Europhysics Letters). 103 (5): 57008. arXiv:1306.6229v1. Bibcode:2013EL....10357008N. doi:10.1209/0295-5075/103/57008. ISSN 0295-5075.Quản lý CS1: ref=harv (liên kết)
Sacha, Krzysztof (2015). “Modeling spontaneous breaking of time-translation symmetry” (PDF). Physical Review A. 91 (3). arXiv:1410.3638v3. Bibcode:2015PhRvA..91c3617S. doi:10.1103/PhysRevA.91.033617. ISSN 1050-2947.Quản lý CS1: ref=harv (liên kết)
Schwinger, Julian (1975). “Casimir effect in source theory”. Letters in Mathematical Physics. 1 (1): 43–47. Bibcode:1975LMaPh...1...43S. doi:10.1007/BF00405585.Quản lý CS1: ref=harv (liên kết)
Schwinger, Julian; DeRaad, Lester L.; Milton, Kimball A. (1978). “Casimir effect in dielectrics”. Annals of Physics. 115 (1): 1–23. Bibcode:1978AnPhy.115....1S. doi:10.1016/0003-4916(78)90172-0.
Scully, Marlan O. (2001). “Extracting Work from a Single Thermal Bath via Quantum Negentropy”. Physical Review Letters. 87 (22). Bibcode:2001PhRvL..87v0601S. doi:10.1103/PhysRevLett.87.220601. ISSN 0031-9007.Quản lý CS1: ref=harv (liên kết)
Scully, Marlan O.; Zubairy, M. Suhail; Agarwal, Girish S.; Walther, Herbert. (2003). “Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence”. Science. 299 (5608): 862–864. Bibcode:2003Sci...299..862S. doi:10.1126/science.1078955. ISSN 0036-8075. PMID 12511655.
Seifert, Udo (2012). “Stochastic thermodynamics, fluctuation theorems and molecular machines” (PDF). Reports on Progress in Physics. 75 (12): 126001. arXiv:1205.4176v1. Bibcode:2012RPPh...75l6001S. doi:10.1088/0034-4885/75/12/126001. ISSN 0034-4885.Quản lý CS1: ref=harv (liên kết)
Senitzky, I. R. (1960). “Dissipation in Quantum Mechanics. The Harmonic Oscillator”. Physical Review. 119 (2): 670–679. Bibcode:1960PhRv..119..670S. doi:10.1103/PhysRev.119.670. ISSN 0031-899X.Quản lý CS1: ref=harv (liên kết)
Shapere, Alfred; Wilczek, Frank (2012). “Classical Time Crystals” (PDF). Physical Review Letters. 109 (16). arXiv:1202.2537v2. Bibcode:2012PhRvL.109p0402S. doi:10.1103/PhysRevLett.109.160402. ISSN 0031-9007.Quản lý CS1: ref=harv (liên kết)
Shirley, Jon H. (1965). “Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time”. Physical Review. 138 (4B): B979–B987. Bibcode:1965PhRv..138..979S. doi:10.1103/PhysRev.138.B979. ISSN 0031-899X.Quản lý CS1: ref=harv (liên kết)
Smith, J.; Lee, A.; Richerme, P.; Neyenhuis, B.; Hess, P. W.; Hauke, P.; Heyl, M.; Huse, D. A.; Monroe, C. (2016). “Many-body localization in a quantum simulator with programmable random disorder” (PDF). Nature Physics. 12 (10): 907–911. arXiv:1508.07026v1. Bibcode:2016NatPh..12..907S. doi:10.1038/nphys3783. ISSN 1745-2473.
Maruyama, Koji; Nori, Franco; Vedral, Vlatko (2009). “Colloquium: The physics of Maxwell's demon and information” (PDF). Reviews of Modern Physics. 81 (1): 1–23. arXiv:0707.3400. Bibcode:2009RvMP...81....1M. doi:10.1103/RevModPhys.81.1. ISSN 0034-6861.
