Geodesic
Zeros of combinations of Bessel functions and the mean charge of graphene nanodots
Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 1, pp. 58-73 Cet article a éte moissonné depuis la source Math-Net.Ru

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We establish some properties of the zeros of sums and differences of contiguous Bessel functions of the first kind. As a by-product, we also prove that the zeros of the derivatives of Bessel functions of the first kind of different orders are interlaced the same way as the zeros of the 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 its dependence on the gate (chemical) potential in detail and also comment on the effect of temperature.
Keywords: Bessel function, quantum nanodot
Mots-clés : graphene, circular billiard. 
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C. G. Beneventano; I. V. Fialkovskii; E. M. Santangelo. Zeros of combinations of Bessel functions and the mean charge of graphene nanodots. Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 1, pp. 58-73. http://geodesic.mathdoc.fr/item/TMF_2016_187_1_a4/

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