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Adiabatic theorems for general linear operators with time-independent domains. (arXiv:1804.11213v2 [math-ph] UPDATED)
来源于:arXiv
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
$\lambda(t)$ 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. 查看全文>>