Perturbation of an eigenvalue from a dense point spectrum: an example

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F97%3A00151626" target="_blank" >RIV/68407700:21340/97:00151626 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1088/0305-4470/30/20/018" target="_blank" >http://dx.doi.org/10.1088/0305-4470/30/20/018</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/0305-4470/30/20/018" target="_blank" >10.1088/0305-4470/30/20/018</a>

Result language
angličtina
Original language name
Perturbation of an eigenvalue from a dense point spectrum: an example
Original language description
We study an example of a perturbed Floquet Hamiltonian K + bV depending on a coupling constant b. The spectrum Spec(K) is pure point and dense. We pick up an eigenvalue, namely 0 from Spec(K), and show the existence of a function lambda(b) defined on I, a subset of R, such that lambda(b) belongs to Spec(K + bV ) for all b from I , 0 is a point of density for the set I , and the Rayleigh--Schroedinger perturbation series represents an asymptotic series for the function lambda(b). All ideas are developed and demonstrated when treating the explicit example, but some of them are expected to have an essentially wider range of application.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA201%2F94%2F0708" target="_blank" >GA201/94/0708: Stability and Instability in Quantum Systems.</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
1997
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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