arXiv subjects

D. Cassi

Publications and source records attributed to D. Cassi.

At least 19 recordsLinked to original sources

arXiv2020

Conditioning of Superconductive Properties in Graph-Shaped Reticles

We report on phenomena observed in planar integrated networks obtained connecting superconducting island by Josephson tunnel junctions. These networks, identifiable as tree-like graphs, have branches consisting of series arrays of Josephson junctions which can be individually current biased and characterized. Both Josephson supercurrents and gap parameters of the arrays embedded in the graph structures display properties significantly different from those of reference arrays fabricated on the same chips and having identical geometrical shape. The temperature and magnetic field dependencies of the Josephson current of the embedded arrays both show a singular behavior when a critical value is reached by the Josephson characteristic energy. The gap parameter of the junctions generating the embedded arrays is higher than that of the junctions forming the reference geometrical arrays.

cond-mat.supr-con↗

arXiv2008

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: $A + B \to 2A$. 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.

cond-mat.stat-mech↗

arXiv2008

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.

cond-mat.stat-mech↗

arXiv2008

Diffusive thermal dynamics for the spin-S Ising ferromagnet

We introduce an alternative thermal diffusive dynamics for the spin-S Ising ferromagnet realized by means of a random walker. The latter hops across the sites of the lattice and flips the relevant spins according to a probability depending on both the local magnetic arrangement and the temperature. The random walker, intended to model a diffusing excitation, interacts with the lattice so that it is biased towards those sites where it can achieve an energy gain. In order to adapt our algorithm to systems made up of arbitrary spins, some non trivial generalizations are implied. In particular, we will apply the new dynamics to two-dimensional spin-1/2 and spin-1 systems analyzing their relaxation and critical behavior. Some interesting differences with respect to canonical results are found; moreover, by comparing the outcomes from the examined cases, we will point out their main features, possibly extending the results to spin-S systems.

cond-mat.stat-mech↗

arXiv2008

Random walks interacting with evolving energy landscapes

We introduce a diffusion model for energetically inhomogeneous systems. A random walker moves on a spin-S Ising configuration, which generates the energy landscape on the lattice through the nearest-neighbors interaction. The underlying energetic environment is also made dynamic by properly coupling the walker with the spin lattice. In fact, while the walker hops across nearest-neighbor sites, it can flip the pertaining spins, realizing a diffusive dynamics for the Ising system. As a result, the walk is biased towards high energy regions, namely the boundaries between clusters. Besides, the coupling introduced involves, with respect the ordinary diffusion laws, interesting corrections depending on either the temperature and the spin magnitude. In particular, they provide a further signature of the phase-transition occurring on the magnetic lattice.

cond-mat.stat-mech↗

arXiv2007

Random walk on a population of random walkers

We consider a population of $N$ labeled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label $\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be viewed as a stochastic process, where the transition probabilities are a stochastic process themselves. Upon mapping onto two simpler processes, the quantities characterizing $\mathcal{X}(t)$ can be calculated in the limit of long times and low walkers density. The results are compared with numerical simulations. Several different topologies for the substrate underlying diffusion are considered.

cond-mat.stat-mech↗

arXiv2007

Electrical networks on $n$-simplex fractals

The decimation map $\mathcal{D}$ for a network of admittances on an $n$-simplex lattice fractal is studied. The asymptotic behaviour of $\mathcal{D}$ 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 $n \geq 4$; 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 $\ln[(n+2)/3]/\ln 2$ to $\ln[(n+2)^3/n(n+1)^2]/\ln 2$.

cond-mat.dis-nn↗

arXiv2007

Autocatalytic reaction on low-dimensional substrates

We discuss a model for the autocatalytic reaction $A+B\to 2A$ on substrates where the reactants perform a compact exploration of the space, i.e., on lattices whose spectral dimension $\tilde{d}$ is $< 2$. For finite systems, the total time $τ$ for the reaction to end scales according to two different regimes, for high and low concentrations of reactants. The functional dependence of $τ$ on the volume of the substrate and the concentration of reactants is discussed within a mean-field approximation. Possible applications are discussed.

cond-mat.stat-mech↗

arXiv2007

Universal features of information spreading efficiency on $d$-dimensional lattices

