Quantum quasiballistic dynamics and thick point spectrum

We obtain dynamical lower bounds for some self-adjoint operators with pure point spectrum in terms of the spacing properties of their eigenvalues. In particular, it is shown that for systems with thick point spectrum, typically in Baire’s sense, the dynamics of each initial condition (with respect t...

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Veröffentlicht in:Letters in mathematical physics 2019-08, Vol.109 (8), p.1891-1906
Hauptverfasser: Aloisio, Moacir, Carvalho, Silas L., de Oliveira, César R.
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Sprache:eng
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Zusammenfassung:We obtain dynamical lower bounds for some self-adjoint operators with pure point spectrum in terms of the spacing properties of their eigenvalues. In particular, it is shown that for systems with thick point spectrum, typically in Baire’s sense, the dynamics of each initial condition (with respect to some orthonormal bases of the space) presents a quasiballistic behaviour. We present explicit applications to some Schrödinger operators.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-019-01166-y