I Convegno della Società Italiana di Fisica Statistica - SIFS

Out of equilibrium physics of strongly correlated quantum systems is a fascinating yet complex research topic. One−dimensional systems recently attracted a great deal of attention, due to their strongly interacting nature and to the fact that they sit at an extremely alluring sweet spot, at the intersection between the state−of−the−art experimental, numerical, and analytical techniques. Integrability has been at the centre of intense research, fuelled by its promise of delivering exact results far beyond any perturbative or numerical approach. A recent theoretical breakthrough proposed a hydrodynamic approach to nearly−integrable systems and it is a promising pathway in describing experiments.In this talk, I will introduce the basic hydrodynamic concepts and discuss their application to the 1 dimensional interacting Bose gas: in particular, I will discuss the integrability breaking effect of external trapping and the late−time thermalization.

Ref: A. Bastianello, A. De Luca, B. Doyon, J. De Nardis, Physical Review Letters 125 (24), 240604

The Fisher information divergences, imputable to the critical behaviour of many−body systems, are widely used in metrological scenarios as tools to achieve huge precision in the estimation of some parameters of interest. Moreover, the critical behaviour of many−body systems can improve also the compatibility in multi−parameter estimation schemes. This compatibility can be estimated introducing a scalar index, proportional to the ratio between the mean Uhlmann curvature and the Fisher information. It turns out that, thanks to the Fisher information’s divergences, the values of this index are affected by criticality. The systems analyzed, both related to the critical behaviour of Ising chains in a multi−parameter scenario, are: a XY Ising model that undergoes a continuum quantum phase transition and a 1−D Ising chain with transverse and longitudinal magnetic fields that undergoes a continuum quantum phase transition and a first order quantum phase transition. In both the situations the criticality plays a pivotal role in the behaviour of the compatibility index, revealing high compatibility regions in the phase diagram.

We address the study of the superradiant phase transition by resorting to a recently proposed entanglement measure [PRA 101, 042129 (2020)]. We show that the quantum phase transition that takes place in the Tavis−Cummings model is associated with an entanglement crossover that, for this reason, represents an order parameter for this quantum phase transition. Our study, clearly shows that the Tavis−Cummings model exhibits a true quantum phase transition at the finite size. Furthermore, we show such quantum phase/entanglement transition is persistent when the system size is increased.

Inspired by the idea that quantum computers can be useful in advancing basic science, we use a quantum processor to experimentally validate a number of theoretical results in non-equilibrium quantum thermodynamics, that were not (or were very little) corroborated so far. In order to do so, we first put forward a novel method to implement the so called two point measurement scheme, which is at the basis of the study of non-equilibrium energetic exchanges in quantum systems. Like the well-established interferometric method, our method uses an ancillary system, but at variance with it, it provides direct access to the energy exchange statistics, rather than its Fourier transform, thus being extremely more effective. We first experimentally validate our ancilla-assisted two point measurement scheme, and then apply it to i) experimentally verify that fluctuation theorems are robust against projective measurements, a theoretical prediction which was not validated so far, ii) experimentally verify the so called heat engine fluctuation relation, by implementing a SWAP quantum heat engine. iii) experimentally verify that the heat engine fluctuation relation continues to hold in presence of intermediate measurements, by implementing the design at the basis of the so called quantum-measurement-cooling concept. For both engines, we report the measured average heat and work exchanged and single out their operation mode. Our experiments constitute the experimental basis for the understanding of the non-equilibrium energetics of quantum computation and for the implementation of energy management devices on quantum processors.

Investigation of the geometric, and possibly also topological, characteristics of the potential energy landscape in configuration space capable of giving rise to a phase transition associated with spontaneous Z2−symmetry breaking in the canonical treatment [1]. The recurring feature in infinite−range systems is the presence of a double well with a gap proportional to the number of degrees of freedom (N) of the system [2]. This characteristic causes the formation of so−called 'dumbbell−shaped' equipotential surfaces under a certain critical potential which have been shown to be a necessary and sufficient condition to generate spontaneous Z2−symmetry breaking [3]. This feature was found in the Ising model [2], in the φ4 model [4] and in some other models solvable analytically built for this research specifically [5,6]. Currently, we are trying to extend these results to the most interesting case from the physical point of view of short−range potentials. In this framework, a Z2−symmetry breaking phase transition can also be defined without invoking the thermodynamic limit.

[1] F. Baroni, L. Casetti, Topological conditions for discrete symmetry breaking and phase transitions, J. Phys. A: Math. Gen. 39 529–545 (2006)
[2] F. Baroni, Symmetry breaking phase transitions in mean−field models triggered by double−well potentials. , Eur. Phys. J. B 93, 45 (2020)
[3] F. Baroni, Necessary and sufficient conditions for Z2−symmetry−breaking phase transitions J. Stat. Mech. (2020) 103202
[4] F. Baroni, Topology of configuration space of the mean−field φ4 model by Morse theory, Phys. Rev. E 100, 012124 (2019)
[5] F. Baroni, A simple topological model with continuous phase transition, J. Stat. Mech. P08010 (2011)
[6] F. Baroni, Models with symmetry−breaking phase transitions triggered by dumbbell−shaped equipotential surfaces, Phys. Rev. E 102, 012119 (2020)

