139 research outputs found
Suspended graphene films and their Casimir interaction with ideal conductor
We adopt the Dirac model for graphene and calculate the Casimir interaction
energy between a plane suspended graphene sample and a parallel plane ideal
conductor. We employ both the Quantum Field Theory (QFT) approach, and the
Lifshitz formula generalizations. The first approach turns out to be the
leading order in the coupling constant of the second one. The Casimir
interaction for this system appears to be rather weak but experimentally
measurable. It exhibits a strong dependence on the mass of the quasi-particles
in graphene.Comment: 5 pages, 1 fig., presented at the Ninth Conference on Quantum Field
Theory under the influence of External Conditions, Oklahoma, 200
Casimir energy of finite width mirrors: renormalization, self-interaction limit and Lifshitz formula
We study the field theoretical model of a scalar field in presence of spacial
inhomogeneities in form of one and two finite width mirrors (material slabs).
The interaction of the scalar field with the defect is described with
position-dependent mass term. Within this model we derive the interaction of
two finite width mirrors, establish the correspondence of the model to the
Lifshitz formula and construct limiting procedure to obtain finite self-energy
of a single mirror without any normalization condition.Comment: 5 pages, based on the presentation on the Ninth Conference on Quantum
Field Theory under the influence of External Conditions, Oklahoma, 200
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 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.Comment: vesrion accepted to Theoretical and Mathematical Physics, 18 pages, 1
figur
Localized Solutions of the Non-Linear Klein-Gordon Equation in Many Dimensions
We present a new complex non-stationary particle-like solution of the
non-linear Klein-Gordon equation with several spatial variables. The
construction is based on reduction to an ordinary differential equation.Comment: 4 pages, 1 figur
Charge density and conductivity of disordered Berry-Mondragon graphene nanoribbons
We consider gated graphene nanoribbons subject to Berry-Mondragon boundary
conditions in the presence of weak impurities. Using field--theoretical
methods, we calculate the density of charge carriers (and, thus, the quantum
capacitance) as well as the optical and DC conductivities at zero temperature.
We discuss in detail their dependence on the gate (chemical) potential, and
reveal a non-linear behaviour induced by the quantization of the transversal
momentum.Comment: 17 pages, version accepted for publication in EPJ
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