Adiabatic theorems for general linear operators with time-independent domains

Abstract

We establish adiabatic theorems with and without spectral gap condition for general -- typically dissipative -- linear operators $A(t):D(A(t))\subset X\to X$ with time-independent domains $D(A(t))=D$ in some Banach space $X$. Compared to the previously known adiabatic theorems -- especially those without spectral gap condition -- we do not require the considered spectral values $\hat{I}»(t)$ 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.

66 pages, 3 figures. Correction of some typos, update of the references. arXiv admin note: text overlap with arXiv:1401.0089