Mendonça, J. T.; Dodonov, V. V. (2014). “Time Crystals in Ultracold Matter” (PDF). Journal of Russian Laser Research. 35 (1): 93–100. doi:10.1007/s10946-014-9404-9. ISSN 1071-2836.Quản lý CS1: ref=harv (liên kết)
Modi, Kavan; Brodutch, Aharon; Cable, Hugo; Paterek, Tomasz; Vedral, Vlatko (2012). “The classical-quantum boundary for correlations: Discord and related measures” (PDF). Reviews of Modern Physics. 84 (4): 1655–1707. arXiv:1112.6238. Bibcode:2012RvMP...84.1655M. doi:10.1103/RevModPhys.84.1655. ISSN 0034-6861.
Ray, M. W.; Ruokokoski, E.; Kandel, S.; Möttönen, M.; Hall, D. S. (2014). “Observation of Dirac monopoles in a synthetic magnetic field” (PDF). Nature. 505 (7485): 657–660. arXiv:1408.3133v1. Bibcode:2014Natur.505..657R. doi:10.1038/nature12954. ISSN 0028-0836.
Ray, M. W.; Ruokokoski, E.; Tiurev, K.; Mottonen, M.; Hall, D. S. (2015). “Observation of isolated monopoles in a quantum field” (PDF). Science. 348 (6234): 544–547. Bibcode:2015Sci...348..544R. doi:10.1126/science.1258289. ISSN 0036-8075.
Reimann, Peter; Grifoni, Milena; Hänggi, Peter (1997). “Quantum Ratchets” (PDF). Physical Review Letters. 79 (1): 10–13. Bibcode:1997PhRvL..79...10R. doi:10.1103/PhysRevLett.79.10. ISSN 0031-9007.
Roßnagel, J.; Abah, O.; Schmidt-Kaler, F.; Singer, K.; Lutz, E. (2014). “Nanoscale Heat Engine Beyond the Carnot Limit” (PDF). Physical Review Letters. 112 (3). arXiv:1308.5935. Bibcode:2014PhRvL.112c0602R. doi:10.1103/PhysRevLett.112.030602. ISSN 0031-9007.
Roßnagell, J.; Dawkins, S. T.; Tolazzi, K. N.; Abah, O.; Lutz, E.; Schmidt-Kaler, F.; Singer, K. (2016). “A single-atom heat engine” (PDF). Science. 352 (6283): 325–329. arXiv:1510.03681. Bibcode:2016Sci...352..325R. doi:10.1126/science.aad6320. ISSN 0036-8075.
Tatara, Gen; Kikuchi, Makoto; Yukawa, Satoshi; Matsukawa, Hiroshi (1998). “Dissipation Enhanced Asymmetric Transport in Quantum Ratchets” (PDF). Journal of the Physical Society of Japan. 67 (4): 1090–1093. arXiv:cond-mat/9711045. doi:10.1143/JPSJ.67.1090. ISSN 0031-9015.
Volovik, G. E. (2013). “On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order” (PDF). JETP Letters. 98 (8): 491–495. arXiv:1309.1845v2. Bibcode:2013JETPL..98..491V. doi:10.1134/S0021364013210133. ISSN 0021-3640.Quản lý CS1: ref=harv (liên kết)
von Keyserlingk, C. W.; Khemani, Vedika; Sondhi, S. L. (2016). “Absolute stability and spatiotemporal long-range order in Floquet systems” (PDF). Physical Review B. 94 (8). arXiv:1605.00639v3. Bibcode:2016PhRvB..94h5112V. doi:10.1103/PhysRevB.94.085112. ISSN 2469-9950.
Wang, Y. H.; Steinberg, H.; Jarillo-Herrero, P.; Gedik, N. (2013). “Observation of Floquet-Bloch States on the Surface of a Topological Insulator” (PDF). Science. 342 (6157): 453–457. arXiv:1310.7563v1. Bibcode:2013Sci...342..453W. doi:10.1126/science.1239834. ISSN 0036-8075.
