Ali, S. Twareque, Bagarello, F. and Gazeau, Jean Pierre (2010) Modified Landau levels, damped harmonic oscillator, and two-dimensional pseudo-bosons. Journal of Mathematical Physics, 51 (12). p. 123502. ISSN 00222488
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Official URL: http://dx.doi.org/10.1063/1.3514196
Abstract
In a series of recent papers, one of us has analyzed in some details a class of elementary excitations called pseudo-bosons. They arise from a special deformation of the canonical commutation relation [a, a†] = 11, which is replaced by [a, b] = 11, with b not necessarily equal to a†. Here, after a two-dimensional extension of the general framework, we apply the theory to a generalized version of the two-dimensional Hamiltonian describing Landau levels. Moreover, for this system, we discuss coherent states and we deduce a resolution of the identity. We also consider a different class of examples arising from a classical system, i.e., a damped harmonic oscillator.
| Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
|---|---|
| Item Type: | Article |
| Refereed: | Yes |
| Authors: | Ali, S. Twareque and Bagarello, F. and Gazeau, Jean Pierre |
| Journal or Publication: | Journal of Mathematical Physics |
| Date: | 2010 |
| Digital Object Identifier (DOI): | 10.1063/1.3514196 |
| Keywords: | boson systems, harmonic oscillators, Landau levels |
| ID Code: | 976814 |
| Deposited By: | Danielle Dennie |
| Deposited On: | 28 Jan 2013 17:27 |
| Last Modified: | 18 Jan 2018 17:43 |
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19 Recall that a set of vectors φ1, φ2, φ3, . . . , is a Riesz basis of a Hilbert space H, if there exists a bounded operator V, with
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