The Adiabatic Theorem for Quantum Systems with Spectral Degeneracy

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 expenses 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 to assess 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.

4 pages, no figures, RevTex4-1; v2: published version

References in corpus (3)

• Non-Abelian Anyons and Topological Quantum Computation
• Nonequilibrium dynamics of closed interacting quantum systems
• Comment on "Quantitative Condition is Necessary in Guaranteeing the Validity of the Adiabatic Approximation" [arXiv:1004.3100]

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