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Geometric phase
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== Sources == * {{cite journal |author1=Jeeva Anandan |author2=Joy Christian |author3=Kazimir Wanelik | title=Resource Letter GPP-1: Geometric Phases in Physics | journal=Am. J. Phys. | year=1997 | volume=65 | issue=3 | pages=180 | arxiv=quant-ph/9702011| doi=10.1119/1.18570|bibcode = 1997AmJPh..65..180A |s2cid=119080820 }} * {{Cite journal | doi = 10.1007/BF00675086| title = Three-point phase, symplectic measure, and Berry phase| journal = International Journal of Theoretical Physics| volume = 31| issue = 6| pages = 937| year = 1992| last1 = Cantoni | first1 = V.| last2 = Mistrangioli | first2 = L.|bibcode = 1992IJTP...31..937C | s2cid = 121235416}} * {{cite book|author=Richard Montgomery|title=A Tour of Subriemannian Geometries, Their Geodesics and Applications|url=https://books.google.com/books?id=DYAt3gVB7Q4C&pg=PR11|date=8 August 2006|publisher=American Mathematical Soc.|isbn=978-0-8218-4165-5|pages=11–}} ''(See chapter 13 for a mathematical treatment)'' * Connections to other physical phenomena (such as the [[Jahn–Teller effect]]) are discussed here: [https://web.archive.org/web/20150327152821/http://www.mi.infm.it/manini/berryphase.html Berry's geometric phase: a review] * Paper by Prof. Galvez at Colgate University, describing Geometric Phase in Optics: [http://departments.colgate.edu/physics/faculty/EGalvez/articles/PreprintRflash.pdf Applications of Geometric Phase in Optics] {{Webarchive|url=https://web.archive.org/web/20070824144631/http://departments.colgate.edu/physics/faculty/EGalvez/articles/PreprintRflash.pdf |date=2007-08-24 }} * Surya Ganguli, [https://web.archive.org/web/20130426082630/http://www.keck.ucsf.edu/~surya/cats.ps ''Fibre Bundles and Gauge Theories in Classical Physics: A Unified Description of Falling Cats, Magnetic Monopoles and Berry's Phase''] * Robert Batterman, [http://philsci-archive.pitt.edu/794/ ''Falling Cats, Parallel Parking, and Polarized Light'' ] * {{Cite journal | doi = 10.1016/0009-2614(75)85599-0| title = Adiabatic and diabatic representations for atom-molecule collisions: Treatment of the collinear arrangement| journal = Chemical Physics Letters| volume = 35| issue = 1| pages = 112–118| year = 1975| last1 = Baer | first1 = M. |bibcode = 1975CPL....35..112B }} * M. Baer, [https://web.archive.org/web/20150924012151/http://www.fh.huji.ac.il/~michaelb/Postscripts/molphys40,1011.pdf ''Electronic non-adiabatic transitions: Derivation of the general adiabatic-diabatic transformation matrix''], Mol. Phys. 40, 1011 (1980); * M. Baer, [https://web.archive.org/web/20140314102116/http://chemlabs.nju.edu.cn/cai/book/The%20Role%20of%20Degenerate%20States%20in%20Chemistry/2.pdf ''Existence of diabetic potentials and the quantization of the nonadiabatic matrix''], J. Phys. Chem. A 104, 3181–3184 (2000). * {{Cite journal | pmid = 15549915 | year = 2004 | last1 = Ryb | first1 = I | title = Combinatorial invariants and covariants as tools for conical intersections | journal = The Journal of Chemical Physics | volume = 121 | issue = 21 | pages = 10370–5 | last2 = Baer | first2 = R | doi = 10.1063/1.1808695 |bibcode = 2004JChPh.12110370R }} * {{cite book|first1=Frank |last1=Wilczek |author1-link=Frank Wilczek|first2=A. |last2=Shapere|title=Geometric Phases in Physics|url=https://books.google.com/books?id=5jOvlny96AkC|year=1989|publisher=World Scientific|isbn=978-9971-5-0621-6}} * {{cite book |title=Reduction, Symmetry, and Phases in Mechanics |page=69 |url=https://books.google.com/books?id=s7vcui7zUL0C&pg=PA69 |isbn=978-0-8218-2498-6 |publisher=AMS Bookstore |year=1990 |author1=Jerrold E. Marsden |author2=Richard Montgomery |author3=Tudor S. Ratiu }} * {{cite book |author=C. Pisani |title=Quantum-mechanical Ab-initio Calculation of the Properties of Crystalline Materials |isbn=978-3-540-61645-0 |year=1994 |publisher=Springer |edition=Proceedings of the IV School of Computational Chemistry of the Italian Chemical Society |page=282 |url=https://books.google.com/books?id=5ak5TwSLreAC&pg=PA282}} * {{cite book |title=Gauge Mechanics |author= L. Mangiarotti, Gennadiĭ Aleksandrovich [[Sardanashvily|Sardanashvili]] |page=281 |url=https://books.google.com/books?id=-N6F44hlnhgC&pg=PA281 |publisher=World Scientific |year=1998 |isbn=978-981-02-3603-8 }} * {{cite book |title=Physics of Ferroelectrics a Modern Perspective |author1=Karin M Rabe|author1-link= Karin M. Rabe |author2=Jean-Marc Triscone |author3=Charles H Ahn |page=43 |url=https://books.google.com/books?id=CWTzxRCDJdMC&pg=PA43 |publisher=Springer |year=2007 |isbn=978-3-540-34590-9}} * {{cite book |title=Beyond Born Oppenheimer |author= Michael Baer |url=https://books.google.com/books?id=K8XKybgdDGgC&pg=PP1 |publisher=Wiley |year=2006 |isbn=978-0-471-77891-2}} * {{cite journal|title=Geometrical phase and amplitude accumulations in dissipative systems with cyclic attractors|author=C. Z. Ning, H. Haken|journal=Phys. Rev. Lett.|volume=68|year=1992|issue=14|pages=2109–2122|doi=10.1103/PhysRevLett.68.2109|bibcode = 1992PhRvL..68.2109N|pmid=10045311}} * {{cite journal|title=The geometric phase in nonlinear dissipative systems|author=C. Z. Ning, H. Haken|journal=Mod. Phys. Lett. B|volume=6|year=1992|issue=25|pages=1541–1568|doi=10.1142/S0217984992001265|bibcode = 1992MPLB....6.1541N }}
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