Statistical mechanics is often the only approach to treat the dynamics of interacting many−body systems. Because of the difficulty in finding exact solutions, predicting and controlling the behavior of complex structures of interacting atoms is an interesting challenge, both from a theoretical and practical points of view. Additionally, the presence of many sources of errors, can make the dynamics even more unpredictable. We consider the internal dynamics of single atoms affected by errors in the control parameters, and we propose a method to exploit atom−atom interactions in order to compensate such errors [1]. Since the investigation of too many atoms would be analytically unfeasible due to the increasing complexity, we focus our studies on a couple of interacting atoms both driven by periodic fields. We show that, by properly choosing the interaction strength, it is possible to recover the original error−free dynamics of the atoms. In order to find the suitable interaction strength, we use a Fourier argument extracted from the time series of the atomic level populations. While two−level atoms can be treated analytically, we use numerical simulations to handle more complicated setups.

[1] M. Delvecchio, F. Petiziol, E. Arimondo and S. Wimberger, ”Atomic interactions for qubit−error compensations”, arXiv:2104.10928 (2021)

Soft matter systems are renowned for being able to display complex emerging phenomena such as clustering phases, even for some purely repulsive pair potentials models [Likos et al., Phys. Rev. E 63, 031206 (2001)]. Recently, a surprising quantum phase transition has been revealed in a one−dimensional (1D) system composed of bosons interacting via a pairwise soft potential in the continuum [Rossotti et al., Phys. Rev. Lett. 119, 21, 215301 (2017)]. It was shown that the spatial coordinates undergoing two−particle clustering could be mapped into quantum spin variables of a 1D transverse Ising model. In this work ([Mambretti et al., Phys. Rev. E 102, 042134 (2020)]) we investigate the manifestation of an analogous critical phenomenon in 1D classical fluids of soft particles in the continuum. In particular, we explored with stochastic simulation techniques the low–temperature behavior of three different classical models of 1D soft matter, whose inter–particle interactions allow for clustering. The same string variables highlight that, at the commensurate density for the two–particle cluster phase, the peculiar pairing of neighboring soft particles can be nontrivially mapped onto a 1D discrete classical Ising model. We also observe a related phenomenon, namely the presence of an anomalous peak in the low−temperature specific heat, thus indicating the emergence of Schottky phenomenology in a non−magnetic fluid.

A huge effort is currently devoted to understand the relaxation properties of isolated out−of−equilibrium quantum systems. In presence of integrability there is a growing theoretical consensus that the proper late time statistical description is encoded in a Generalized Gibbs Ensemble (GGE), which is built out of all the conserved observables. However, only a few experimental signatures of such behavior have been observed, and are mostly limited to Bose gases. In our work we propose a conceptually simple and realistic protocol to observe, through optical measurements, the effects of a GGE pre−thermalization in a one−dimensional (1D) fermionic system: we rigorously show that, by quenching a suitable local external potential in a 1D free Fermi gas, the post−quench system is characterized by a partially occupied bound state lying below a continuum of fully occupied states; such striking population inversion induces a negative peak in the absorption spectrum, i.e. a stimulated emission of radiation in a well defined frequency range. This result could thus pave the way to the observation of GGE fingerprints through optical measurements in fermionic systems.

xrRNAs are short viral RNAs endowed with unique properties: they can be unfolded by enzymes that copy them inside the infected cell, but they cannot be unfolded and degraded by enzymes deployed by the defense system of the cell. Here we report on a theoretical study based on modeling and simulations that unveils, for the first time, the physical bases of such sophisticated response of xrRNAs to different types of enzymes. We model the enzymatic processing of xrRNAs as a mechanical translocation of the molecule through a narrow pore (the enzymatic lumen) and use different translocation protocols based on constant, pulsed and linearly ramped forces. We use Bell−Evans theory and the waiting−times profiling to analyze how the secondary and tertiary elements modulate xrRNA's resistance to translocation. We thus show that the molecule has an outstanding directional resistance to translocation, which explains the different response to copying enzymes (that work xRNAs from the ”easy” end) and to degrading enzymes (that work xrRNAs from the ”difficult” end). These results provide a useful reference to interpret and design future theoretical and experimental studies of RNA translocation. Moreover, the uncovered mechanistic principle might be co−opted to design molecular meta−materials.

References:Nat Commun 11, 3749 (2020). https://doi.org/10.1038/s41467−020−17508−7J.
Phys. Chem. B 2021, 125, 4, 1098–1106 https://doi.org/10.1021/acs.jpcb.0c09966

Water plays a fundamental role in protein stability. However, the effect of the properties of water on the behaviour of proteins is only partially understood. Several theories have been proposed to give insight into the mechanisms of cold and pressure denaturation, or the limits of temperature and pressure above which no protein has a stable, functional state, or how unfolding and aggregation are related. Here we review our results based on a theoretical approach that can rationalise the water contribution to protein solutions' free energy. We show, using Monte Carlo simulations, how we can rationalise experimental data with our recent results. We discuss how our findings can help develop new strategies for the design of novel synthetic biopolymers or possible approaches for mitigating neurodegenerative pathologies.

