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Adiabatic theorems for general linear operators with time-independent domains

: Schmid, Jochen


Reviews in mathematical physics 31 (2019), Nr.5, Art. 1950014, 66 S.
ISSN: 0129-055X
Deutsche Forschungsgemeinschaft DFG
GRK 1838
Fraunhofer ITWM ()

We establish adiabatic theorems with and without spectral gap conditions for general - typically dissipative - linear operators A(t):D(A(t))⊂X→X with time-independent domains D(A(t))=D in some Banach space X. Compared to the previously known adiabatic theorems - especially those without a spectral gap condition - we do not require the considered spectral values λ(t) of A(t) to be (weakly) semisimple. We also impose only fairly weak regularity conditions. Applications are given to slowly time-varying open quantum systems and to adiabatic switching processes.