Pseudo-Bosons from Landau Levels
Symmetry, integrability and geometry: methods and applications, Tome 6 (2010) Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct examples of pseudo-bosons in two dimensions arising from the Hamiltonian for the Landau levels. We also prove a no-go result showing that non-linear combinations of bosonic creation and annihilation operators cannot give rise to pseudo-bosons.
Keywords: non-hermitian Hamiltonians; pseudo-bosons.
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     author = {Fabio Bagarello},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a92/}
}
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Fabio Bagarello. Pseudo-Bosons from Landau Levels. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a92/

[1] Bagarello F., “Pseudobosons, Riesz bases and coherent states”, J. Math. Phys., 51 (2010), 023531, 10 pp., arXiv: 1001.1136 | DOI | MR

[2] Bagarello F., “Construction of pseudobosons systems”, J. Math. Phys., 51 (2010), 053508, 12 pp., arXiv: 1003.4620 | DOI | MR

[3] Bagarello F., “Mathematical aspects of intertwining operators: the role of Riesz bases”, J. Phys. A: Math. Theor., 43 (2010), 175203, 11 pp., arXiv: 1003.2288 | DOI | MR | Zbl

[4] Bagarello F., Calabrese F., “Pseudo-bosons arising from Riesz bases”, Boll. Dip. Met. Mod. Mat. Palermo, 2 (2010), 15–26

[5] Bagarello F., “Two-parameters pseudo-bosons”, Internat. J. Theoret. Phys. (to appear) , arXiv: 1010.0204 | DOI

[6] Bagarello F., “(Regular) pseudo-bosons versus bosons”, J. Phys. A: Math. Theor., 44 (2011), 015205, 11 pp. | DOI

[7] Besnard F., “Number operator algebras and deformations of $\epsilon$-Poisson algebras”, Lett. Math. Phys., 55 (2001), 113–125, arXiv: math-ph/0006012 | DOI | MR | Zbl

[8] Trifonov D. A., “Pseudo-boson coherent and Fock states”, Proceedings of the 9th International Workshop on “Complex Structures, Integrability and Vector Fields” (August 25–29, 2008, Sofia), eds. K. Sekigawa, V. Gerdjikov and S. Dimiev, World Scientific Publishing Co., 2009, 241–250, arXiv: 0902.3744 | MR | Zbl

[9] Bagarello F., “Examples of Pseudo-bosons in quantum mechanics”, Phys. Lett. A, 374 (2010), 3823–3827, arXiv: 1007.4349 | DOI | MR

[10] Ali S. T., Bagarello F., Gazeau J.-P.,, “Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons”, J. Math. Phys., 51 (2010), 123502, 11 pp., arXiv: 1010.4221 | DOI

[11] Young R. M., An introduction to nonharmonic Fourier series, Academic Press, New York, 1980 | MR

[12] Bagarello F., Pseudo-bosons, so far, submitted

[13] Kuru S., Tegmen A., Vercin A., “Intertwined isospectral potentials in an arbitrary dimension”, J. Math. Phys., 42 (2001), 3344–3360, arXiv: ; Kuru S., Demircioglu B., Onder M., Vercin A., “Two families of superintegrable and isospectral potentials in two dimensions”, J. Math. Phys., 43 (2002), 2133–2150, arXiv: ; Aghababaei Samani K., Zarei M., “Intertwined Hamiltonians in two-dimensional curved spaces”, Ann. Physics, 316 (2005), 466–482, arXiv: quant-ph/0111034quant-ph/0201099math-ph/0411030 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[14] Bagarello F., “Extended SUSY quantum mechanics, intertwining operators and coherent states”, Phys. Lett. A, 372 (2008), 6226–6231, arXiv: ; Bagarello F., “Vector coherent states and intertwining operators”, J. Phys. A: Math. Theor., 42 (2009), 075302, 11 pp., arXiv: ; Bagarello F., “Intertwining operators between different Hilbert spaces: connection with frames”, J. Math. Phys., 50 (2009), 043509, 13 pp., arXiv: 0904.01990904.02010904.0203 | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl