240 research outputs found
The theory of electron states on the dynamically deformed adsorbed surface of a solid
Dispersion relations for the spectra of surface electron states on a
dynamically deformed adsorbed surface of a monocrystal with the Zinc blende
structure are received. It is established that the dependences of the band gap
width and of the concentration of electrons on the concentration of adatoms
upon the solid surface are of nonmonotonous character.Comment: 9 pages, 3 figure
Recommended from our members
Implementing the Magdalena Ridge Observatory interferometer supervisory system
Snowflake groups, Perron-Frobenius eigenvalues, and isoperimetric spectra
The k-dimensional Dehn (or isoperimetric) function of a group bounds the
volume of efficient ball-fillings of k-spheres mapped into k-connected spaces
on which the group acts properly and cocompactly; the bound is given as a
function of the volume of the sphere. We advance significantly the observed
range of behavior for such functions. First, to each non-negative integer
matrix P and positive rational number r, we associate a finite, aspherical
2-complex X_{r,P} and calculate the Dehn function of its fundamental group
G_{r,P} in terms of r and the Perron-Frobenius eigenvalue of P. The range of
functions obtained includes x^s, where s is an arbitrary rational number
greater than or equal to 2. By repeatedly forming multiple HNN extensions of
the groups G_{r,P} we exhibit a similar range of behavior among
higher-dimensional Dehn functions, proving in particular that for each positive
integer k and rational s greater than or equal to (k+1)/k there exists a group
with k-dimensional Dehn function x^s. Similar isoperimetric inequalities are
obtained for arbitrary manifold pairs (M,\partial M) in addition to
(B^{k+1},S^k).Comment: 42 pages, 8 figures. Version 2: 47 pages, 8 figures; minor revisions
and reformatting; to appear in Geom. Topo
Random Surfing Without Teleportation
In the standard Random Surfer Model, the teleportation matrix is necessary to
ensure that the final PageRank vector is well-defined. The introduction of this
matrix, however, results in serious problems and imposes fundamental
limitations to the quality of the ranking vectors. In this work, building on
the recently proposed NCDawareRank framework, we exploit the decomposition of
the underlying space into blocks, and we derive easy to check necessary and
sufficient conditions for random surfing without teleportation.Comment: 13 pages. Published in the Volume: "Algorithms, Probability, Networks
and Games, Springer-Verlag, 2015". (The updated version corrects small
typos/errors
Finite type approximations of Gibbs measures on sofic subshifts
Consider a H\"older continuous potential defined on the full shift
A^\nn, where is a finite alphabet. Let X\subset A^\nn be a specified
sofic subshift. It is well-known that there is a unique Gibbs measure
on associated to . Besides, there is a natural nested
sequence of subshifts of finite type converging to the sofic subshift
. To this sequence we can associate a sequence of Gibbs measures
. In this paper, we prove that these measures weakly converge
at exponential speed to (in the classical distance metrizing weak
topology). We also establish a strong mixing property (ensuring weak
Bernoullicity) of . Finally, we prove that the measure-theoretic
entropy of converges to the one of exponentially fast.
We indicate how to extend our results to more general subshifts and potentials.
We stress that we use basic algebraic tools (contractive properties of iterated
matrices) and symbolic dynamics.Comment: 18 pages, no figure
Nonequilibrium stationary states and equilibrium models with long range interactions
It was recently suggested by Blythe and Evans that a properly defined steady
state normalisation factor can be seen as a partition function of a fictitious
statistical ensemble in which the transition rates of the stochastic process
play the role of fugacities. In analogy with the Lee-Yang description of phase
transition of equilibrium systems, they studied the zeroes in the complex plane
of the normalisation factor in order to find phase transitions in
nonequilibrium steady states. We show that like for equilibrium systems, the
``densities'' associated to the rates are non-decreasing functions of the rates
and therefore one can obtain the location and nature of phase transitions
directly from the analytical properties of the ``densities''. We illustrate
this phenomenon for the asymmetric exclusion process. We actually show that its
normalisation factor coincides with an equilibrium partition function of a walk
model in which the ``densities'' have a simple physical interpretation.Comment: LaTeX, 23 pages, 3 EPS figure
Classification and realizations of type III factor representations of Cuntz-Krieger algebras associated with quasi-free states
We completely classify type III factor representations of Cuntz-Krieger
algebras associated with quasi-free states up to unitary equivalence.
Furthermore, we realize these representations on concrete Hilbert spaces
without using GNS construction. Free groups and their type
factor representations are used in these realizations.Comment: 11 page
Survival, extinction and approximation of discrete-time branching random walks
We consider a general discrete-time branching random walk on a countable set
X. We relate local, strong local and global survival with suitable inequalities
involving the first-moment matrix M of the process. In particular we prove
that, while the local behavior is characterized by M, the global behavior
cannot be completely described in terms of properties involving M alone.
Moreover we show that locally surviving branching random walks can be
approximated by sequences of spatially confined and stochastically dominated
branching random walks which eventually survive locally if the (possibly
finite) state space is large enough. An analogous result can be achieved by
approximating a branching random walk by a sequence of multitype contact
processes and allowing a sufficiently large number of particles per site. We
compare these results with the ones obtained in the continuous-time case and we
give some examples and counterexamples.Comment: 32 pages, a few misprints have been correcte
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