Watanabe, Haruki; Oshikawa, Masaki (2015). “Absence of Quantum Time Crystals” (PDF). Physical Review Letters. 114 (25). arXiv:1410.2143v3. Bibcode:2015PhRvL.114y1603W. doi:10.1103/PhysRevLett.114.251603. ISSN 0031-9007.Quản lý CS1: ref=harv (liên kết)
Wilczek, Frank (2012). “Quantum Time Crystals” (PDF). Physical Review Letters. 109 (16). arXiv:1202.2539v2. Bibcode:2012PhRvL.109p0401W. doi:10.1103/PhysRevLett.109.160401. ISSN 0031-9007.Quản lý CS1: ref=harv (liên kết)
Wilczek, Frank (2013a). “Wilczek Reply:” (PDF). Physical Review Letters. 110 (11). Bibcode:2013PhRvL.110k8902W. doi:10.1103/PhysRevLett.110.118902. ISSN 0031-9007.Quản lý CS1: ref=harv (liên kết)
Wilczek, Frank (2013b). “Superfluidity and Space-Time Translation Symmetry Breaking” (PDF). Physical Review Letters. 111 (25). arXiv:1308.5949v1. Bibcode:2013PhRvL.111y0402W. doi:10.1103/PhysRevLett.111.250402. ISSN 0031-9007.Quản lý CS1: ref=harv (liên kết)
Willett, R. L.; Nayak, C.; Shtengel, K.; Pfeiffer, L. N.; West, K. W. (2013). “Magnetic-Field-Tuned Aharonov-Bohm Oscillations and Evidence for Non-Abelian Anyons atν=5/2” (PDF). Physical Review Letters. 111 (18). arXiv:1301.2639v1. Bibcode:2013PhRvL.111r6401W. doi:10.1103/PhysRevLett.111.186401. ISSN 0031-9007.
Yao, N. Y.; Potter, A. C.; Potirniche, I.-D.; Vishwanath, A. (2017). “Discrete Time Crystals: Rigidity, Criticality, and Realizations” (PDF). Physical Review Letters. 118 (3). arXiv:1608.02589v2. Bibcode:2016arXiv160802589Y. doi:10.1103/PhysRevLett.118.030401. ISSN 0031-9007.
Yoshii, Ryosuke; Takada, Satoshi; Tsuchiya, Shunji; Marmorini, Giacomo; Hayakawa, Hisao; Nitta, Muneto (2015). “Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions” (PDF). Physical Review B. 92 (22). arXiv:1404.3519v2. Bibcode:2015PhRvB..92v4512Y. doi:10.1103/PhysRevB.92.224512. ISSN 1098-0121.
Yukawa, Satoshi; Kikuchi, Macoto; Tatara, Gen; Matsukawa, Hiroshi (1997). “Quantum Ratchets” (PDF). Journal of the Physical Society of Japan. 66 (10): 2953–2956. arXiv:cond-mat/9706222. Bibcode:1997JPSJ...66.2953Y. doi:10.1143/JPSJ.66.2953. ISSN 0031-9015.
Yukawa, Satoshi (2000). “A Quantum Analogue of the Jarzynski Equality” (PDF). Journal of the Physical Society of Japan. 69 (8): 2367–2370. arXiv:cond-mat/0007456. Bibcode:2000JPSJ...69.2367Y. doi:10.1143/JPSJ.69.2367. ISSN 0031-9015.Quản lý CS1: ref=harv (liên kết)
Zel'Dovich, Y. B. (1967). “The quasienergy of a quantum-mechanical system subjected to a periodic action” (PDF). Soviet Physics JETP. 24 (5): 1006–1008. Bibcode:1967JETP...24.1006Z.Quản lý CS1: ref=harv (liên kết)
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. (2017). “Observation of a Discrete Time Crystal” (PDF). Nature. 543 (7644): 217–220. arXiv:1609.08684v1. Bibcode:2016arXiv160908684Z. doi:10.1038/nature21413. ISSN 0028-0836.


Lỗi chú thích: Đã tìm thấy thẻ <ref> với tên nhóm “lower-alpha”, nhưng không tìm thấy thẻ tương ứng <references group="lower-alpha"/> tương ứng, hoặc thẻ đóng </ref> bị thiếu

Lấy từ “https://vi.wikipedia.org/w/index.php?title=Tinh_thể_thời_gian&oldid=26321866”