248 research outputs found
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 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
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
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
Autocatalytic reaction-diffusion processes in restricted geometries
We study the dynamics of a system made up of particles of two different
species undergoing irreversible quadratic autocatalytic reactions: . We especially focus on the reaction velocity and on the average time at
which the system achieves its inert state. By means of both analytical and
numerical methods, we are also able to highlight the role of topology in the
temporal evolution of the system
Fractal geometry of Ising magnetic patterns: signatures of criticality and diffusive dynamics
We investigate the geometric properties displayed by the magnetic patterns
developing on a two-dimensional Ising system, when a diffusive thermal dynamics
is adopted. Such a dynamics is generated by a random walker which diffuses
throughout the sites of the lattice, updating the relevant spins. Since the
walker is biased towards borders between clusters, the border-sites are more
likely to be updated with respect to a non-diffusive dynamics and therefore, we
expect the spin configurations to be affected. In particular, by means of the
box-counting technique, we measure the fractal dimension of magnetic patterns
emerging on the lattice, as the temperature is varied. Interestingly, our
results provide a geometric signature of the phase transition and they also
highlight some non-trivial, quantitative differences between the behaviors
pertaining to the diffusive and non-diffusive dynamics
Topological thermal instability and length of proteins
We present an analysis of the effects of global topology on the structural
stability of folded proteins in thermal equilibrium with a heat bath. For a
large class of single domain proteins, we computed the harmonic spectrum within
the Gaussian Network Model (GNM) and determined the spectral dimension, a
parameter describing the low frequency behaviour of the density of modes. We
find a surprisingly strong correlation between the spectral dimension and the
number of amino acids of the protein. Considering that larger spectral
dimension value relate to more topologically compact folded state, our results
indicate that for a given temperature and length of the protein, the folded
structure corresponds to the less compact folding compatible with thermodynamic
stability.Comment: 15 pages, 6 eps figures, 2 table
Universal features of information spreading efficiency on -dimensional lattices
A model for information spreading in a population of mobile agents is
extended to -dimensional regular lattices. This model, already studied on
two-dimensional lattices, also takes into account the degeneration of
information as it passes from one agent to the other. Here, we find that the
structure of the underlying lattice strongly affects the time at which
the whole population has been reached by information. By comparing numerical
simulations with mean-field calculations, we show that dimension is
marginal for this problem and mean-field calculations become exact for .
Nevertheless, the striking nonmonotonic behavior exhibited by the final degree
of information with respect to and the lattice size appears to be
geometry independent.Comment: 8 pages, 9 figure
Autocatalytic reaction-diffusion processes in restricted geometries
We study the dynamics of a system made up of particles of two different
species undergoing irreversible quadratic autocatalytic reactions: . We especially focus on the reaction velocity and on the average time at
which the system achieves its inert state. By means of both analytical and
numerical methods, we are also able to highlight the role of topology in the
temporal evolution of the system
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