Zeroes of combinations of Bessel functions and mean charge of graphene nanodots
arXiv:1407.0615 · doi:10.1134/S004057791604005X
Abstract
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.
vesrion accepted to Theoretical and Mathematical Physics, 18 pages, 1 figure
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- Observation of excited states in a graphene quantum dot
- Analytic Model for the Energy Spectrum of a Graphene Quantum Dot in a Perpendicular Magnetic Field
- Interlacing of positive real zeros of Bessel functions
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