Adiabatic theorem and generalized geometrical phase in the case of continuous spectra

By defining "a virtual gap" for the continuous spectrum through the notion of eigendifferential (Weyl's packet) and using the differential projector operator, we present a rigorous demonstration and discussion of the quantum adiabatic theorem for systems having a nondegenerate continu...

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Veröffentlicht in:	Physical review letters 2008-10, Vol.101 (15), p.150407-150407, Article 150407
Hauptverfasser:	Maamache, M, Saadi, Y
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Sprache:	eng
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creator	Maamache, M Saadi, Y
description	By defining "a virtual gap" for the continuous spectrum through the notion of eigendifferential (Weyl's packet) and using the differential projector operator, we present a rigorous demonstration and discussion of the quantum adiabatic theorem for systems having a nondegenerate continuous spectrum. An explicit formula for a generalized geometrical phase is derived in terms of the eigenstates of the Hamiltonian. Examples are given for illustration.
doi_str_mv	10.1103/PhysRevLett.101.150407
format	Article
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title	Adiabatic theorem and generalized geometrical phase in the case of continuous spectra
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