By means of hybrid multiparticle collsion-particle-in-cell (MPC-PIC) simulations we study the dynamical scaling of energy and density correlations at equilibrium in moderately coupled two-dimensional (2D) and quasi-one-dimensional (1D) plasmas. We find that the predictions of nonlinear fluctuating hydrodynamics for the structure factors of density and energy fluctuations in 1D systems with three global conservation laws hold true also for 2D systems that are more extended along one of the two spatial dimensions. Moreover, from the analysis of the equilibrium energy correlators and density structure factors of both 1D and 2D neutral plasmas, we find that neglecting the contribution of the fluctuations of the vanishing self-consistent electrostatic fields overestimates the interval of frequencies over which the anomalous transport is observed. Such violations of the expected scaling in the currents correlation are found in different regimes, hindering the observation of the asymptotic scaling predicted by the theory.

Bose-Einstein condensates (BECs) are one of the most promising experimental setups used in the field of analogue gravity in order to detect the Hawking effect (J. Steinhauer, Nature Physics 12, 2016). Exploiting a peculiar state of hard core bosons in 1D (i.e. the Tonks-Girardeau gas) we are able to obtain the exact solution of a BEC flowing against an obstacle and we examine it in the framework of sonic black holes; in this limit we recover Hawking result without making use of the gravitational analogy and we find that a precise correspondence between the emission of phonons in the upstream region and the Hawking-like mechanism requires additional conditions to be met. Finally we study the correlations between the Hawking quanta and the in-falling partner, recovering the expected pattern (A. Parola et al., arXiv:1703.05041).

Peculiar out-of-equilibrium stationary processes may emerge in a Discrete Nonlinear Schroedinger chain with a heat reservoir and a pure mass dissipator acting at its opposite edges. By increasing the temperature of the reservoir, a transition between two distinct regimes occurs. In the low temperature regime the temperature and chemical potential profiles display a smooth shape characteristic of thermodiffusive processes. Remarkably, a regime of negative absolute temperatures emerges spontaneously. In the high temperature regime, localized structures (discrete breathers) naturally arise out of the fluctuations and act as a "thermal wall" that strongly inhibits the flows of energy and mass towards the dissipator. The systems turns into a quasi-insulator.

Nonlinear systems may sustain localized, oscillating excitations. We focus on a deterministic, Hamiltonian system (the Discrete NonLinear Schroedinger Equation, DNLS) and a purely stochastic model which have the common feature to present two conservation laws (the energy and the mass) and which display a similar phenomenology with varying the conserved quantities. In particular, for large energy they are both characterized by breather-like excitations and both their dynamics are exponentially slow. These similarities should help to understand the origin of frozen dynamics displayed by DNLS equation. In collaboration with: Stefano Iubini (University of Florence), Antonio Politi (University of Aberdeen, UK), Liviu Chirondojan and Gian-Luca Oppo (University of Glasgow, UK)

The dispersion curves $n(\omega)$ (refractive index vs frequency) of ionic crystals in the infrared are calculated by means of the Green-Kubo theory, in terms of a time correlation function involving the motions of the ions only. The aim of the study is to investigate how well the experimental data are reproduced by a classical approximation of the theory, in which the time correlation functions are expressed in terms of the ion orbits, obtained by molecular-dynamics simulations. We report the results for a LiF lattice of 4096 ions. The theoretical curves are in surprisingly good agreement with experimental data. In collaboration with: A. Carati, G. Galgani, R. Gangemi, and A. Maiocchi

The Mott insulator is characterized by having small deviations around the (integer) average particle density $n$, with pairs with $n - 1$ and $n + 1$ particles forming bound states. In one dimension, the effect is captured by a nonzero value of a nonlocal “string” of parities, which instead vanishes in the superfluid phase where density fluctuations are large. Here, we investigate the interaction induced transition from the superfluid to the Mott insulator, in the paradigmatic Bose Hubbard model at $n = 1$. By means of quantum Monte Carlo simulations and finite size scaling analysis on $L \times M$ ladders, we explore the behavior of “brane” parity operators from one dimension (i.e., $M = 1$ and $L \to \infty$ ) to two dimensions (i.e., $M\to\infty$ and $L\to\infty$). We confirm the conjecture that, adopting a standard definition, their average value decays to zero in two dimensions also in the insulating phase, evaluating the scaling factor of the “perimeter law” [S. P. Rath et al., Ann. Phys. (Berlin) 334, 256 (2013)]. Upon introducing a further phase in the brane parity, we show that its expectation value becomes nonzero in the insulator, while still vanishing at the transition to the superfluid phase. These quantities are directly accessible to experimental measures, thus providing an insightful signature of the Mott insulator. [Ref: S. Fazzini, F. Becca, A. Montorsi, Phys. Rev. Lett. 118, 157602 (2017)]

It is widely believed that the atomic structure of amorphous solids, network glasses in particular, is characterized by homogeneous disorder (despite the known Dynamical Heterogeneities above Tg) and, at cryogenic temperatures, is described by the Standard Tunneling Model (two-level systems, linear specific heat). It will be shown that careful consideration of low-T data in real glasses challenges both of these beliefs and that at low-temperatures glasses appear inhomogeneous and organized in quasi-ordered cells that are separated by mobile atoms that give rise to two types of tunneling systems. The cellular model will be shown to provide a new and natural scenario for both the Boson peak and for the glass-transition phenomenology.