A model for information spreading in a population of $N$ mobile agents is extended to $d$-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 $τ$ at which the whole population has been reached by information. By comparing numerical simulations with mean-field calculations, we show that dimension $d=2$ is marginal for this problem and mean-field calculations become exact for $d > 2$. Nevertheless, the striking nonmonotonic behavior exhibited by the final degree of information with respect to $N$ and the lattice size $L$ appears to be geometry independent.

cond-mat.stat-mech↗

arXiv2007

Phase-ordering kinetics on graphs

We study numerically the phase-ordering kinetics following a temperature quench of the Ising model with single spin flip dynamics on a class of graphs, including geometrical fractals and random fractals, such as the percolation cluster. For each structure we discuss the scaling properties and compute the dynamical exponents. We show that the exponent $a_χ$ for the integrated response function, at variance with all the other exponents, is independent on temperature and on the presence of pinning. This universal character suggests a strict relation between $a_χ$ and the topological properties of the networks, in analogy to what observed on regular lattices.

cond-mat.stat-mech↗

arXiv2007

Soliton Propagation in Chains with Simple Nonlocal Defects

We study the propagation of solitons on complex chains built by inserting finite graphs at two sites of an unbranched chain. We compare numerical findings with the results of an analytical linear approximation scheme describing the interaction of large-fast solitons with non-local topological defects on a chain. We show that the transmission properties of the solitons strongly depend on the structure of the inserted graph, giving a tool to control the soliton propagation through the choice of pertinent graphs to be attached to the chain.

nlin.PS↗

arXiv2006

Aging dynamics and the topology of inhomogenous networks

We study phase ordering on networks and we establish a relation between the exponent $a_χ$ of the aging part of the integrated autoresponse function $χ_{ag}$ and the topology of the underlying structures. We show that $a_χ>0$ in full generality on networks which are above the lower critical dimension $d_L$, i.e. where the corresponding statistical model has a phase transition at finite temperature. For discrete symmetry models on finite ramified structures with $T_c = 0$, which are at the lower critical dimension $d_L$, we show that $a_χ$ is expected to vanish. We provide numerical results for the physically interesting case of the $2-d$ percolation cluster at or above the percolation threshold, i.e. at or above $d_L$, and for other networks, showing that the value of $a_χ$ changes according to our hypothesis. For $O({\cal N})$ models we find that the same picture holds in the large-${\cal N}$ limit and that $a_χ$ only depends on the spectral dimension of the network.

cond-mat.stat-mech↗

arXiv2006

Efficiency of Information Spreading in a population of diffusing agents

We introduce a model for information spreading among a population of N agents diffusing on a square LxL lattice, starting from an informed agent (Source). Information passing from informed to unaware agents occurs whenever the relative distance is < 1. Numerical simulations show that the time required for the information to reach all agents scales as N^{-alpha}L^{beta}, where alpha and beta are noninteger. A decay factor z takes into account the degeneration of information as it passes from one agent to another; the final average degree of information of the population, I_{av}(z), is thus history-dependent. We find that the behavior of I_{av}(z) is non-monotonic with respect to N and L and displays a set of minima. Part of the results are recovered with analytical approximations.

cond-mat.stat-mech↗

arXiv2005

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.

nlin.PS↗

arXiv2005

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.

cond-mat.stat-mech↗

arXiv2005

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.

cond-mat.stat-mech↗

arXiv2004

Topology-induced confined superfluidity in inhomogeneous arrays

We report the first study of the zero-temperature phase diagram of the Bose-Hubbard model on topologically inhomogeneous arrays. We show that the usual Mott-insulator and superfluid domains, in the paradigmatic case of the comb lattice, are separated by regions where the superfluid behaviour of the bosonic system is confined along the comb backbone. The existence of such {\it confined superfluidity}, arising from topological inhomogeneity, is proved by different analytical and numerical techniques which we extend to the case of inhomogeneous arrays. We also discuss the relevance of our results to real system exhibiting macroscopic phase coherence, such as coupled Bose condensates and Josephson arrays.

cond-mat.soft↗

arXiv2004

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.

q-bio.BM↗