We present simulations about the parallel version of the Ising model, focussing on phase transitions. We show the effect of "diluting" the parallel update, thus exploring the transition between the parallel and the usual sequential version of the model, and the effects of a nonlinear Hamiltonian. In this case the mean-field approximation is a chaotic map, a behaviour that can be recovered also in microscopic simulations by changing the topology of the network, i.e., exploiting the small-world effect.

In collaboration with R. Rechtman and T. Matteuzzi

We investigate zero temperature liquid \(^4\)He in strictly one dimension by means of state-of-the-art Quantum Monte Carlo and analytic continuation techniques [1].
The system displays the unique feature of spanning all the possible values of the Luttinger liquid parameter \(K_L\) by only changing the density.
We explore the behavior of the dynamical structure factor \(S(q,\omega)\) beyond the limits of applicability of Luttinger liquid theory in the whole range in \(K_L\). We observe a crossover from a weakly interacting Bose gas regime at low density (\(K_L\gg 1\)) to a quasi-solid regime at high density (\(K_L\ll 1\)), which we interpret in terms of novel analytical expressions for the spectrum of hard-rods. During this transition the interplay between dimensionality and interaction makes \(S(q,\omega)\) manifest a pseudo particle-hole continuum typical of a fermionic system, while the Bogoliubov mode evolves into a remnant of the roton mode. We provide also a perturbative estimation of the drag force experienced by a soft impurity moving along the system.

References
[1] G. Bertaina, M. Motta, M. Rossi, E. Vitali, and D.E. Galli, arXiv:1412.7179 (2014).

Synchronization is one of the most surprising phenomena that occurs in systems of coupled oscillators. A system is synchronized if its individual elements show a common or a temporal correlated evolution and therefore a coherent collective dynamics, which largely depends on the interactions structure of the system, on its individual elements and on their coupling. Synchronization is a universal phenomenon, which appears in systems belonging to various research fields and particularly in the brain tissue, which can be modelled through neural networks. A neural network is a dynamic system built on a graph, whose nodes are occupied by individual oscillators (neurons), and whose links represent their synapses. These neural systems can reproduce the synchronous phases that are experimentally observed and that in brain tissues are linked, depending on the cerebral area in which they occur, with cognitive processes, such as memory, or malfunction phases.In the present work we want to see how synchronization properties of a neural network change if the interactions structure of the system is modified, especially if some nodes with a very high number of connections (hubs) are present and if we take into account both the excitatory and inhibitory mechanisms. The starting idea is based on a recent study1, which from analysis of electrical activity in some cerebral areas of mice proves the existence of population of inhibitory hubs nodes, which carry out a regulatory function for the whole system.

[1] P. Bonifazi and et al., Science, 326(5958):1419–1424, December 2009

Predicting epidemic processes on networks is still a challenging problem. Indeed in most of the cases dealing with incomplete or noisy data about the epidemics is unavoidable. Previous works provided a Belief propagation algorithm to deal with inference problems for irreversible stochasti epidemic model (SIR). They derived equations which allow to compute posterior distributions of the time evolution of the state of each node given some observation. We use this BP algorithm in order to predict characteristic quantity for SIR epidemic process relying only on partial observation at an early time.

We study in momentum-conserving systems, how non-integrable dynamics may affect thermal transport properties. As illustrating examples, two one-dimensional (1D) diatomic chains, representing 1D fluids and lattices, respectively, are numerically investigated. In both models, the two species of atoms are assigned two different masses and are arranged alternatively. The systems are non-integrable unless the mass ratio is one. We find that when the mass ratio is slightly different from one, the heat conductivity may keep significantly unchanged over a certain range of the system size and as the mass ratio tends to one, this range may expand rapidly. These results establish a new connection between the macroscopic thermal transport properties and the underlying dynamics.

Reference:
[1] S. Chen, J. Wang, G. Casati, and G. Benenti, Phys. Rev. E 90, 032134 (2014).

