Canonical forms for perturbations of the harmonic oscillator
We consider a class of perturbations of the 2D harmonic oscillator, and of some other dynamical systems, which we show are isomorphic to a function of a toric system (a Birkhoff canonical form). We show that for such systems there exists a quantum normal form as well, which is determined by spectral...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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New York Journal of Mathematics
2020
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| Online Access: | https://hdl.handle.net/1721.1/126432 |
| _version_ | 1826201802030186496 |
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| author | Guillemin, Victor W Uribe, A. Wang, Zuoqin |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Guillemin, Victor W Uribe, A. Wang, Zuoqin |
| author_sort | Guillemin, Victor W |
| collection | MIT |
| description | We consider a class of perturbations of the 2D harmonic oscillator, and of some other dynamical systems, which we show are isomorphic to a function of a toric system (a Birkhoff canonical form). We show that for such systems there exists a quantum normal form as well, which is determined by spectral data. |
| first_indexed | 2024-09-23T11:57:08Z |
| format | Article |
| id | mit-1721.1/126432 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:57:08Z |
| publishDate | 2020 |
| publisher | New York Journal of Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/1264322022-10-01T07:13:59Z Canonical forms for perturbations of the harmonic oscillator Guillemin, Victor W Uribe, A. Wang, Zuoqin Massachusetts Institute of Technology. Department of Mathematics We consider a class of perturbations of the 2D harmonic oscillator, and of some other dynamical systems, which we show are isomorphic to a function of a toric system (a Birkhoff canonical form). We show that for such systems there exists a quantum normal form as well, which is determined by spectral data. 2020-07-29T20:47:56Z 2020-07-29T20:47:56Z 2015-07 2019-11-13T16:00:39Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/126432 Guillemin, V. et al. "Canonical forms for perturbations of the harmonic oscillator." New York Journal of Mathematics 21 (July 2015): 163-180 © 2015 New York Journal of Mathematics en http://nyjm.albany.edu/j/2015/21-7.html New York Journal of Mathematics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf New York Journal of Mathematics arXiv |
| spellingShingle | Guillemin, Victor W Uribe, A. Wang, Zuoqin Canonical forms for perturbations of the harmonic oscillator |
| title | Canonical forms for perturbations of the harmonic oscillator |
| title_full | Canonical forms for perturbations of the harmonic oscillator |
| title_fullStr | Canonical forms for perturbations of the harmonic oscillator |
| title_full_unstemmed | Canonical forms for perturbations of the harmonic oscillator |
| title_short | Canonical forms for perturbations of the harmonic oscillator |
| title_sort | canonical forms for perturbations of the harmonic oscillator |
| url | https://hdl.handle.net/1721.1/126432 |
| work_keys_str_mv | AT guilleminvictorw canonicalformsforperturbationsoftheharmonicoscillator AT uribea canonicalformsforperturbationsoftheharmonicoscillator AT wangzuoqin canonicalformsforperturbationsoftheharmonicoscillator |