Abstract
We derive a necessary and sufficient asymptotic condition assuring that a quantum dynamical system in equilibrium is stable in linear response.
We prove, in particular, that if the Hamiltonian has no singular-continuous spectrum and zero is the only eigenvalue, the dynamical system is stable.
Finally we prove that a dynamical system is strongly clustering, if and only if, it is weakly clustering and stable in linear response.
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Communicated by J. L. Lebowitz
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Verbeure, A., Weder, R.A. Stability in linear response and clustering properties. Commun.Math. Phys. 44, 101–105 (1975). https://doi.org/10.1007/BF01609061
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DOI: https://doi.org/10.1007/BF01609061