With the aid of \(N\)-body simulations we study the problems of relaxation and energy transport and diffusion in one dimensional chains of non-linear oscillators with interaction strength decaying with a power \(\alpha\) of their spacing. Moreover, we study the effects of a thermal bath coupled to one or more degrees of freedom of the system for different values of the force exponent \(\alpha\). Results are then compared with those of other long-range models such as for example the \(\alpha\)-HMF model.

The theory of isothermal Brownian motion relies on fundamental principles of equilibrium statistical mechanics, such as the equipartition theorem, embedded in the stochastic framework of the Langevin equation. In the presence of a nonisothermal solvent it becomes questionable whether a Langevin-like description still applies and, if so, no general criterion exists which uniquely determines friction and thermal fluctuations. Starting from the fluctuating hydrodynamics of a solvent in local equilibrium, we constructively show that a generalized Langevin description does hold and derive the statistics of the corresponding thermal noise. The coupling between the hydrodynamic modes excited by the particle itself and the solvent temperature gradient turns the energy spectrum of the Langevin noise into a frequency-dependent tensor. We derive an explicit expression for this energy spectrum in the analytically tractable case of hot Brownian motion, i.e. a constantly heated particle generating a comoving radial temperature field. This allows us to explain the break of energy equipartition and to express the energy content of the particle velocity and position in terms of effective temperatures.

We introduce the study of the eigenvectors of a random matrix. Traditionally, the requirement of base invariance has lead to the conclusion that invariant models describe extended systems. We show that deviations of the eigenvalue statistics from the Wigner-Dyson universality reflects itself on the eigenvector distribution. In particular, gaps in the eigenvalue density spontaneously break the U(N) symmetry to a smaller one. Models with log-normal weight, such as those emerging in Chern-Simons and ABJM theories, break the U(N) in a critical way, resulting into a multi-fractal eigenvector statistics. These results pave the way to the exploration of localization problems using random matrices via the study of new classes of observables and potentially to novel, interdisciplinary, applications of matrix models.

– F. Franchini; "On the Spontaneous Breaking of U(N) symmetry in invariant Matrix Models"; arXiv:1412.6523.
– F. Franchini; "Toward an invariant matrix model for the Anderson Transition"; arXiv:1503.03341

The numerical propagation of a wavepacket in two dimensions (2D) finds a wide range of applications in surface scattering problems, in particular if the potential structure of interest is such that the Schroedinger equation cannot be solved analytically. In this project, a highly optimised, norm-preserving algorithm is used to solve numerically the Time-Dependent Schroedinger Equation in order to propagate a wavepacket in time across a two-dimensional spatial domain. The aim of our study is to investigate the quantum reflection of slow atoms as they approach an attractive surface. This will finally enable experimental tests of potentials of the Casimir-Van der Waals form to be carried out in Heidelberg, which accounts for the interaction with a periodically corrugated effectively 2D surface.

We have performed a microscopic study of a quantized vortex line in condensed 4He at zero temperature using the shadow path integral ground state method and the fixed phase approximation [Phys. Rev. B 89, 224516 (2014)]. The inclusion of backflow correlations in the phase improves the description of the vortex with respect to the Onsager-Feynman phase by a large reduction of the core energy of the topological excitation. A vortex line has excited states in the form of Kelvin waves in which the vortex is no longer straight but its core moves in a helical way. The phase with backflow induces a partial filling of the vortex core; we interpret the delocalization of vorticity achieved with the backflow phase as due to the zero point motion of Kelvin waves. This opens the possibility to investigate microscopically Kelvin waves via analytic continuation of suitable imaginary time correlation functions computed via Quantum Monte Carlo simulations. Preliminary results will be shown.

Annealed importance sampling is a simulation method devised by Neal [Stat. Comput. 11, 125 (2001)] to assign weights to configurations generated by simulated annealing trajectories. In particular, the equilibrium average of a generic physical quantity can be computed by a weighted average exploiting weights and estimates of this quantity associated to the final configurations of the annealed trajectories. Here, we review annealed importance sampling from the perspective of nonequilibrium path-ensemble averages [G. E. Crooks, Phys. Rev. E 61, 2361 (2000)]. The equivalence of Neal’s and Crooks’ treatments highlights the generality of the method, which goes beyond the mere thermal-based protocols. Furthermore, we show that a temperature schedule based on a constant cooling rate outperforms stepwise cooling schedules and that, for a given elapsed computer time, performances of annealed importance sampling are, in general, improved by increasing the number of intermediate temperatures.

