Anharmonic collective excitation in a solvable model |
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| Affiliation: | 1. Institute for Nuclear Theory, Department of Physics, University of Washington, Seattle, WA 98195, USA;2. Dipartimento di Fisica, Università di Milano, and INFN, Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy;3. Department of Physics, Tohoku University, Sendai 980-8578, Japan;1. Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0225, USA;2. Helmholtz-Zentrum Potsdam Deutsches GeoForschungsZentrum – GFZ Telegrafenberg, D-14473 Potsdam, Germany;1. Department of Plastic Surgery, Erasmus Medical Center Sophia Children’s Hospital, Rotterdam, The Netherlands;2. Department of Pediatric Surgery, Erasmus Medical Center Sophia Children’s Hospital, Rotterdam, The Netherlands;3. Department of Pathology, Erasmus Medical Center, Rotterdam, The Netherlands;1. Institute of Solid State Physics RAS, 142432 Chernogolovka, Moscow District, Russia;2. Centre for Science at Extreme Conditions and School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom;3. National Research University Higher School of Economics, 20 Myasnitskaya ulitsa, 101000 Moscow, Russia;4. Institut Laue-Langevin, 71 avenue des Martyrs CS 20156, 38042 Grenoble Cedex 9, France;5. Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA;6. Institute of Physical Chemistry PAS, 44/52 Kasprzaka, 01-224 Warsaw, Poland;1. Bay Area Environmental Research Institute, Moffett Field, CA, 95035, USA;2. NASA Ames Research Center, Moffett Field, CA, 95035, USA;3. Geosciences Department, Idaho State University, Pocatello, ID, 83209, USA |
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| Abstract: | ![]()
We apply the time-dependent variational principle, the nuclear field theory, and the boson expansion method to the Lipkin model to discuss anharmonicities of collective vibrational excitations. It is shown that all of these approaches lead to the same anharmonicity to leading order in the number of particles. Comparison with the exact solution of the Lipkin model shows that these theories reproduce quite well. |
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