Adiabatic theorem for quantum systems with spectral degeneracy

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Date
2012
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American Physical Society
Abstract
By stating the adiabatic theorem of quantum mechanics in a clear and rigorous way, we establish a necessary condition and a sufficient condition for its validity, where the latter is obtained employing our recently developed adiabatic perturbation theory. Also, we simplify further the sufficient condition into a useful and simple practical test at the expense of its mathematical rigor. We present results for the most general case of quantum systems, i.e. those with degenerate energy spectra. These conditions are of upmost importance for assessing the validity of practical implementations of non-Abelian braiding and adiabatic quantum computation. To illustrate the degenerate adiabatic approximation, and the necessary and sufficient conditions for its validity, we analyze in depth an exactly solvable time-dependent degenerate problem.
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Rigolin, G., & Ortiz, G. (2012). Adiabatic theorem for quantum systems with spectral degeneracy. Physical Review A - Atomic, Molecular, and Optical Physics, 85(6), 062111. http://dx.doi.org/10.1103/PhysRevA.85.062111
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© 2012 American Physical Society.
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Article