2000 character limit reached
Berry phase of spin-one system in a rotating electric field
Published 27 Jul 2023 in quant-ph | (2307.15093v2)
Abstract: We consider in sufficient detail how the Berry phase arises in a rotating electric field in a model system with spin one. The goal is to help the student who first encountered this interesting problem, which is fraught with some subtleties that require attention in order not to go astray.
- Wilczek F and Shapere A 1989 Geometric Phases in Physics (Singapore: World Scientific) URL https://www.worldscientific.com/doi/abs/10.1142/0613
- Zwanziger J W, Koenig M and Pines A 1990 Berry’s phase Annu. Rev. Phys. Chem. 41 601–646 URL https://doi.org/10.1146/annurev.pc.41.100190.003125
- Sakurai JÂ J and Napolitano J 2020 Modern Quantum Mechanics 3rd ed (Cambridge: Cambridge University Press) URL https://doi.org/10.1017/9781108587280
- Berry M V 1984 Quantal phase factors accompanying adiabatic changes Proc. Roy. Soc. Lond. A 392 45–57 URL https://doi.org/10.1098/rspa.1984.0023
- Nakahara M 2003 Geometry, Topology and Physics 2nd ed (Boca Raton: CRC Press) URL https://doi.org/10.1201/9781315275826
- Chruściński D and Jamiołkowski A 2004 Geometric Phases in Classical and Quantum Mechanics (Birkhäuser) URL https://doi.org/10.1007/978-3-662-10333-3
- Griffiths DÂ J and Schroeter DÂ F 2018 Introduction to Quantum Mechanics 3rd ed (Cambridge University Press) URL https://doi.org/10.1017/9781316995433
- Commins E D 2014 Quantum mechanics : an experimentalist’s approach (Cambridge: Cambridge University Press)
- Budker D, Kimball DÂ F and Demille DÂ P 2008 Atomic Physics: An Exploration Through Problems and Solutions 2nd ed (Oxford: Oxford University Press)
- Vutha A and DeMille D 2009 Geometric phases without geometry (Preprint arXiv:0907.5116) URL https://doi.org/10.48550/arXiv.0907.5116
- Zhang X and Hu L 2006 Geometric phase of spin-1 in a rotating magnetic field Chin. Opt. Lett. 4 487–489 URL https://opg.optica.org/col/abstract.cfm?URI=col-4-8-487
- Xu C T and Liang J Q 2006 Dynamics and geometric phase of two spins with exchange coupling in a rotating magnetic field Phys. Lett. A 356 206–209 URL https://www.sciencedirect.com/science/article/pii/S0375960106004919
- Chaichian M and Hagedorn R 1998 Symmetries in quantum mechanics: From angular momentum to supersymmetry (Bristol: Institute of physics publishing)
- Morrison M A and Parker G A 1987 A guide to rotations in quantum mechanics Aust. J. Phys. 40 465–498 URL https://doi.org/10.1071/PH870465
- Millot Y and Man P P 2012 Active and passive rotations with euler angles in NMR Concepts Magn. Reson. A 40A 215–252 URL https://onlinelibrary.wiley.com/doi/abs/10.1002/cmr.a.21242
- Biedenharn LÂ C, Louck JÂ D and Carruthers PÂ A 1984 Angular Momentum in Quantum Physics: Theory and Application Encyclopedia of Mathematics and its Applications (Cambridge University Press) URL https://doi.org/10.1017/CBO9780511759888
- Devanathan V 2002 Angular Momentum Techniques in Quantum Mechanics Fundamental Theories of Physics (Springer) URL https://doi.org/10.1007/0-306-47123-X
- Bjorken JÂ D and Drel SÂ D 1964 Relativistic Quantum Mechanics (McGraw-Hill)
- Anandan J 1992 The geometric phase Nature 360 307–313 URL https://doi.org/10.1038/360307a0
- Aharonov Y and Anandan J 1987 Phase change during a cyclic quantum evolution Phys. Rev. Lett. 58(16) 1593–1596 URL https://link.aps.org/doi/10.1103/PhysRevLett.58.1593
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.