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arXiv:quant-ph/0606195 · Annals of Physics

Two-level systems: Exact solutions and underlying pseudo-supersymmetry

V.V. Shamshutdinova, Boris F. Samsonov, D.M. Gitman

Published Jul 12, 2006• 6 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2006.05.004

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1 Two-level systems: exact solutions and underlying pseudo-supersymmetry

V. V. Shamshutdinova, B. F. Samsonov, Dmitri M Gitman

Chains of first-order SUSY transformations for the spin equation are studied in detail. It is shown that the transformation chains are related with a olynomial pseudo-supersymmetry of the system. Simple determinant formulas for the final Hamiltonian of a chain and for solutions of the spin equation are derived. Applications are intended for a two-level atom in an electromagnetic field with a possible time-dependence of the field frequency. For a specific form of this dependence, the time oscillations of the probability to populate the excited level disappear. Under certain conditions this probability becomes a function tending monotonously to a constant value which can exceed 1/2.

•Jan 1, 2006•5 citations

Interpreting Supersymmetry

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Nonlinear pseudo-supersymmetry in the framework of -fold supersymmetry

Artemio González-López, Toshiaki Tanaka

We recall the importance of recognizing the different mathematical nature of various concepts relating to -symmetric quantum theories. After clarifying the relation between supersymmetry and pseudo-supersymmetry, we prove generically that nonlinear pseudo-supersymmetry, recently proposed by Sinha and Roy, is just a special case of -fold supersymmetry. In particular, we show that all the models constructed by these authors have type A two-fold supersymmetry. Furthermore, we prove that an arbitrary one-body quantum Hamiltonian which admits two (local) solutions in closed form belongs to type A two-fold supersymmetry, irrespective of whether or not it is Hermitian, -symmetric, pseudo-Hermitian and so on.

arXiv:quant-ph/0602177•Journal of Physics A Mathematical and General•Mar 22, 2006•32 citations
Chains of first-order SUSY transformations for the spin equation are studied in detail. It is shown that the transformation chains are related with a olynomial pseudo-supersymmetry of the system. Simple determinant formulas for the final Hamiltonian of a chain and for solutions of the spin equation are derived. Applications are intended for a two-level atom in an electromagnetic field with a possible time-dependence of the field frequency. For a specific form of this dependence, the time oscillations of the probability to populate the excited level disappear. Under certain conditions this probability becomes a function tending monotonously to a constant value which can exceed 1/2.
We recall the importance of recognizing the different mathematical nature of various concepts relating to -symmetric quantum theories. After clarifying the relation between supersymmetry and pseudo-supersymmetry, we prove generically that nonlinear pseudo-supersymmetry, recently proposed by Sinha and Roy, is just a special case of -fold supersymmetry. In particular, we show that all the models constructed by these authors have type A two-fold supersymmetry. Furthermore, we prove that an arbitrary one-body quantum Hamiltonian which admits two (local) solutions in closed form belongs to type A two-fold supersymmetry, irrespective of whether or not it is Hermitian, -symmetric, pseudo-Hermitian and so on.