Potential Reversal and Reflectionless Impurities in Periodic Structures

Chabanov, V. M.; Zakhariev, B. N.; Sofianos, S. A.; Braun, M.

doi:10.1007/978-3-662-14145-8_17

V. M. Chabanov⁴,
B. N. Zakhariev^4,5,
S. A. Sofianos⁵ &
…
M. Braun⁵

Part of the book series: Lecture Notes in Physics ((LNP,volume 488))

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Abstract

We demonstrate that the application of the supersymmetric (SUSY) transformation to a periodic potential in one dimension, which creates a bound state below the lowest allowed band, results in the unexpected phenomenon of potential reversal. This does neither alter other characteristics of the spectrum nor does it result in a reflection of Bloch waves.

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References

Andrianov A. A., Borisov N. V. and Ioffe M. V. (1984), Phys. Lett. 105A, 19.
Article ADS MathSciNet Google Scholar
Andrianov A. A., Ioffe M. V. and Spiridonov V. P. (1993), Phys. Lett. A 174, 273.
Article MathSciNet Google Scholar
Baye D. (1987), Phys. Rev. Lett. 58, 2738.
Article ADS Google Scholar
Chadan K. and Sabatier P.C. (1977), Inverse Problems in Quantum Scattering Theory, Springer, New York.
MATH Google Scholar
Firsova N.E. (1985), Theor. Math. Phys. 62, 130.
Article MATH MathSciNet Google Scholar
Firsova N. E. (1987), Math. Sborn. 58, 351.
Article MATH Google Scholar
Lamb G. L. Jr (1980), Elements odf soliton theory, John Willey & Sons, New York.
Google Scholar
Leeb H. (1994), in Quantum Inversion Theory and Applications, Vol. 427 of Lecture Notes in Physics, ed. H.V. von Geramb, pp. 241–251, Springer-Verlag, Berlin, 1994.
Google Scholar
Levitan B. M. (1984), Sturm-Liouville Inverse Problems, Nauka, Moscow.
MATH Google Scholar
Marchenko V.A. (1986), Sturm-Liuville Operators and Applications, Birkhauser, Basel.
Book Google Scholar
Newton R. G. (1985), J. Math. Phys. 26, 311.
Article ADS MATH MathSciNet Google Scholar
Roberts T. M. (1990), Inverse Probl. 6, 797.
Article ADS MATH Google Scholar
Sukumar C. V. (1985), J. Phys. A 18, 2917; J. Phys. A 18, 2937.
Google Scholar
Witten E. (1981), Nucl. Phys. B188, 513.
Article ADS MATH Google Scholar
Zakhariev B. N. and Suzko A. A. (1990) Direct and Inverse Problems, Springer, New York.
Book Google Scholar
Zakhariev B. N. (1992), Soy. J. Part. & Nucl. 23, 603.
Google Scholar
Zakhariev B. N. and Pashnev A. I. (1994), Commun. JINR P4–94–496, Dubna.
Google Scholar

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Authors and Affiliations

Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, 141980, Russia
V. M. Chabanov & B. N. Zakhariev
Department of Physics, University of South Africa, P.O. Box 392, Pretoria, 0001, South Africa
B. N. Zakhariev, S. A. Sofianos & M. Braun

Authors

V. M. Chabanov
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B. N. Zakhariev
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S. A. Sofianos
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M. Braun
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Editors and Affiliations

Department of Theoretical Physics, Technical University of Budapest, Budafoki u. 8., 1521, Budapest, Hungary
Barnabás Apagyi & Péter Lévay &
Computer Center of Eötvös University, ELTE, Budapest, Hungary
Gábor Endrédi

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Chabanov, V.M., Zakhariev, B.N., Sofianos, S.A., Braun, M. (1997). Potential Reversal and Reflectionless Impurities in Periodic Structures. In: Apagyi, B., Endrédi, G., Lévay, P. (eds) Inverse and Algebraic Quantum Scattering Theory. Lecture Notes in Physics, vol 488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-14145-8_17

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DOI: https://doi.org/10.1007/978-3-662-14145-8_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-14147-2
Online ISBN: 978-3-662-14145-8
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