NDLI: Two Point Eigenvalue Correlation for a Class of Non-Selfadjoint Operators Under Random Perturbations

Content Provider	Springer Nature Link
Author	Vogel, Martin
Copyright Year	2016
Abstract	We consider a non-selfadjoint h-differential model operator P h in the semiclassical limit ( $${h\rightarrow 0}$$ ) subject to random perturbations with a small coupling constant δ. Assume that $${{\rm e}^{-\frac{1}{Ch}} {\text{ < }} \delta \ll h^{\kappa}}$$ for constants $${C,\kappa > 0}$$ suitably large. Let Σ be the closure of the range of the principal symbol.We study the 2-point intensity measure of the random point process of eigenvalues of the randomly perturbed operator $${P_h^{\delta}}$$ and prove an h-asymptotic formula for the average 2-point density of eigenvalues. With this we show that two eigenvalues of $${P_h^{\delta}}$$ in the interior of Σ exhibit close range repulsion and long range decoupling.Nous considérons un opérateur différentiel non-autoadjoint P h dans la limite semiclassique ( $${h\rightarrow 0}$$ ) soumis à de petites perturbations aléatoires. De plus, nous imposons que la constant de couplage δ vérifie $${{\rm e}^{-\frac{1}{Ch}} {\text{ < }} \delta \ll h^{\kappa}}$$ pour certaines constantes $${C,\kappa > 0}$$ choisies assez grandes. Soit Σ l’adhérence de l’image du symbole principal de P h .Dans cet article, nous donnons une formule h-asymptotique pour la 2-points densité des valeurs propres en étudiant la mesure de comptage aléatoire des valeurs propres à l’intérieur de Σ. En étudiant cette densité, nous prouvons que deux valeurs propres sont répulsives à distance courte et indépendantes à long distance.
Starting Page	31
Ending Page	78
Page Count	48
File Format	PDF
ISSN	00103616
Journal	Communications in Mathematical Physics
Volume Number	350
Issue Number	1
e-ISSN	14320916
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-09-17
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical, Mathematical and Computational Physics Mathematical Physics Quantum Physics Complex Systems Classical and Quantum Gravitation, Relativity Theory
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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