23,127 research outputs found
Charge confinement and Klein tunneling from doping graphene
In the present work, we investigate how structural defects in graphene can
change its transport properties. In particular, we show that breaking of the
sublattice symmetry in a graphene monolayer overcomes the Klein effect, leading
to confined states of massless Dirac fermions. Experimentally, this corresponds
to chemical bonding of foreign atoms to carbon atoms, which attach themselves
to preferential positions on one of the two sublattices. In addition, we
consider the scattering off a tensor barrier, which describes the rotation of
the honeycomb cells of a given region around an axis perpendicular to the
graphene layer. We demonstrate that in this case the intervalley mixing between
the Dirac points emerges, and that Klein tunneling occurs.Comment: 11 pages, 5 figure
Fractal index, central charge and fractons
We introduce the notion of fractal index associated with the universal class
of particles or quasiparticles, termed fractons, which obey specific
fractal statistics. A connection between fractons and conformal field
theory(CFT)-quasiparticles is established taking into account the central
charge and the particle-hole duality
, for integer-value of the
statistical parameter. In this way, we derive the Fermi velocity in terms of
the central charge as . The Hausdorff dimension
which labelled the universal classes of particles and the conformal anomaly are
therefore related. Following another route, we also established a connection
between Rogers dilogarithm function, Farey series of rational numbers and the
Hausdorff dimension.Comment: latex, 12 pages, To appear in Mod. Phys. Lett. A (2000
Regularized optimization methods for convex MINLP problems
We propose regularized cutting-plane methods for solving mixed-integer nonlinear programming problems with nonsmooth convex objective and constraint functions. The given methods iteratively search for trial points in certain localizer sets, constructed by employing linearizations of the involved functions. New trial points can be chosen in several ways; for instance, by minimizing a regularized cutting-plane model if functions are costly. When dealing with hard-to-evaluate functions, the goal is to solve the optimization problem by performing as few function evaluations as possible. Numerical experiments comparing the proposed algorithms with classical methods in this area show the effectiveness of our approach
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