594 research outputs found
Diffusion on non exactly decimable tree-like fractals
We calculate the spectral dimension of a wide class of tree-like fractals by
solving the random walk problem through a new analytical technique, based on
invariance under generalized cutting-decimation transformations. These fractals
are generalizations of the NTD lattices and they are characterized by non
integer spectral dimension equal or greater then 2, non anomalous diffusion
laws, dynamical dimension splitting and absence of phase transitions for spin
models.Comment: 5 pages Latex, 3 figures (figures are poscript files
Geometrical universality in vibrational dynamics
A good generalization of the Euclidean dimension to disordered systems and
non crystalline structures is commonly required to be related to large scale
geometry and it is expected to be independent of local geometrical
modifications. The spectral dimension, defined according to the low frequency
density of vibrational states, appears to be the best candidate as far as
dynamical and thermodynamical properties are concerned. In this letter we give
the rigorous analytical proof of its independence of finite scale geometry. We
show that the spectral dimension is invariant under local rescaling of
couplings and under addition of finite range couplings, or infinite range
couplings decaying faster then a characteristic power law. We also prove that
it is left unchanged by coarse graining transformations, which are the
generalization to graphs and networks of the usual decimation on regular
structures. A quite important consequence of all these properties is the
possibility of dealing with simplified geometrical models with
nearest-neighbors interactions to study the critical behavior of systems with
geometrical disorder.Comment: Latex file, 1 figure (ps file) include
Topology, Hidden Spectra and Bose Einstein Condensation on low dimensional complex networks
Topological inhomogeneity gives rise to spectral anomalies that can induce
Bose-Einstein Condensation (BEC) in low dimensional systems. These anomalies
consist in energy regions composed of an infinite number of states with
vanishing weight in the thermodynamic limit (hidden states). Here we present a
rigorous result giving the most general conditions for BEC on complex networks.
We prove that the presence of hidden states in the lowest region of the
spectrum is the necessary and sufficient condition for condensation in low
dimension (spectral dimension ), while it is shown that BEC
always occurs for .Comment: 4 pages, 10 figure
Random walks on graphs: ideas, techniques and results
Random walks on graphs are widely used in all sciences to describe a great
variety of phenomena where dynamical random processes are affected by topology.
In recent years, relevant mathematical results have been obtained in this
field, and new ideas have been introduced, which can be fruitfully extended to
different areas and disciplines. Here we aim at giving a brief but
comprehensive perspective of these progresses, with a particular emphasis on
physical aspects.Comment: LateX file, 34 pages, 13 jpeg figures, Topical Revie
A Diffusive Strategic Dynamics for Social Systems
We propose a model for the dynamics of a social system, which includes
diffusive effects and a biased rule for spin-flips, reproducing the effect of
strategic choices. This model is able to mimic some phenomena taking place
during marketing or political campaigns. Using a cost function based on the
Ising model defined on the typical quenched interaction environments for social
systems (Erdos-Renyi graph, small-world and scale-free networks), we find, by
numerical simulations, that a stable stationary state is reached, and we
compare the final state to the one obtained with standard dynamics, by means of
total magnetization and magnetic susceptibility. Our results show that the
diffusive strategic dynamics features a critical interaction parameter strictly
lower than the standard one. We discuss the relevance of our findings in social
systems.Comment: Major revisions; to appear on the Journal of Statistical Physic
Superdiffusion and Transport in 2d-systems with L\'evy Like Quenched Disorder
We present an extensive analysis of transport properties in superdiffusive
two dimensional quenched random media, obtained by packing disks with radii
distributed according to a L\'evy law. We consider transport and scaling
properties in samples packed with two different procedures, at fixed filling
fraction and at self-similar packing, and we clarify the role of the two
procedures in the superdiffusive effects. Using the behavior of the filling
fraction in finite size systems as the main geometrical parameter, we define an
effective L\'evy exponents that correctly estimate the finite size effects. The
effective L\'evy exponent rules the dynamical scaling of the main transport
properties and identify the region where superdiffusive effects can be
detected.Comment: 12 pages, 19 figure
Complex phase-ordering of the one-dimensional Heisenberg model with conserved order parameter
We study the phase-ordering kinetics of the one-dimensional Heisenberg model
with conserved order parameter, by means of scaling arguments and numerical
simulations. We find a rich dynamical pattern with a regime characterized by
two distinct growing lengths. Spins are found to be coplanar over regions of a
typical size , while inside these regions smooth rotations associated
to a smaller length are observed. Two different and coexisting
ordering mechanisms are associated to these lengths, leading to different
growth laws and violating dynamical
scaling.Comment: 14 pages, 8 figures. To appear on Phys. Rev. E (2009
Topological Reduction of Tight-Binding Models on Complex Networks
Complex molecules and mesoscopic structures are naturally described by
general networks of elementary building blocks and tight-binding is one of the
simplest quantum model suitable for studying the physical properties arising
from the network topology. Despite the simplicity of the model, topological
complexity can make the evaluation of the spectrum of the tight-binding
Hamiltonian a rather hard task, since the lack of translation invariance rules
out such a powerful tool as Fourier transform. In this paper we introduce a
rigorous analytical technique, based on topological methods, for the exact
solution of this problem on branched structures. Besides its analytic power,
this technique is also a promising engineering tool, helpful in the design of
netwoks displaying the desired spectral features.Comment: 19 pages, 14 figure
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