313 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
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
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
The Type-problem on the Average for random walks on graphs
When averages over all starting points are considered, the Type Problem for
the recurrence or transience of a simple random walk on an inhomogeneous
network in general differs from the usual "local" Type Problem. This difference
leads to a new classification of inhomogeneous discrete structures in terms of
{\it recurrence} and {\it transience} {\it on the average}, describing their
large scale topology from a "statistical" point of view. In this paper we
analyze this classification and the properties connected to it, showing how the
average behavior affects the thermodynamic properties of statistical models on
graphs.Comment: 10 pages, 3 figures. to appear on EPJ
The inverse Mermin-Wagner theorem for classical spin models on graphs
In this letter we present the inversion of the Mermin-Wagner theorem on
graphs, by proving the existence of spontaneous magnetization at finite
temperature for classical spin models on transient on the average (TOA) graphs,
i.e. graphs where a random walker returns to its starting point with an average
probability . This result, which is here proven for models with
O(n) symmetry, includes as a particular case , providing a very general
condition for spontaneous symmetry breaking on inhomogeneous structures even
for the Ising model.Comment: 4 Pages, to appear on PR
Electrical networks on -simplex fractals
The decimation map for a network of admittances on an
-simplex lattice fractal is studied. The asymptotic behaviour of
for large-size fractals is examined. It is found that in the
vicinity of the isotropic point the eigenspaces of the linearized map are
always three for ; they are given a characterization in terms of
graph theory. A new anisotropy exponent, related to the third eigenspace, is
found, with a value crossing over from to
.Comment: 14 pages, 8 figure
Percolation on the average and spontaneous magnetization for q-states Potts model on graph
We prove that the q-states Potts model on graph is spontaneously magnetized
at finite temperature if and only if the graph presents percolation on the
average. Percolation on the average is a combinatorial problem defined by
averaging over all the sites of the graph the probability of belonging to a
cluster of a given size. In the paper we obtain an inequality between this
average probability and the average magnetization, which is a typical extensive
function describing the thermodynamic behaviour of the model
Bose-Einstein Condensation on inhomogeneous complex networks
The thermodynamic properties of non interacting bosons on a complex network
can be strongly affected by topological inhomogeneities. The latter give rise
to anomalies in the density of states that can induce Bose-Einstein
condensation in low dimensional systems also in absence of external confining
potentials. The anomalies consist in energy regions composed of an infinite
number of states with vanishing weight in the thermodynamic limit. We present a
rigorous result providing the general conditions for the occurrence of
Bose-Einstein condensation on complex networks in presence of anomalous
spectral regions in the density of states. We present results on spectral
properties for a wide class of graphs where the theorem applies. We study in
detail an explicit geometrical realization, the comb lattice, which embodies
all the relevant features of this effect and which can be experimentally
implemented as an array of Josephson Junctions.Comment: 11 pages, 9 figure
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