The patient-zero problem consists in finding the initial source of an epidemic outbreak given observations at a later time. In this seminar, I will describe a Bayesian method which is able to infer details on the past history of an epidemics based solely on the topology of the contact network and a single snapshot of partial and noisy observations. The method is built on a Bethe approximation for the posterior distribution, and is inherently exact on tree graphs. Moreover, it can be coupled to a set of equations, based on the variational expression of the Bethe free energy, to find the patient-zero along with maximum-likelihood epidemic parameters. I will describe the method and some results for simulated epidemics on random graphs, and briefly mention future directions of research in the discrete-time setting, as well as a new method that can perform inference on a continuous time spreading model and deal efficiently with real contact-time data.

References:
F Altarelli et al J. Stat. Mech. (2013) P09011
Fabrizio Altarelli et al J. Stat. Mech. (2014) P10016
Fabrizio Altarelli et al Phys Rev Lett (2014) 112, 118701

The study of the structure of glasses (esp. network glasses) has been dominated since the 1930s by the random-network model due to Zachariasen, with its variants in case of mixing with good crystal formers. It will be shown that Zachariasen's scheme fails to explain low-temperature physics data even for a single-component glass with ppm contaminants. The scheme fails even more dramatically when trying to explain magnetic field- and composition-dependent effects at low and higher temperatures in multi-component glasses. A new cellular model for the intermediate-range atomic structure of glasses will be proposed that leads to a low-energy excitations' description in agreement with all available experimental data. The model is applied to predict the paramagnetism of the weak, SQUID-detected magnetization M of ordinary window glasses with surprising features in the magnetic-field dependence of M and in the (non-Curie) temperature dependence of the susceptibility.

We study the unzipping of a double stranded DNA whose ends are subjected to a time dependent periodic force with frequency \(\omega\) and amplitude \(G\). By varying the frequency of the applied force it is possible to bring the DNA from the zipped or and unzipped state to a dynamic state showing hysteresis. We found that the area of the hystresis loop scales as \(1/\omega\) in high frequencies whereas, it scales as \(G^{\alpha} \omega^{\beta}\) with exponents \(\alpha = 1\) and \(\beta = 5/4\) at low frequencies.

We investigate the Quantum Phase transitions of two-component bosonic systems within the framework of Quantum Monte Carlo simulations. Our work is performed by considering two identical bosonic species in a square lattice and half-filling conditions. We study the formation of different quantum phases depending on the interplay between species' interactions, showing the presence of demixed Superfluid and demixed Mott insulator phases when the interspecies potential becomes greater than the intraspecies repulsion. An interesting relationship between the the topography of the demixed regions and the demixed quantum phase has been found, revealing interesting scenarios in terms of possible experimental detection.
We finally reconstruct the corresponding phase diagram emphasizing that, for large enough (but finite) intra-species interaction, one can observe the presence of the transition from the demixed Mott Insulator to the super-counterflow (SCF) state.

We study the evolution of a Bose-Einstein condenstate across engineered potential landscapes. Our approach is based on a numerical mean-field description in one, two and three spatial dimensions. We numerically prepare initial wave packets as done also in typical experiments with ultracold bosons. These wave packets are then traveling across several potential structures, thus realizing an atomic current. We discuss our setup and preliminary results on how this new type of atomic transport depends on the mean-field nonlinearity.

