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

V. V. Shamshutdinova·Boris F. Samsonov·D. M. Gitman
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Abstract

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.

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V. V. Shamshutdinova, Boris F. Samsonov, D. M. Gitman. 2006-06-23. Two-level systems: exact solutions and underlying pseudo-supersymmetry. https://doi.org/10.1016/j.aop.2006.05.004

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