[1] Bianco V, Franzese G. Contribution of Water to Pressure and Cold Denaturation of Proteins, Physical Review Letters 115, 108101 (2015).
[2] Bianco V, Franzese G, Dellago C, Coluzza I. Role of Water in the Selection of Stable Proteins at Ambient and Extreme Thermodynamic Conditions, Physical Review X 7, 021047 (2017).
[3] Bianco V, Franzese G, Coluzza I. Cover Feature: In Silico Evidence That Protein Unfolding is a Precursor of Protein Aggregation, ChemPhysChem 21 (5), pp 377−384 (2019).
[4] March D, Bianco V, Franzese G. Protein Unfolding and Aggregation near a Hydrophobic Interface, Polymers 13 (1), 156 (2021).
[5] Franzese G, àguila−Rojas J, Bianco V, Coluzza I. Water Contribution to the Protein Folding and its Relevance in Protein Design and Protein Aggregation. arXiv:2103.13093 (2021).
[6] We acknowledge the support of the Spanish Grant N. PGC2018−099277−B−C22 (MCIU/AEI/ERDF) and the support by ICREA Foundation (ICREA Academia prize).

The non−equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions under oscillatory shear flow are investigated by Brownian multi−particle collision dynamics. Two different scenarios will be considered: Filaments with both fixed ends [1] and wall−anchored chains [2].The results of the numerical studies will be presented and discussed.

1] A. Lamura, R. G. Winkler, 'Tethered semiflexible polymer under large amplitude oscillatory shear', Polymers 11, 737 (2019)
[2] A. Lamura, R. G. Winkler, G. Gompper, 'Wall−anchored semiflexible polymer under large oscillatory shear flow', pre−print (2021)

We study the dynamics of a dilute solution of rigid rodlike polymers in a viscous fluid at low Reynolds number by means of numerical simulations of a simple rheological model. We show that the rotational dynamics of polymers destabilizes the laminar flow and causes the emergence of a turbulent−like chaotic flow with a wide range of active scales.This regime displays an increased flow resistance, corresponding to a reduced mean flow at fixed external forcing, as well as an increased mixing efficiency. The latter effect is quantified by measuring the decay of the variance of a scalar field transported by the flow.By comparing the results of numerical simulations of the model in two and three dimensions, we show that the phenomena observed are qualitatively independent from the dimensionality of the space.

A common issue when analysing complex systems is that the interactions that characterise them often change in time. This can make it difficult to find optimal models that describe this evolution and can be estimated from data, particularly when the driving dynamics is unknown. In this work we offer a new perspective on the development of models for time−varying interactions introducing a generalisation of the Kinetic Ising Model (KIM), a minimalistic pairwise constant interactions model which has found applications in multiple disciplines. To do so we adopt the Score−Driven methodology, which is designed to keep arbitrary choices of dynamics at a minimum and to achieve information theoretical optimality. In this framework the model’s time−varying parameters are deterministic functions of the observations through the model’s log−likelihood function: this significantly reduces the computational complexity of the estimation and the exposure to misspecification errors, resulting in less stringent sample selection criteria. The flexibility of our approach allows to tailor the model to a wide range of applications: we show that the model can be employed to forecast stocks volatility at high−frequency, to separate the response to external drivers from endogenous interactions in trading strategies or neuron populations, and to generalise Temporal Exponential Random Graph Models (TERGM) for social networks analysis.

This is a joint work with Domenico Di Gangi (Scuola Normale Superiore, Pisa), Prof. Fabrizio Lillo (Scuola Normale Superiore, Pisa and University of Bologna) and Prof. Daniele Tantari (University of Bologna). Preprint available at https://arxiv.org/pdf/2007.15545.pdf

An Euclidean Random Assignment Problem (ERAP) is the study of the statistical properties of the ground state energy of assigning n points (blues) to n points (reds) randomly distributed on a d−dimensional domain \Omega depending on the choice of \Omega, on the law(s) of the random points of both colors, and on an energy−distance exponent p.ERAPs, which are notably difficult and comparatively little understood, have attracted much interest since they can provide a ”simple” model of finite−dimensional spin−glass (MÉzard−Parisi) and due to their connection with optimal transport in the calculus of variations (Monge−Kantorovich problem).A field−theoretical approach to ERAPs has been proposed by Caracciolo, Lucibello, Parisi and Sicuro (Phys. Rev. E 2014) in which, among other things, the asymptotic behavior for large n of the expected ground state energy E(n) can be understood under an appropriate ultraviolet regularization of the associated field theory.Remarkably, in two dimensions at p =2, where it was known that E(n) ~ c logn, the field−theoretical approach correctly predicted the leading coefficient c, a result which has been rigorously proven by Ambrosio, Stra and Trevisan (Probab. Theory Relat. Fields 2019).In this talk, I will present new results for two−dimensional ERAPs at p =2 contained in a recent paper in collaboration with Benedetto, Caglioti, Caracciolo, Sicuro and Sportiello (J. Stat. Phys. 2021). The main tool was the celebrated Weyl's law, in the sharp form due to Ivrii, relating the coefficients appearing in the spectral asymptotic expansion of the Laplace−Beltrami operator on \Omega to its volume |\Omega| (leading order) and to the measure of its border |\partial \Omega| (sub−leading order, if the domain has a border).I will also show how the results based on Weyl's law extend to three−dimensional ERAPs at p =2, following a work in preparation with Caracciolo, Sicuro and Sportiello.