Systems with long-range interactions display a short-time relaxation towards quasistationary states (QSS) whose lifetime increases with the system size. In the paradigmatic Hamiltonian mean-field model (HMF) out-of-equilibrium phase transitions are predicted and numerically detected which separate homogeneous (zero magnetization) and inhomogeneous (nonzero magnetization) QSS. In the former regime, the velocity distribution presents two large, symmetric, bumps, which cannot be self-consistently explained by resorting to the conventional Lynden-Bell maximum entropy approach. To improve the theory in this respect and eventually fill the gap with the observation, we here propose a generalized maximum entropy scheme which accounts for the pseudo-conservation of a additional charges, the even momenta of the single particle distribution. These latter are set to the asymptotic values, as estimated by direct integration of the underlying Vlasov equation, which formally holds in the thermodynamic limit. Methodologically, we operate in the framework of generalized Gibbs ensemble, as sometimes defined in statistical quantum mechanics, which contains an infinite number of conserved charges. The agreement between theory and simulations is extremely satisfying, both above and below the out of equilibrium transition threshold. The fine details of the velocity profile are adequately captured upon truncation at the tenth order in the hierarchy of pseudo-conserved momenta.

In this work we integrate existing soil infiltration modeling with particle based methods in order to simulate landslides triggered by rainfall. In literature, usually, the infiltration models are based on continuum schemes (e.g. Eulerian approach) by means of which it is possible to define the field of the pore pressure within a soil. Differently, the particle based method implements a Lagrangian scheme which allows to follow the trajectory of the particles and their dynamical properties. In order to simulate the triggering mechanism, we test the classical and fractional Richards equations adapted to the molecular dynamics approach using the failure criterion of Mohr-Coulomb. In our scheme the local positive pure pressures are simply interpreted as a perturbation of the rest state of each grain, i.e., the pore pressure function can be interpreted as a time-space dependent scalar field acting on the particles. To initialize the system we generate, using a molecular dynamics based algorithm, a mechanically stable sphere packing simulating a consolidate soil. In this way we obtain the input structure of our "fictitious" soil to model landslides, considering the infiltration processes caused by rainfall. Moreover, in our scheme, the particles are porous and therefore we take into consideration the micro pore structure at intra-particle level, while the macro pore structure is due to inter-particle interstices. In this way we have two different infiltration time scales, as observed experimentally. The inter-particle interactions are modeled through a force which, in the absence of suitable experimental data and due to the arbitrariness of the grain dimension, is derived from a Lennard-Jones like potential. For the prediction of the particle positions, after and during a rainfall, we use a standard molecular dynamics approach. We analyze the sensitivity of the models by varying some parameters (hydraulic conductivity, cohesion, slope and friction angle, soil depth, variation of random properties, fractional order of the generalized infiltration model, etc.) and considering both regular and random configuration of the particles. The outcome of the simulations is quite satisfactory and therefore, we can claim that this is a promising new method to simulate landslides triggered by rainfall.

The problem of competition, cooperation and the emergence of collective behaviour in the presence of limited resources is quite general, and one of cornerstones of evolutionary dynamics both in the natural and the in the artificial worlds. For instance, trading is nowadays mainly performed by algorithms which act autonomously and almost form ecosystem. These models exhibit complex phenomena, governed by various parameters that describe the quantity and the quality of agents involved. We study how these parameters influence the efficiency of the models, measured as efficient distribution of limited resources, and how the additional information like vicinity, it's structure, the number and the cognitive abilities of participants modify these models efficiency. We extend the classical prototype of such environment, i.e, minority games, by allowing agents to process additional information. We analyse how this exchange information affects the dynamics of the system. The main focus is put on the role of the information from each agents vicinity and study the influence of different community structures on the model. We investigate several topologies like simple patch vicinity, von Neumann vicinity, small world, scale-free networks and a hierarchical small world network. We have found that there is a distinct relation between the structure and dimension of the vicinity, ie. the information given to each agent, and the efficiency of the model. These results could be used to optimise any kind of distributed algorithmic ecosystem that has a finite resources and needs an efficient use of it. We further investigate how these finding can be used in algorithmic ecosystems. The context within which we elaborate some of our ideas is high-frequency financial markets, that are run by an enormous number of trading algorithms. Among other possible applications we consider optimizing the routing protocols for Delay Tolerant Networks, more efficient smart-grid energy systems and so on.