Vector spin glass models have been scarcely studied, mostly on fully connected topologies, which provide some unphysical predictions. We focus instead on diluted topologies, which yield more reliable results. By exploiting belief-propagation, we find that the XY model (the simplest vector model) is by far more unstable toward replica symmetry breaking (RSB), due to the combined effect of the graph sparsity and the spin continuous nature. Several interesting consequences arise, among which the appearance of RSB in the random field XY model and the recovering of the frequency density of vibrations in glasses in the zero–temperature limit. Coautori: Giorgio Parisi, Federico Ricci-Tersenghi

The assignment problem is a long standing problem in combinatorial optimization which consists in finding the perfect matching between two sets of $N$ points that minimizes the total length. In the random assignment, the costs for all the ​possible pairs to be matched are independent random variables identically distributed​ according to a distribution law $\rho(w)$​. Among the many great successes of the replica formalism there is the derivation of the exact value of the average density cost for the random assignment. It is well known that, in the limit of an infinite number of possible pairs, the average optimal cost depends only on the behavior of the disorder distribution near lowest possible pair cost. Here we present how the choice of the disorder distribution affects the finite size corrections to the average cost. We have found that corrections are smaller in the case of a pure power law probability distribution, i.e. $\rho(w) \sim w^r$. In this case, only analytical corrections are present, that is in inverse powers of the number of points. On the contrary, and interestingly enough, the exponent of the leading correction changes as a function of $r$ whenever $\rho(w) \sim w^r (\eta_0 + \eta_1 \, w + \dots )$ with $\eta_1\neq 0$. We believe that this is the first example in which the effects of the choice of the distribution law for disorder has been fully taken into account. References: [1] S. Caracciolo, M.P. D’Achille, E.M. Malatesta, G. Sicuro, Finite size corrections in the random assignment problem, Physical Review E 95, 052129, 2017.

We present a dynamics on symbolic sequences that model the action of some biological processes considered as one of the major mechanisms shaping DNA. We investigate the link between symmetries and structure that emerges through such a dynamics. Numerical results agree with our predictions.

The problem of training neural networks is in general non-convex and in principle computationally hard. This, however, does not seem to be a problem in practice, as many fairly greedy heuristics based on variants of Stochastic Gradient Descent are routinely employed with surprisingly good results by the machine learning community in real-life scenarios. Starting from a large-deviation analysis of the simplest non-convex neural network, the discrete perceptron, we developed a series of analytical and numerical results which reveal the existence of rare dense regions of the optimization landscape that have a number of highly desirable properties. In particular, they are wide, easily accessible minima with good generalization properties. The analysis allowed us to develop a large number of algorithms which are able to exploit the existence of these states in a variety of models, including state-of-the art neural networks trained on real data, stochastic processes and quantum annealing devices. Overall, these results appear to be rather general with respect to the details of the underlying model and of the data, and may be relevant biologically and technologically, as well as apply to other inference and constraint satisfaction problems.

The dynamics of chemical reactions inside a cell can be mathematically described by a set of ordinary differential equations for the concentrations of metabolites. Assuming a steady-state condition within a cell, concentrations are stationary and the rate at which reactions occur (called metabolic fluxes) satisfy an under-determined system of linear equations. Characterizing the space of fluxes that satisfy such equations along with given bounds (and possibly additional relevant constraints) is considered of utmost importance for the understanding of cellular metabolism. Extreme values for each individual flux can be computed with Linear Programming (as Flux Balance Analysis), and their marginal distributions can be approximately computed with Monte-Carlo sampling. Here we present an analytic method for the latter task based on a statistical mechanics inspired method, the Expectation Propagation approximation, that does not involve sampling and can achieve much better predictions than other existing analytic methods. With respect to sampling, we show that it has some advantages including computation time, and the ability to efficiently fix empirically estimated distributions of fluxes.

The complex three-dimensional organization of chromosomes inside the cell nucleus is fundamental for regulating the cell biological functions. Genomic structural variants (SVs), such as deletions, duplications or inversions, often lead to abnormal chromosome folding causing gene misexpression and disease. However, the mechanisms determining the 3D genome organization are still largely unknown and the prediction of the effects of SVs remains a challenge. I discuss a polymer physics based method (PRISMR) to model chromosome folding and to predict enhancer-promoter contacts. In particular, the effects of pathogenic SVs at the EPHA4 locus are predicted in-silico and compared to experimental capture Hi-C data in mouse limb buds and human fibroblasts. 

Amyloid aggregation is a process in which dispersed proteins and peptides assemble spontaneously to form ordered elongated structures. This phenomenon is an essential characteristic of life but is also at the heart of pathologies of many types, including Parkinson’s and Alzheimer’s diseases. To curtail amyloid assembly for medical purposes it is necessary to quantify the fundamental principles that control the way dispersed molecules assemble into these ordered structures. The fundamental challenge in establishing such an understanding in a rigorous manner is the disparate nature of the spatial and temporal scales involved, which range from the molecular to the organism scale. In this talk, I demonstrate how this challenge can be addressed by bringing the power of physical methods to amyloid aggregation to connect microscopic mechanisms with macroscopic observations of such phenomena. I discuss a unified theory of the kinetics of amyloid assembly and show how these results reveal simple rate laws that provide the basis for interpreting experimental data in terms of specific mechanisms controlling the proliferation of amyloid fibrils. I then demonstrate the power of this approach by presenting a full kinetic analysis of cytotoxic oligomer populations formed during the aggregation of the amyloid-β 1-42 (Aβ42) peptide of Alzheimer’s disease. Specifically, this analysis shows that Aβ42 oligomers are not able to undergo elongation processes to grow into fibrillar morphologies characteristic of mature amyloid fibrils, but that a rare structural transition exists which converts oligomers into growth-competent fibrils. Moreover, this strategy reveals that even through all mature amyloid fibrils originate as oligomers, the majority of oligomers dissociate into monomeric peptides before the conversion step has taken place. These results illuminate in molecular detail the mechanistic steps of amyloid formation, suggesting potential targets for intervention against neurodegenerative diseases.