We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural andsocial phenomena, depend on the temporal resolution used to dene individual bursts of activity. To thisend, we consider time series of microscopic events produced by a self−exciting Hawkes process, and leverage apercolation framework to study the formation of macroscopic bursts of activity as a function of the resolutionparameter. We nd that the very same process may result, when analyzed at dierent resolutions, in dierentdistributions of avalanche size and duration, which are understood in terms of the competition between theone−dimensional percolation and the branching process universality class. Pure regimes for the individualclasses are observed at specic values of the resolution parameter corresponding to the critical points of thepercolation diagram. A regime of crossover characterized by a mixture of the two universal behaviors isobserved in a wide region of the diagram. Such an hybrid scaling appears to be a likely outcome for ananalysis of the time series based on a reasonably chosen, but not precisely adjusted, value of the resolutionparameter. See D. Notarmuzi, C. Castellano, A. Flammini, D. Mazzilli, F. Radicchi, Phys. Rev. E 103,L020302

Alessio Perinelli 1, Veronica Mazza 1, Michele Castelluzzo 2, Leonardo Ricci 1,2
1. CIMeC, Center for Mind/Brain Sciences, University of Trento, 38068 Rovereto, Italy
2. Department of Physics, University of Trento, 38123 Trento, Italy


Identifying and characterizing network structures by relying on experimentally observed time series is a task that can be tackled through different solutions, like entropy-based techniques or evaluation of suitable correlation estimators. We present a method that allows to assess the connectivity strength of a link in terms of a "time scale of its observability" [1] and discuss recent developments. The time scale corresponds to the minimum width of a time window required to observe a significant cross-correlation between sequence pairs, where significance is evaluated by relying on the generation of surrogate time series. The method has been successfully applied to different experimental contexts: as major examples we discuss human brain electrophysiological recordings [2]. Finally, we also show that the time-scale of observability is related, though not completely equivalent, to mutual information: the combined use of the two metrics provides an additional insight into the identification and characterization of connectivity in complex networks.

[1] A. Perinelli, D. E. Chiari, and L. Ricci, "Correlation in brain networks at different time scale resolution", Chaos 28, 063127 (2018).
[2] A. Perinelli, D. Tabarelli, C. Miniussi, and L. Ricci, "Dependence of connectivity on geometric distance in brain networks", Sci. Rep. 9, 13412 (2019), and M. Castelluzzo, A. Perinelli, D. Tabarelli, and L. Ricci, "Dependence of Connectivity on the Logarithm of Geometric Distance in Brain Networks", Front. Physiol. 11, 611125 (2021).

At the intersection between statistical physics and social science, the aim of this presentation is that of illustrating a novel approach to study, in a fully data−driven fashion, the socio−semantic interactions between Twitter users within a specific discussion. Our approach is based on the constrained maximization of Shannon entropy, a well−known unbiased procedure that makes our method applicable to any Twitter discussion regardless of the users' nationality, topic and language.On the social side, our method infers the presence of communities of Twitter users from the online activity of those users who share the same contents. First, we employ the Bipartite Configuration Model (BiCM) as a benchmark to obtain a statistically−validated monopartite projection of the empirical bipartite user−hashtag network; second, we run a community detection algorithm on this projection to detect the presence of clusters of users. Hence, the first core result of our analysis is the operational definition of ”discursive communities” which are groups of Twitter users who share a significantly−similar retweeting pattern.Remarkably, the discursive communities recovered with our method display a coherent picture of their users behavior, in terms of retweeting and mentioning activities; besides, these communities are consistent with the offline political coalitions and sensitive to the dynamics characterizing the relationships within and between these coalitions.On the semantic side, a core result of our analysis concerns the study of the mechanisms that shape the Twitter discussion characterizing each of the aforementioned discursive communities. By monitoring, on both a daily and a monthly basis, the structural evolution of each community−specific semantic network, the users in each community are observed to be characterized by a significantly different online behavior, thus inducing semantic networks with diverse topological structures. Particularly insightful is the analysis of the semantic networks at the mesoscale: what emerges is the presence of a core−periphery structure, i.e. a densely−connected bulk surrounded by a periphery of loosely inter−connected hashtags.

Collision avoidance is a common goal in collective behaviors of animals and robots. We consider a system of active Brownian particles in two dimensions and we frame this objective as an optimization problem with a tradeoff between avoiding collisions and minimizing control costs. We employ optimal control theory and a mean−field game approach to derive an analytic solution which displays a critical behavior with a second order discontinuity in the alignment order parameter. Remarkably, we find that a mean−field version of a standard Vicsek−like model for collective motion performs remarkably close to the optimal control. Our results offer a theoretical ground for the use of simple biomimetic algorithms for artificial agents.

