1,009 research outputs found
Local and average behavior in inhomogeneous superdiffusive media
We consider a random walk on one-dimensional inhomogeneous graphs built from
Cantor fractals. Our study is motivated by recent experiments that demonstrated
superdiffusion of light in complex disordered materials, thereby termed L\'evy
glasses. We introduce a geometric parameter which plays a role
analogous to the exponent characterizing the step length distribution in random
systems. We study the large-time behavior of both local and average
observables; for the latter case, we distinguish two different types of
averages, respectively over the set of all initial sites and over the
scattering sites only. The "single long jump approximation" is applied to
analytically determine the different asymptotic behaviours as a function of
and to understand their origin. We also discuss the possibility that
the root of the mean square displacement and the characteristic length of the
walker distribution may grow according to different power laws; this anomalous
behaviour is typical of processes characterized by L\'evy statistics and here,
in particular, it is shown to influence average quantities
Phase Diagram for Ultracold Bosons in Optical Lattices and Superlattices
We present an analytic description of the finite-temperature phase diagram of
the Bose-Hubbard model, successfully describing the physics of cold bosonic
atoms trapped in optical lattices and superlattices. Based on a standard
statistical mechanics approach, we provide the exact expression for the
boundary between the superfluid and the normal fluid by solving the
self-consistency equations involved in the mean-field approximation to the
Bose-Hubbard model. The zero-temperature limit of such result supplies an
analytic expression for the Mott lobes of superlattices, characterized by a
critical fractional filling.Comment: 8 pages, 6 figures, submitted to Phys. Rev.
Customer Complaining and Probability of Default in Consumer Credit
In many countries, Banking Authorities have adopted an Alternative Dispute Resolution (ADR) procedure to manage complaints that customers and financial intermediaries cannot solve by themselves. As a consequence, banks have had to implement complaint management systems in order to deal with customers’ demands. The growth rate of customer complaints has been increasing during the last few years. This does not seem to be only related to the quality of financial services or to lack of compliance in banking products. Another reason lies in the characteristics of the procedures themselves, which are very simple and free of charge. The paper analyzes some determinants regarding the willingness to complain. In particular, it examines whether a high customers’ probability of default leads to an increase in non-valid complaints. The paper uses a sample of approximately 1,000 customers who received a loan and made a claim against the lender. The analysis shows that customers with higher Probability of Default are more likely to make claims against Financial Institutions. Moreover, it shows that opportunistic behaviors and non-valid complaints are more likely if the customer is supported by a lawyer or other professionals and if the reason for the claim may result in a refund or damage compensation
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
Steering random walks with kicked ultracold atoms
A kicking sequence of the atom optics kicked rotor at quantum resonance can
be interpreted as a quantum random walk in momentum space. We show how to steer
such a random walk by applying a random sequence of intensities and phases of
the kicking lattice chosen according to a probability distribution. This
distribution converts on average into the final momentum distribution of the
kicked atoms. In particular, it is shown that a power-law distribution for the
kicking strengths results in a L\'evy walk in momentum space and in a power-law
with the same exponent in the averaged momentum distribution. Furthermore, we
investigate the stability of our predictions in the context of a realistic
experiment with Bose-Einstein condensates.Comment: detailed study of random walks and their implementation with a Bose
condensate, 12 pages, 7 figure
L\'evy walks and scaling in quenched disordered media
We study L\'evy walks in quenched disordered one-dimensional media, with
scatterers spaced according to a long-tailed distribution. By analyzing the
scaling relations for the random-walk probability and for the resistivity in
the equivalent electric problem, we obtain the asymptotic behavior of the mean
square displacement as a function of the exponent characterizing the scatterers
distribution. We demonstrate that in quenched media different average
procedures can display different asymptotic behavior. In particular, we
estimate the moments of the displacement averaged over processes starting from
scattering sites, in analogy with recent experiments. Our results are compared
with numerical simulations, with excellent agreement.Comment: Phys. Rev. E 81, 060101(R) (2010
Ground-state Properties of Small-Size Nonlinear Dynamical Lattices
We investigate the ground state of a system of interacting particles in small
nonlinear lattices with M > 2 sites, using as a prototypical example the
discrete nonlinear Schroedinger equation that has been recently used
extensively in the contexts of nonlinear optics of waveguide arrays, and
Bose-Einstein condensates in optical lattices. We find that, in the presence of
attractive interactions, the dynamical scenario relevant to the ground state
and the lowest-energy modes of such few-site nonlinear lattices reveals a
variety of nontrivial features that are absent in the large/infinite lattice
limits: the single-pulse solution and the uniform solution are found to coexist
in a finite range of the lattice intersite coupling where, depending on the
latter, one of them represents the ground state; in addition, the single-pulse
mode does not even exist beyond a critical parametric threshold. Finally, the
onset of the ground state (modulational) instability appears to be intimately
connected with a non-standard (``double transcritical'') type of bifurcation
that, to the best of our knowledge, has not been reported previously in other
physical systems.Comment: 7 pages, 4 figures; submitted to PR
Topological Filters for Solitons in Coupled Waveguides Networks
We study the propagation of discrete solitons on chains of coupled optical
waveguides where finite networks of waveguides are inserted at some points. By
properly selecting the topology of these networks, it is possible to control
the transmission of traveling solitons: we show here that inhomogeneous
waveguide networks may be used as filters for soliton propagation. Our results
provide a first step in the understanding of the interplay/competition between
topology and nonlinearity for soliton dynamics in optical fibers
Propagation of Discrete Solitons in Inhomogeneous Networks
In many physical applications solitons propagate on supports whose
topological properties may induce new and interesting effects. In this paper,
we investigate the propagation of solitons on chains with a topological
inhomogeneity generated by the insertion of a finite discrete network on the
chain. For networks connected by a link to a single site of the chain, we
derive a general criterion yielding the momenta for perfect reflection and
transmission of traveling solitons and we discuss solitonic motion on chains
with topological inhomogeneities
Bose-Einstein condensation in inhomogeneous Josephson arrays
We show that spatial Bose-Einstein condensation of non-interacting bosons
occurs in dimension d < 2 over discrete structures with inhomogeneous topology
and with no need of external confining potentials. Josephson junction arrays
provide a physical realization of this mechanism. The topological origin of the
phenomenon may open the way to the engineering of quantum devices based on
Bose-Einstein condensation. The comb array, which embodies all the relevant
features of this effect, is studied in detail.Comment: 4 pages, 5 figure
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