24,254 research outputs found
On the Synchronizing Probability Function and the Triple Rendezvous Time for Synchronizing Automata
Cerny's conjecture is a longstanding open problem in automata theory. We
study two different concepts, which allow to approach it from a new angle. The
first one is the triple rendezvous time, i.e., the length of the shortest word
mapping three states onto a single one. The second one is the synchronizing
probability function of an automaton, a recently introduced tool which
reinterprets the synchronizing phenomenon as a two-player game, and allows to
obtain optimal strategies through a Linear Program.
Our contribution is twofold. First, by coupling two different novel
approaches based on the synchronizing probability function and properties of
linear programming, we obtain a new upper bound on the triple rendezvous time.
Second, by exhibiting a family of counterexamples, we disprove a conjecture on
the growth of the synchronizing probability function. We then suggest natural
follow-ups towards Cernys conjecture.Comment: A preliminary version of the results has been presented at the
conference LATA 2015. The current ArXiv version includes the most recent
improvement on the triple rendezvous time upper bound as well as formal
proofs of all the result
Orbital magnetic moments in insulating Dirac systems: Impact on magnetotransport in graphene van der Waals heterostructures
In honeycomb Dirac systems with broken inversion symmetry, orbital magnetic
moments coupled to the valley degree of freedom arise due to the topology of
the band structure, leading to valley-selective optical dichroism. On the other
hand, in Dirac systems with prominent spin-orbit coupling, similar orbital
magnetic moments emerge as well. These moments are coupled to spin, but
otherwise have the same functional form as the moments stemming from spatial
inversion breaking. After reviewing the basic properties of these moments,
which are relevant for a whole set of newly discovered materials, such as
silicene and germanene, we study the particular impact that these moments have
on graphene nanoengineered barriers with artificially enhanced spin-orbit
coupling. We examine transmission properties of such barriers in the presence
of a magnetic field. The orbital moments are found to manifest in transport
characteristics through spin-dependent transmission and conductance, making
them directly accessible in experiments. Moreover, the Zeeman-type effects
appear without explicitly incorporating the Zeeman term in the models, i.e., by
using minimal coupling and Peierls substitution in continuum and the
tight-binding methods, respectively. We find that a quasiclassical view is able
to explain all the observed phenomena
Spin-valley filtering in strained graphene structures with artificially induced carrier mass and spin-orbit coupling
The interplay of massive electrons with spin-orbit coupling in bulk graphene
results in a spin-valley dependent gap. Thus, a barrier with such properties
can act as a filter, transmitting only opposite spins from opposite valleys. In
this Letter we show that strain induced pseudomagnetic field in such a barrier
will enforce opposite cyclotron trajectories for the filtered valleys, leading
to their spatial separation. Since spin is coupled to the valley in the
filtered states, this also leads to spin separation, demonstrating a
spin-valley filtering effect. The filtering behavior is found to be
controllable by electrical gating as well as by strain
Collider Constraints on Dipole-Interacting Dark Matter
Dark matter which interacts through a magnetic or electric dipole moment is
an interesting possibility which may help to resolve the discrepancy between
the DAMA annual modulation signal and the null results of other searches. In
this article we examine relic density and collider constraints on such dark
matter, and find that for couplings needed to explain DAMA, the thermal relic
density is generically in the right ballpark to account for cosmological
measurements. Collider constraints are relevant for light WIMPs, but less
constraining that direct searches for masses above about 10 GeV.Comment: 11 pages, 2 figures, extended discussion, added references,
conclusion unchange
Spin and Valley dependent analysis of the two-dimensional low-density electron system in Si-MOSFETS
The 2-D electron system (2DES) in Si metal-oxide field-effect transistors
(MOSFETS) consists of two distinct electron fluids interacting with each other.
We calculate the total energy as a function of the density , and the spin
polarization in the strongly-correlated low-density regime, using a
classical mapping to a hypernetted-chain (CHNC) equation inclusive of bridge
terms. Here the ten distribution functions, arising from spin and valley
indices, are self-consistently calculated to obtain the total free energy, the
chemical potential, the compressibility and the spin susceptibility. The T=0
results are compared with the 2-valley Quantum Monte Carlo (QMC) data of Conti
et al. (at T=0, ) and found to be in excellent agreement. However,
unlike in the one-valley 2DES, it is shown that {\it the unpolarized phase is
always the stable phase in the 2-valley system}, right up to Wigner
Crystallization at . This leads to the insensitivity of to the
spin polarization and to the density. The compressibility and the
spin-susceptibility enhancement calculated from the free energy confirm the
validity of a simple approach to the two-valley response based on coupled-mode
formation. The three methods, QMC, CHNC, and Coupled-mode theory agree closely.
Our results contain no {\it ad hoc} fit parameters. They agree with experiments
and do not invoke impurity effects or metal-insulator transition phenomenology.Comment: 10 pages 4 figure
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