Enhanced diffusion and anti-chemotaxis of enzymes have been reported in several experiments in the last decade, opening up entirely new avenues of research in the bio-nanosciences both at the applied and fundamental level. Here, we introduce a novel theoretical framework, rooted in non-equilibrium effects characteristic of catalytic cycles, that explains all observations made so far in this field. In addition, our theory predicts entirely novel effects, such as dissipation-induced switch between anti-chemotactic and chemotactic behavior.

The current understanding of aging phenomena is mainly confined to systems with short−ranged interactions. Little is known about the aging of long−ranged systems. Here we present first results of Monte Carlo simulations for the aging in the phase−ordering kinetics of the d =2 dimensional Ising model with power−law long−range interactions ∝r^(−d+σ) . The dynamical scaling of the two−time spin−spin autocorrelator is shown to be well described by simple aging for all interaction ranges studied. The autocorrelation exponents are consistent with λ =1.25 in the effectively short−range regime with σ>1, while for stronger long−range interactions with σ<1 the data are consistent with λ =d/2 =1. For very long−ranged interactions, strong finite−size effects are observed. We discuss whether such finite−size effects could be misinterpreted phenomenologically as sub−aging.

[1] H. Christiansen, S. Majumder, M. Henkel, and W. Janke, {\em Aging in the Long−Range Ising Model\/}, Phys. Rev. Lett. {\bf 125}, 180601−1−−7 (2020).

In the past decades considerable efforts have been made in order to understand the critical features of long−range interacting models, i.e. those where the couplings decay algebraically as r^(−d−σ) with σ>0, d being the dimension of the system. According to the well−established Sak's criterion for O(N) models, the short−range critical behavior survives up to a given σ* ≤ 2. However, the applicability of this picture to describe the the two dimensional classical XY model is complicated by the the presence, in the short−range regime, of a line of RG fixed points, which gives rise to the celebrated Berezinskii − Kosterlitz − Thouless (BKT) phenomenology. Our first argument, based on Self−Consistent−Harmonic−Approximation, suggests that that the BKT transition survives for σ < 2. This is confirmed by our more recent field−theoretical analysis. In particular we find there is not a specific, temperature−independent, value of σ*: while for σ < 7/4 the BKT fixed line vanishes and we have an order−disorder transition, for 7/4 < σ < 2 we have the coexistence of a low−temperature broken phase and an intermediate quasi−ordered one. In this regime we were able to full characterize the critical properties of this new transition.

Resetting of stochastic processes is currently a very active research topic, because of its relevance in a variety of phenomena, both natural and artificial, ranging from biology to chemistry to computer science. In this context, local resetting is a novel paradigm, basically dealing with interacting particle systems, where different particles undergo resetting independently of one another. Such a case is thought to be more challenging than its global counterpart, due to the absence of the unifying framework provided by renewal theory. Here we investigate the (nonequilibrium) steady state of simple exclusion processes with local resetting, on a one−dimensional lattice with either periodic or open boundary conditions, using mean−field approximations and kinetic Monte Carlo simulations. In all cases, in the thermodynamic limit we observe different regimes, depending on how the resetting rate scales with the system size. Moreover, the totally asymmetric version of the model exhibits a considerably rich behaviour, with a number of different phases, including coexistence regions characterized by stable domain walls. Interestingly, the mean field theory turns out to provide extremely accurate predictions for both density profiles and phase diagrams.

Lasing in 1D arrays of resonators or polariton wires provides an example of an out−of−equilibrium quasi−condensate. We will discuss the spatio−temporal coherence properties of these systems by highlighting the interplay between Kardar−Parisi−Zhang (KPZ) universality and Bogoliubov−Schawlow−Townes phase diffusion.In particular, the lack of long−range order determines an important broadening of the linewidth of the emission spectrum, with exponents related to KPZ. As an application we will discuss edge emission from 2D topological lasers, where, remarkably, disorder can enhance the temporal coherence.

[1] I Amelio, I Carusotto, Physical Review X 10 (4), 041060
[2] I Amelio, A Chiocchetta, I Carusotto, in preparation

In the context of long Josephson junctions, which are usually described in terms of the perturbed sine−Gordon equation, there exists a particularly elusive solitonic excitation, known as breather, whose experimental observation has yet to be achieved. We propose, together with appropriate detection techniques, the use of magnetic pulses at the edge of the junction for the generation of single breathers by means of the nonlinear supratransmission effect. Our theoretical/computational analysis, based on a model which includes a dissipative term and an external current source, shows the effectiveness of the approach both in a deterministic regime and in the presence of a random perturbation. We further investigate the dynamics of the induced breathers by studying how their radiative decay process is influenced by thermal fluctuations.

