Adiabatic Theorem in the Case of Continuous Spectra

Details Adiabatic Theorem in the Case of Continuous Spectra Adiabatic Theorem in the Case of Continuous Spectra

2008-04-25

arxiv.org/abs/0804.4077v1

Physics

Quantum Physics

7pages, 2 figures

Scientific paper

In this paper,we present a rigorous demonstration and discussion of the quantum adiabatic theorem for systems having a non degenerate continuous spectrum. A new strategy is initiated by defining a kind of gap, "a virtual gap", for the continuous spectrum through the notion of eigendifferential (Weyl's packet) and using the differential projector operator. Finally we obtain the validity condition of the adiabatic approximation.

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