Loughborough University
Leicestershire, UK
LE11 3TU
+44 (0)1509 263171
Loughborough University

Loughborough University Institutional Repository

Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/27631

Title: Spectral properties of the massless relativistic quartic oscillator
Authors: Lorinczi, Jozsef
Durugo, Samuel O.
Keywords: Fractional Laplacian
Non-local Schr odinger operator
Higher order Airy functions
Cauchy process
Relativistic quantum oscillators
Issue Date: 2018
Publisher: © Elsevier
Citation: LORINCZI, J. and DURUGO, S.O., 2018. Spectral properties of the massless relativistic quartic oscillator. Journal of Differential Equations, [in press]
Abstract: An explicit solution of the spectral problem of the non-local Schr odinger operator obtained as the sum of the square root of the Laplacian and a quartic potential in one dimension is presented. The eigenvalues are obtained as zeroes of special functions re- lated to the fourth order Airy function, and closed formulae for the Fourier transform of the eigenfunctions are derived. These representations allow to derive further spectral properties such as estimates of spectral gaps, heat trace and the asymptotic distribution of eigenvalues, as well as a detailed analysis of the eigenfunctions. A subtle spectral effect is observed which manifests in an exponentially tight approximation of the spectrum by the zeroes of the dominating term in the Fourier representation of the eigenfunctions and its derivative.
Description: This paper is closed access until 12 months after publication.
Version: Accepted for publication
URI: https://dspace.lboro.ac.uk/2134/27631
Publisher Link: https://www.journals.elsevier.com/journal-of-differential-equations/
ISSN: 0022-0396
Appears in Collections:Closed Access (Maths)

Files associated with this item:

File Description SizeFormat
JDE17.pdfAccepted version213.49 kBAdobe PDFView/Open

 

SFX Query

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.