A basic and ubiquitous phenomenon in nonequilibrium dynamics of isolated quantum many-body systems is thermalization. This is commonly described as the ability of a system to act as an effective thermal bath for its local subsystems. Understanding the microscopic mechanism of quantum thermalization, and above all of its failures, is currently the subject of intensive theoretical and experimental investigations. Here, I will introduce an approach to study quantum many-body dynamics, inspired by the Feynman-Vernon influence functional theory of quantum baths. Its central object is the influence matrix (IM), which describes the effect of a Floquet many-body system on the evolution of its local subsystems. For translationally invariant one-dimensional systems, the IM obeys a self-consistency equation. For certain fine-tuned models, remarkably simple exact solutions appear, which physically represent perfect dephasers (PD), i.e., many-body systems acting as perfectly Markovian baths on their parts. Such PDs include certain solvable quantum circuits discovered and investigated in recent works. In the vicinity of PD points, the system is not perfectly Markovian, but rather acts as a quantum bath with a short memory time. In this case, we demonstrate that the self-consistency equation can be solved using matrix-product states (MPS) methods, as the IM temporal entanglement is low. The underlying “principle of efficiency” of quantum dynamics computations is complementary to that of standard methods, as it only relies on short-range temporal correlations. Using a combination of analytical insights and MPS computations, we characterize the structure of the IM in terms of an effective "statistical-mechanics" description for local quantum trajectories and illustrate its predictive power by analytically computing the relaxation rate of an impurity embedded in the system. In the last part, I will describe how to extend these ideas to study the many-body localized (MBL) phase of strongly disordered periodically kicked interacting spin chains. This approach allows to study exact disorder-averaged time evolution in the thermodynamic limit. MBL systems fail to act as efficient baths, and this property is encoded in their IM. I will discuss the structure of an MBL IM and link it to the onset of temporal long-range order.

Based on:
[1] Influence matrix approach to many-body Floquet dynamics arXiv:2009.10105 (2020) Phys. Rev. X 11, 021040
[2] Characterizing many-body localization via exact disorder-averaged quantum noise arXiv:2012.00777 (2020)
[3] Influence functional of many-body systems: temporal entanglement and matrix-product state representation arXiv:2103.13741 (2021) (to appear in Annals of Physics)
[4] Scaling of temporal entanglement in proximity to integrability arXiv:2104.07607 (2021)

The realization of effective Hamiltonians featuring many-body interactions beyond pairwise coupling would enable the quantum simulation of central models underpinning topological physics and quantum computation. We overcome crucial limitations of perturbative Floquet engineering in periodically-driven quantum systems and discuss the accurate realization of purely three-body Hamiltonians implementable, e.g., in superconducting circuits and molecular nanomagnets.

Ref.: Phys. Rev. Lett. 126, 250504 (2021).

The Discrete Non−Linear Schrodinger (DNLS) model is well known to display a high energy−density phase in which the equivalence between statistical ensambles is not valid. In this phase, the charge accumulates on few sites and resides there for times that diverge quickly in the thermodynamic limit. As a consequence, in such regime the dynamics of the system shows breaking of ergodicity. In this talk I will argue that such localization mechanism can be attributed, in a mean−field scenario, to some geometric properties of the microcanonical potential energy surface, that we characterize using Morse theory. Moreover, I will also show that this localization transition coincides with a phase transition in the lowest eigenvalue of the Laplacian on said surface, once the Hamiltonian motion is substituted with a Brownian motion.

The spatial organization of chromosomes has key functional roles, as it controls for instance gene regulation. Yet, the molecular mechanisms underlying chromosome folding remain poorly understood. Here, we employ models of interacting polymers from Statistical Mechanics, combined with machine learning strategies, to understand the fundamental physical principles of chromosome organization. Our approach, validated against diverse, independent experiments, predicts the 3D structure of specific DNA regions at the single−molecule level and also the effects of pathogenic mutations on chromosome folding [1−4].

[1] Conte et al. Nature Communications (2020)
[2] Kubo et al. Nature Structural & Molecular Biology (2021)
[3] Bianco et al. Nature Genetics (2018)
[4] Fiorillo, Musella, Conte et al. Nature Methods (2021, in press)

Water transport through plants is a key driver of the carbon and other biogeochemical cycles and is a crucial link in plant adaptation to climate and vegetation response to climate change. Plants lift water from their roots to their leaves through narrow conduits, called xylems. Some models predict that conduits should be of uniform diameter, while others predict that they should widen tip to base following power−laws. However, there is no agreement on the exact power−law exponents and on the use of some untested assumptions, such as the xylems’ branching or the Da Vinci’s rule making difficult to identify the biological causes of the predictions that previous models make. In this talk/poster, I present a general theory which invokes the trade−off between two opposing and essential evolutionary drivers: selection minimizing fluid dynamic resistance R, while at the same time minimizing the rate of tip−to−base conduit widening W. Using Pareto optimization, we derived an exact closed−form solution of a universal tip−to−base conduit widening profile. The analytical solution optimizes the competing requirements of minimizing transport resistance, carbon cost, and embolism risk. The prediction of the xylems’ universal profile is in excellent accord with empirical data we collected across terrestrial plant orders, life forms, and habitats.

We present a prediction of the building blocks of protein structures with no chemistry and no adjustable parameters. Our predictions arise from one constructive hypothesis that the dominant folding mechanism of a protein is the drive to maximize its self-interaction, thereby attaining a space-filling folded state. Our results are in good accord with experimental data on more than four thousand protein structures and they underscore the consilience in the fit of chemistry and biology to the dictates of mathematics and physics. Our work has consequences for the energy landscape of proteins and the role of evolution in shaping sequences and functionalities.

