The Adiabatic Theorem for Quantum Systems with Spectral Degeneracy

Details The Adiabatic Theorem for Quantum Systems with Spectral Degeneracy The Adiabatic Theorem for Quantum Systems with Spectral Degeneracy

2011-11-22

arxiv.org/abs/1111.5333v1

Physics

Quantum Physics

4 pages, no figures, RevTex4-1

Scientific paper

By stating the adiabatic theorem of quantum mechanics in a clear and rigorous way, we establish necessary and sufficient conditions for its validity employing our recently developed adiabatic perturbation theory. 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.

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