Zeroes of combinations of Bessel functions and mean charge of graphene nanodots

We establish some properties of the zeroes of sums and differences of contiguous Bessel functions of the first kind. As a byproduct, we also prove that the zeroes of the derivatives of Bessel functions of the first kind of different orders are interlaced the same way as the zeroes of Bessel function...

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Bibliographic Details
Published in:arXiv.org 2015-07
Main Authors: Beneventano, C G, Fialkovsky, I V, Santangelo, E M
Format: Article
Language:English
Subjects:
Bessel functions
Boundary conditions
Dependence
Energy levels
Graphene
Mathematical analysis
Organic chemistry
Online Access:Get full text
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Summary:We establish some properties of the zeroes of sums and differences of contiguous Bessel functions of the first kind. As a byproduct, we also prove that the zeroes of the derivatives of Bessel functions of the first kind of different orders are interlaced the same way as the zeroes of Bessel functions themselves. As a physical motivation, we consider gated graphene nanodots subject to Berry-Mondragon boundary conditions. We determine the allowed energy levels and calculate the mean charge at zero temperature. We discuss in detail its dependence on the gate (chemical) potential.
ISSN:2331-8422
DOI:10.48550/arxiv.1407.0615