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Title: Spectral properties of the massless relativistic quartic oscillator
Authors: Durugo, Samuel O.
Lorinczi, Jozsef
Keywords: Fractional Laplacian
Non-local Schrodinger operator
Higher order Airy functions
Cauchy process
Relativistic quantum oscillators
Issue Date: 2018
Publisher: © Elsevier
Citation: DURUGO, S.O. and LORINCZI, J., 2018. Spectral properties of the massless relativistic quartic oscillator. Journal of Differential Equations, 264 (5), pp. 3775-3809.
Abstract: An explicit solution of the spectral problem of the non-local Schrodinger 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 8th December 2018.
Version: Accepted for publication
DOI: 10.1016/j.jde.2017.11.030
URI: https://dspace.lboro.ac.uk/2134/27631
Publisher Link: https://doi.org/10.1016/j.jde.2017.11.030
ISSN: 0022-0396
Appears in Collections:Closed Access (Maths)

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