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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2011
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1102.0990 |
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| _version_ | 1866914916764483584 |
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| author | Aldaya, V. Cossío, F. Guerrero, J. López-Ruiz, F. F. |
| author_facet | Aldaya, V. Cossío, F. Guerrero, J. López-Ruiz, F. F. |
| contents | For the Caldirola-Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg algebra can be found. The inclusion of the standard time evolution symmetry in this algebra for damped systems, in a unitary manner, requires a non-trivial extension of this basic algebra and hence the physical system itself. Surprisingly, this extension leads directly to the so-called Bateman's dual system, which now includes a new particle acting as an energy reservoir. The group of symmetries of the dual system is presented, as well as a quantization that implies, in particular, a first-order Schrödinger equation. The usual second-order equation and the inclusion of the original Caldirola-Kanai model in Bateman's system are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1102_0990 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | A symmetry trip from Caldirola to Bateman damped systems Aldaya, V. Cossío, F. Guerrero, J. López-Ruiz, F. F. Mathematical Physics Quantum Physics For the Caldirola-Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg algebra can be found. The inclusion of the standard time evolution symmetry in this algebra for damped systems, in a unitary manner, requires a non-trivial extension of this basic algebra and hence the physical system itself. Surprisingly, this extension leads directly to the so-called Bateman's dual system, which now includes a new particle acting as an energy reservoir. The group of symmetries of the dual system is presented, as well as a quantization that implies, in particular, a first-order Schrödinger equation. The usual second-order equation and the inclusion of the original Caldirola-Kanai model in Bateman's system are also discussed. |
| title | A symmetry trip from Caldirola to Bateman damped systems |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/1102.0990 |