Perturbation of an Eigen-Value from a Dense Point Spectrum : An Example

P. Duclos; P. Stovicek; M. Vittot

doi:10.1088/0305-4470/30/20/018

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arXiv · quant-ph/9702052

Perturbation of an Eigen-Value from a Dense Point Spectrum : An Example

P. Duclos·P. Stovicek·M. Vittot

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Abstract

We study a perturbed Floquet Hamiltonian $K+βV$ depending on a coupling constant $β$. The spectrum $σ(K)$ is assumed to be pure point and dense. We pick up an eigen-value, namely $0\inσ(K)$, and show the existence of a function $λ(β)$ defined on $I\subset\R$ such that $λ(β) \in σ(K+βV)$ for all $β\in I$, 0 is a point of density for the set $I$, and the Rayleigh-Schrödinger perturbation series represents an asymptotic series for the function $λ(β)$. All ideas are developed and demonstrated when treating an explicit example but some of them are expected to have an essentially wider range of application.

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P. Duclos, P. Stovicek, M. Vittot. 1997-02-26. Perturbation of an Eigen-Value from a Dense Point Spectrum : An Example. https://doi.org/10.1088/0305-4470/30/20/018

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