In collaboration with F. Bagnoli

Quantum Monte Carlo (QMC) simulations of many body fermionic systems are considerably complicated by the well known sign problem [1]. Although very accurate approximation schemes have been developed for the calculation of static properties, the possibility of extending such methodologies to the investigation of dynamical properties is still largely unexplored [2]. Recently, a number of innovative QMC methods have been conceived, which map the imaginary time evolution into a random walk in the manifold of Slater determinants. In such methods the sign problem emerges in a different form, and can be treated introducing approximations that are more likely to permit the study of excited states [5]. We have focused on the phaseless auxiliary Fields QMC method (AFQMC), developed by S. Zhang [3]. Generalizing the formal manipulations suggested by F. Assaad et al. [4], we propose a practical scheme to evaluate dynamic correlation functions in imaginary time, giving access to the response functions of interacting fermionic systems. We assess the accuracy of the methodology via the study of exactly solvable simple models, comparing AFQMC predictions with exact solutions [5]. We also compute the imaginary time correlation functions and the effective mass of the two-dimensional homogeneous electron gas in the high-density regime, providing comparison between AFQMC and recent experimental data [6].

REFERENCES:

[1] R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill (1965)
[2] M. Nava, D. Galli, S. Moroni and E. Vitali: arXiv:1302.1799 (2013)
[3] S. Zhang: 'Quantum Monte Carlo Methods for Strongly Correlated Electron Systems', in Theoretical Methods for Strongly Correlated Electron Systems, Springer Verlag (2003)
[4] M. Feldbacher and F. F. Assaad: Phys. Rev. B 63, 073105 (2001)
[5] M. Motta, D.E. Galli, S. Moroni and E. Vitali, J Chem Phys. 140, 024107 (2014)
[6] M. Motta, D.E. Galli, S. Moroni and E. Vitali, in preparation

In this poster we summarize the results of the experiments on on-line support for science cafés conducted with the help of the The SciCafe2.0 Virtual Platform. The SciCafe2.0 consortium, funded under the Collective Awareness Platforms Objectives of the European Commission FP7 Research Programme, aims at supporting participative exchange and co-generation of knowledge, also using the science café paradigm.
The SciCafe2.0 Virtual Platform was designed aiming at reproducing the experience of discussing between peers in a science café. The present version is a first step towards this goal, and was used in a number of science café in Florence. The core of our instrument is the live streaming of the event using Google hangout, to which we added the possibility of intection among participants, storage and classification of material, online and offline discussion tools.

In collaboration with F. Bagnoli

We study a lattice polymer model that incorporates as special cases two different models previously studied in the literature, namely, the Wu-Bradley model and the asymmetric interacting self-avoiding trail (AISAT) model. Both models are characterized by the presence of different microscopic interactions, driving different collapse transitions. Our motivation is that, while the phase diagram and universality classes occurring in the former model are rather well established, some contradictory results have recently emerged for the latter. We consider a square Husimi lattice, which is expected to best approximate the model on the ordinary 2d square lattice. Even though such (mean-field-like) calculations do not provide information about critical exponents for the corresponding finite-dimensional model, the phase diagram can be worked out with high numerical precision. Our results show that the phase diagrams of the two aforementioned models are fully equivalent from the topological point of view. Heuristic arguments, and the availability of exact results in certain limit cases, lead us to conjecture that such an equivalence might extend to the finite-dimensional case and the related universality classes.

People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion, so we speak of reasonable contrarians. We present the opinion dynamics of a society of conformists and reasonable contrarians where each agent can express one of two opinions. The model is a cellular automaton of Ising type. In the mean field approximation the model exhibits bifurcations and a chaotic phase, interpreted as coherent oscillations of the whole society. We study the model on Watts-Strogatz networks and on scale free networks. In these cases, we use a suitably defined entropy to characterize disorder.

The aim is calculating the ground and excited states properties of one-dimensional bosons interacting with a soft repulsive potential at zero temperature, as a function of density and interaction strength. I am characterizing the liquid phase in terms of Luttinger Liquid theory and I am investigating the high-density Cluster Luttinger Liquid phase. Through the Genetic Inversion via Falsification of Theories (GIFT) method, I am extracting the excitation spectrum of density fluctuations from the density-density imaginary-time correlation functions.