References:
[1] T. Škrbić, A. Maritan, A. Giacometti, G. D. Rose and J. R. Banavar, Phys. Rev. E (2021) – in press.
[2] T. Škrbić, A. Maritan, A. Giacometti, G. D. Rose and J. R. Banavar, bioRxiv (2021), doi: https://doi.org/10.1101/2020.11.10.375105

We perform numerical simulations of dense granular packings confined in a quasi 2D geometry with a vertically shaken bottom wall. For low driving, the system is stuck in an almost fixed spatial configuration where the particles vibrate around their positions. This configuration can be ordered (with eventually defects) or disordered depending on polydispersity and size ratios. In presence of periodic boundary conditions in the horizontal direction the system exhibits a coordinated translation along it. Such a mode involves the entire system and is characterized by a constant velocity of the center of mass that persists for very long times. We also found that sudden changes of direction and/or magnitude of this collective drift can be triggered by small deformations in the contact network.Moreover, for packings that are arranged in symmetric structures with respect the vertical axis, no net direction of motion is observed. We understand our results as a frictional ratchet effect induced by asymmetries in the contact network.We also show how these results explains the mechanism underlying the emergence of coordinated motion in previous experimental and numerical studies.

The World Trade Web (WTW) is the network `induced' by the trade relationships between world countries − respectively, the links and the nodes of such a configuration. Despite its popularity among researchers − coming from disciplines as different as economics, network science, social sciences, etc. − characterizing the WTW via a simple, yet accurate, model is still an open issue. While the the traditional Gravity Model (GM) successfully reproduces the volume of trade between any two connected countries via macroeconomic properties such as their GDP, their geographic distance, etc. it also predicts a fully−connected network, thus failing to reproduce the heterogeneous WTW structure. To overcome this problem and successfully reproduce the complex topology of the WTW, two different classes of models can be employed: on the one hand, ”econometric models” `dress' the traditional GM by interpreting it as the expected value of a probability distribution whose functional form can be arbitrarily chosen; on the other, ”maximum entropy network models” `constrain' the purely topological properties of the WTW in order to derive the maximally unbiased probability distribution compatible with them.Here, we compare these two approaches and inspect their accuracy in reproducing both the topological and the weighted properties of the WTW.As our analysis clearly points out, entropy−based models achieve a better performance than purely econometric ones, suggesting maximum entropy as a viable econometric framework wherein extensive margins (i.e. the presence of trade relationships) and intensive margins (i.e. the corresponding trade volumes) can be separately controlled by carefully combining topological constraints and dyadic macroeconomic variables.

Isolation of symptomatic individuals and tracing of their contacts are fundamental strategies for the control of epidemic spreading. Recently two protocols for contact tracing (CT) have been proposed: a manual (interview-based) CT and a digital (app-based) CT. The containment effects of the CT protocols can be modelled by an epidemic process describing the spread of SARS-CoV-2 upon an adaptive temporal network. The model features a phase transition between an absorbing and an active phase: within the empirically validated framework of activity-driven networks, a closed relation for the epidemic threshold can be obtained estimating the effectiveness of CT. Manual CT robustly performs better than digital CT, due to the stochastic annealed nature of manual CT, in which each node randomly recalls a fraction of its contacts, in contrast with the quenched nature of digital CT, where traced nodes belong deterministically to the fraction of individuals adopting the app. The better performance of manual CT is enhanced by heterogeneity in agent activity, i.e. by the presence of superspreaders. Moreover, heterogeneity and the intrinsic difference in contacts exploration make the manual procedure dominant also in hybrid contact tracing protocols [1].

[1] M. Mancastroppa, C. Castellano, A. Vezzani and R. Burioni, "Stochastic sampling effects favor manual over digital contact tracing", Nature Communications 12, 1919 (2021)

The maximum entropy principle (MEP) is a powerful statistical inference tool that provides a rigorous way to guess the probability distribution of the states of a system which is known only through partial information. Generalizing the Shore and Johnson's axioms, Jos Uffink (1995) proved that the functionals which are suitable to be used in the MEP belong to a one−parameter family, which the Shannon entropy is a member of.The resulting probability distributions are generalized exponentials, of which Boltzmann distribution is a special case.It has been discussed (P. Jizba and J. Korbel, 2019) that this generalized approach is suitable to study systems which do not respect standard hypothesis such as ergodicity, short−range interactions or exponential growth of the sample space: the resulting probability distributions take into account correlations that may not have been observed. In this presentation, the maximum likelihood method to evaluate the parameters of such distributions and to perform model selection starting from empirical data will be discussed.In particular, it will be shown that the maximum likelihood approach to estimate the Lagrange multipliers leads to an equation that justifies the use of the q−generalized momenta as constraints in the entropy maximization. Lastly, simple examples based on synthetic data will be presented in order to show that this approach provides accurate estimations of the parameters.

