3,189 research outputs found
Two repelling random walks on
We consider two interacting random walks on such that the
transition probability of one walk in one direction decreases exponentially
with the number of transitions of the other walk in that direction. The joint
process may thus be seen as two random walks reinforced to repel each other.
The strength of the repulsion is further modulated in our model by a parameter
. When both processes are independent symmetric
random walks on , and hence recurrent. We show that both random
walks are further recurrent if . We also show that these
processes are transient and diverge in opposite directions if . The
case remains widely open. Our results are obtained by
considering the dynamical system approach to stochastic approximations.Comment: 17 pages. Added references and corrected typos. Revised the argument
for the convergence to equilibria of the vector field. Improved the proof for
the recurrence when beta belongs to (0,1); leading to the removal of a
previous conjectur
Affine semigroups having a unique Betti element
We characterize affine semigroups having one Betti element and we compute
some relevant non-unique factorization invariants for these semigroups. As an
example, we particularize our description to numerical semigroups.Comment: 8 pages, 1 figure. To appear in Journal of Algebra and its
Application
Bound states in the continuum: localization of Dirac-like fermions
We report the formation of bound states in the continuum for Dirac-like
fermions in structures composed by a trilayer graphene flake connected to
nanoribbon leads. The existence of this kind of localized states can be proved
by combining local density of states and electronic conductance calculations.
By applying a gate voltage, the bound states couple to the continuum, yielding
a maximum in the electronic transmission. This feature can be exploited to
identify bound states in the continuum in graphene-based structures.Comment: 7 pages, 5 figure
Ripples in a string coupled to Glauber spins
Each oscillator in a linear chain (a string) interacts with a local Ising
spin in contact with a thermal bath. These spins evolve according to Glauber
dynamics. Below a critical temperature, a rippled state in the string is
accompanied by a nonzero spin polarization. The system is shown to form ripples
in the string which, for slow spin relaxation, vibrates rapidly about
quasi-stationary states described as snapshots of a coarse-grained stroboscopic
map. For moderate observation times, ripples are observed irrespective of the
final thermodynamically stable state (rippled or not).Comment: 5 pages, 2 figure
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