Login | Register

Modified Landau levels, damped harmonic oscillator, and two-dimensional pseudo-bosons

Title:

Modified Landau levels, damped harmonic oscillator, and two-dimensional pseudo-bosons

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

[img]
Preview
Text (application/pdf)
ali2010.pdf - Published Version
415kB

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

References:

1 F. Bagarello, J. Math. Phys. 50, 023531 (2010).
2 F. Bagarello, J. Math. Phys. 51, 023531 (2010).
3 F. Bagarello, J. Phys. A 43, 175203 (2010).
4 F. Bagarello, Examples of pseudo-bosons in quantum mechanics, Phys. Lett. A, in press.
5 D.A. Trifonov, Pseudo-boson coherent and Fock states, quant-ph/0902.3744.
6 S. T. Ali and F. Bagarello, J. Math Phys. 49, (2008).
7 R. Banerjee and P. Mukherjee, J. Phys. A 35, 5591 (2002).
8 S. Kuru, A. Tegmen, and A. Vercin, J. Math. Phys. 42, 3344 (2001); S. Kuru, B. Demircioglu and M. Onder, and A.
Vercin, J. Math. Phys. 43, 2133 (2002); K. A. Samani and M. Zarei, Ann. Phys. 316, 466 (2005).
9 F. Bagarello, Phys. Lett. A. 372, 6226 (2008); F. Bagarello, J. Phys. A. 42, 075302 (2009); F. Bagarello, J. Math. Phys.
50, 043509 (2009).
10 A. Mostafazadeh, e-print arXiv:quant-ph/0810.5643; C. Bender, Rep. Progr. Phys., 70, 947 (2007).
11 S. T. Ali, J.-P. Antoine, and J.-P. Gazeau, Coherent States, Wavelets and Their Generalizations (Springer-Verlag,
New York, 2000).
12 J.-P. Gazeau, Coherent States in Quantum Physics (Wiley-VCH, Berlin, 2009).
13 J. P. Antoine and F. Bagarello, “Localization Properties and Wavelet-Like Orthonormal Bases for the Lowest Landau
Level”, in Advances in Gabor Analysis, edited by H. G. Feichtinger and T. Strohmer (Birkh¨auser, Boston, 2003).
14 S. T. Ali, F. Bagarello, and G. Honnouvo, J. Phys. A 43, 105202 (2010).
15 R. Young, An Introduction to Nonharmonic Fourier Series (Academic, New York, 1980).
16 O. Christensen, An Introduction to Frames and Riesz Bases (Birkh¨auser, Boston, 2003).
17 H. Feshbach and Y. Tikochinsky, N.Y. Acad. Sci., 38, 44 (1977).
18 F. Bagarello, Phys. Lett. A 374, 3823 (2010).
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
bounded inverse, on H, and an orthonormal basis of H, ϕ1, ϕ2, ϕ3, . . . , such that φj = Vϕj , for all j = 1, 2, 3, . . . .
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Research related to the current document (at the CORE website)
- Research related to the current document (at the CORE website)
Back to top Back to top