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- W1535832247 abstract "We consider a perturbed Floquet Hamiltonian $-ipartial_t + H + beta V(omega t)$ in the Hilbert space $L^2([0,T],E,dt)$. Here $H$ is a self-adjoint operator in $E$ with a discrete spectrum obeying a growing gap condition, $V(t)$ is a symmetric bounded operator in $E$ depending on $t$ $2pi$-periodically, $omega = 2pi/T$ is a frequency and $beta$ is a coupling constant. The spectrum $Spec(-ipartial_t + H)$ of the unperturbed part is pure point and dense in $R$ for almost every $omega$. This fact excludes application of the regular perturbation theory. Nevertheless we show, for almost all $omega$ and provided $V(t)$ is sufficiently smooth, that the perturbation theory still makes sense, however, with two modifications. First, the coupling constant is restricted to a set $I$ which need not be an interval but 0 is still a point of density of $I$. Second, the Rayleigh-Schrodinger series are asymptotic to the perturbed eigen-value and the perturbed eigen-vector." @default.
- W1535832247 created "2016-06-24" @default.
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- W1535832247 date "1997-12-01" @default.
- W1535832247 modified "2023-09-27" @default.
- W1535832247 title "Perturbation of an eigenvalue from a dense point spectrum: a general Floquet Hamiltonian" @default.
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