I will present our latest results on the response to perturbations of the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non−equilibrium conditions. The coupling among subsystems creates a memory effect that renormalises the microscopic susceptibility into a macroscopic quantity that takes into account the intricate microscopic structure of the total system.We show the occurrence of a class of transitions specifically due to system−to−system interactions. Such (phase) transitions exist in the thermodynamic limit and are associated with the divergence of the linear response but are not accompanied by the divergence in the integrated autocorrelation time for a suitably defined observable. Such endogenous phase transitions are fundamentally different from other pathologies in the linear response that can be framed in the context of critical transitions. We will show our results through numerical investigation of the Desai–Zwanzig model and of the Bonilla–Casado–Morillo model, which feature paradigmatic equilibrium and non−equilibrium phase transitions, respectively. In particular, by investigating the linear response of a system composed of a finite number of agents, we are able to probe the emergence in the thermodynamic limit of a singular behaviour of the susceptibility. We find clear evidence of the loss of analyticity due to a pole crossing the real axis of frequencies, signifying the occurrence of a phase transition in the system.

We study the applicability of tools developed by the computer vision community for feature learning and semantic image inpainting to perform data reconstruction of fluid turbulence configurations. The aim is twofold. First, we explore on a quantitative basis, the capability of Convolutional Neural Networks embedded in a Deep Generative Adversarial Model (Deep−GAN) to generate missing data in turbulence, a paradigmatic high dimensional chaotic system. In particular, we investigate their use in reconstructing two−dimensional damaged snapshots extracted from a large database of numerical configurations of 3d turbulencein the presence of rotation, a case with multi−scale random features where both large−scale organised structures and small−scale highly intermittent and non−Gaussian fluctuations are present. Second, following a reverse engineering approach, we aim to rank the input flow properties (features) in terms of their qualitative and quantitative importance to obtain a better set of reconstructed fields. We present two approaches both based on Context Encoders. The first one infers the missing data via a minimization of the L2 pixel−wise reconstruction loss, plus a small adversarial penalisation. The second, searches for the closest encoding of the corrupted flow configuration from a previously trained generator. Finally, we present a comparison with different data assimilation tools, either based on Nudging, an equation−informed unbiased protocol, well known in the numerical weather prediction community or on Gappy POD, developed in the context of image reconstruction. Details on how to download the TURB−Rot database, http://smart−turb.roma2.infn.it, of roughly 300K 2d turbulent images are given.

Memristors are interesting and promising nanoscale components, with applications ranging from novel computing hardware to machine learning. However, the dynamics of connected memristors is interesting on its own. We discuss recent advances on the subject, with a preferential view towards an analytical analysis.

I will describe a theory of bounded critical phenomena based on a geometric approach, introduced in the article arXiv:1904.08919: a curved metric, conformal to the euclidean one, is added to a bounded domain, with the requirement of constant curvature, to enforce homogeneity.This leads to the so−called Yamabe equation, which is then modified, with the introduction of a fractional Laplacian, to account for the anomalous dimension of the fields. Solving this equation provides a point−dependent scale for the system, which can be used to determine one−point and two−point spin correlations functions.After reviewing results for the XY model, we compare the Yamabe predictions with numerical simulations of continuum percolation in three dimensions, and we present a high−precision estimate of its anomalous dimension η.

Overcoming the detrimental effect of disorder at the nanoscale is very hard since disorder induces localization and an exponential suppression of transport efficiency. Here we unveil novel and robust quantum transport regimes achievable in nanosystems by exploiting long−range hopping. We demonstrate that in a 1D disordered nanostructure in the presence of long−range hopping, transport efficiency, after decreasing exponentially with disorder at first, is then enhanced by disorder [disorder−enhanced transport (DET) regime] until, counterintuitively, it reaches a disorder−independent transport (DIT) regime, persisting over several orders of disorder magnitude in realistic systems. To enlighten the relevance of our results, we demonstrate that an ensemble of emitters in a cavity can be described by an effective long−range Hamiltonian. The specific case of a disordered molecular wire placed in an optical cavity is discussed, showing that the DIT and DET regimes can be reached with state−of−the−art experimental setups.

Network reconstruction is an active field of research within the broader field of complex networks. Some of the methods proposed so far assume that the binary and the weighted constraints jointly determine the reconstruction output; others, instead, consider the estimation of topology and that of weights as completely unrelated. Amidst the former ones, the Enhanced Configuration Model (ECM) deserves a special mention; examples of algorithms belonging to the second group are those iteratively adjusting the link weights a posteriori, on top of some previously−determined topological structure.Here we extend the Exponential Random Graph framework, by proposing an analytical procedure to estimate the weighted structure of a network, once its topology has been determined. In our approach, information about the topological structure is treated as prior information; together with the proper weighted constraints, it represents the input of our generalized reconstruction procedure. The probability distribution describing link weights is, then, determined by maximizing the conditional Shannon entropy under a properly−defined set of constraints. Our algorithm returns a conditional probability distribution depending on a vector of unknown parameters whose estimation is carried out by considering a generalized likelihood function. As an application, we explore and compare the reconstruction accuracy of two possible specifications of our framework.The knowledge of the structure of a financial network gives valuable information for estimating the systemic risk. However, since financial data are typically subject to confidentiality, network reconstruction techniques become necessary to infer both the presence of connections and their intensity. Recently, several ”horse races” have been conducted to compare the performance of these methods. Our novel framework allows us to establish a generalised likelihood approach to rigorously compare them: as our results indicate, the best method is obtained by ”dressing” the best−performing, available binary method with an exponential distribution of weights.