7,265 research outputs found
Comment on "Fock-Darwin States of Dirac Electrons in Graphene-Based Artificial Atoms"
Chen, Apalkov, and Chakraborty (Phys. Rev. Lett. 98, 186803 (2007)) have
computed Fock-Darwin levels of a graphene dot by including only basis states
with energies larger than or equal to zero. We show that their results violate
the Hellman-Feynman theorem. A correct treatment must include both positive and
negative energy basis states. Additional basis states lead to new energy levels
in the optical spectrum and anticrossings between optical transition lines.Comment: 1 page, 1 figure, accepted for publication in PR
Sparsity-Sensitive Finite Abstraction
Abstraction of a continuous-space model into a finite state and input
dynamical model is a key step in formal controller synthesis tools. To date,
these software tools have been limited to systems of modest size (typically
6 dimensions) because the abstraction procedure suffers from an
exponential runtime with respect to the sum of state and input dimensions. We
present a simple modification to the abstraction algorithm that dramatically
reduces the computation time for systems exhibiting a sparse interconnection
structure. This modified procedure recovers the same abstraction as the one
computed by a brute force algorithm that disregards the sparsity. Examples
highlight speed-ups from existing benchmarks in the literature, synthesis of a
safety supervisory controller for a 12-dimensional and abstraction of a
51-dimensional vehicular traffic network
States near Dirac points of rectangular graphene dot in a magnetic field
In neutral graphene dots the Fermi level coincides with the Dirac points. We
have investigated in the presence of a magnetic field several unusual
properties of single electron states near the Fermi level of such a
rectangular-shaped graphene dot with two zigzag and two armchair edges. We find
that a quasi-degenerate level forms near zero energy and the number of states
in this level can be tuned by the magnetic field. The wavefunctions of states
in this level are all peaked on the zigzag edges with or without some weight
inside the dot. Some of these states are magnetic field-independent surface
states while the others are field-dependent. We have found a scaling result
from which the number of magnetic field-dependent states of large dots can be
inferred from those of smaller dots.Comment: Physical review B in pres
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