arXiv subjects

Antonio Politi

Publications and source records attributed to Antonio Politi.

At least 19 recordsLinked to original sources

arXiv2026

Multiplicity of Stable Attractors in Disordered Neural Models

We show how large-deviation statistics allows one to obtain reliable estimates of the multiplicity of stable fixed-points in a model of neural ordinary differential equations previously employed in computational tasks. The result is obtained by developing a suitable perturbative method in the amplitude of the disorder. It turns out that for not-too-large coupling strengths there are no qualitative differences between the symmetric case, when the dynamics is a purely gradient evolution, and the asymmetric case, when limit cycles and chaos can, in principle, arise. The selection of this specific model is dictated by pedagogical reasons, but we are confident that the approach can be extended to other many-degree-of-freedom dynamical models characterized by different classes of random coupling matrices.

cond-mat.dis-nn↗

arXiv2026

A mean field approach to multiple, long-delayed systems

The concept of multiple, long-delayed feedback systems is introduced and discussed with reference to a paradigmatic model. We analyse how the resulting chaotic dynamics is affected by the delay distribution. Via a mean-field approach, we show that a spatio-temporal representation equivalent to the one developed for the single-delay can be extended to this wider class of dynamical systems. Numerical simulations are complemented by a theoretical study based on a multiple-scale analysis, which, in the vicinity of a Hopf bifurcation, allows mapping the initial model onto a complex Ginzburg Landau equation. As a result, we find that the only relevant feature influenced by the multiple delays is the size of the coherent spatio-temporal structures which, in turn, depends exclusively on a generalized {\it variance} of the delay distribution.

nlin.CD↗

arXiv2026

Mean-field theory of the DNLS equation at positive and negative absolute temperatures

The Discrete Non Linear Schrödinger (DNLS) model, due to the existence of two conserved quantities, displays an equilibrium transition between a homogeneous phase at positive absolute temperature and a localized phase at negative absolute temperature. Here, we provide a mean-field theory of DNLS through a suitable approximation of the grandcanonical partition function which makes it factorizable and can be used to describe the equilibrium state at positive temperatures as well as the metastable state at negative temperatures. By comparing our mean-field results with numerically exact ones, we show that this approximation is good-to-excellent in the whole grandcanonical phase diagram. Explicit approximate expressions for equilibrium observables are provided in the high-temperature limit. Our theory represents a clear advancement over the model that neglects the interaction between sites.

cond-mat.stat-mech↗

arXiv2026

Anomalous transport in the Fermi-Pasta-Ulam-Tsingou model: a review and open problems

This review provides an up-to-date account of energy transport in Fermi-Pasta-Ulam-Tsingou (FPUT) chains, a key testbed for nonequilibrium statistical physics. We discuss the transition from the historical puzzle of thermalization to the discovery of anomalous heat transport, where the effective thermal conductivity $κ$ diverges with system size $L$ as $κ\propto L^δ$. The article clarifies the distinction between two universality classes: the FPUT-$αβ$ model, characterized by $δ= 1/3$ and linked to Kardar-Parisi-Zhang (KPZ) physics, and the symmetric FPUT-$β$ model, where numerical and theoretical evidence support $δ= 2/5$. We investigate how finite-size effects - unavoidably induced by the thermostatting protocols - can disguise the asymptotic scaling. Additionally, we analyze the role of conservative noise in preserving hydrodynamic properties and examine how proximity to integrable limits leads to long-lived quasi-particles and, thereby, to diffusive regimes over intermediate spatial scales.

cond-mat.stat-mech↗

arXiv2026

Numerical analysis of heat transport in classical one-dimensional systems

Numerical studies of some unidimensional systems suggest that Fourier law is satisfied, where theory predicts a divergence of heat conductivity with the system size. Here, I revisit some such models, finding that in all cases a divergence asymptotically emerges. This includes a variant of the ding-a-ling model, where I find that, contrary to previous claims, the ``anomalous" growth starts already for moderate system sizes. More conceptually interesting is the case of non-binding potentials, whose behavior is well reproduced by assuming that the energy flux across the nonequilibrium stationary state is the sum of two contributions: a diffusive and a hydrodynamic one. This approach, which extends an idea previously formulated for nearly integrable systems, allows to conclude that the asymptotic regime is always dominated by the anomalous hydrodynamic component, but the crossover may occur for extremely long system sizes.

cond-mat.stat-mech↗

arXiv2025

Infinite-temperature thermostats by energy localization in a nonequilibrium setup

Some lattice models having two conservation laws may display an equilibrium phase transition from a homogeneous (positive temperature - PT) to a condensed (negative temperature) phase, where a finite fraction of the energy is localized in a few sites. We study one such stochastic model in an out-of-equilibrium setup, where the ends of the lattice chain are attached to two PT baths. We show that localized peaks may spontaneously emerge, acting as infinite-temperature heat baths. The number $N_b$ of peaks is expected to grow in time $t$ as $N_b \sim \sqrt{\ln t}$, as a consequence of an effective freezing of the dynamics. Asymptotically, the chain spontaneously subdivides into three intervals: the two external ones lying inside the PT region; the middle one characterized by peaks superposed to a background lying along the infinite-temperature line. In the thermodynamic limit, the Onsager formalism allows determining the shape of the whole profile.

cond-mat.stat-mech↗

arXiv2025

Crisis in time-dependent dynamical systems

Many dynamical systems operate in a fluctuating environment. However, even in low-dimensional setups, transitions and bifurcations have not yet been fully understood. In this Letter we focus on crises, a sudden flooding of the phase space due to the crossing of the boundary of the basin of attraction. We find that crises occur also in non-autonomous systems although the underlying mechanism is more complex. We show that in the vicinity of the transition, the escape probability scales as $\exp[-α(\ln δ)^2]$, where $δ$ is the distance from the critical point, while $α$ is a model-dependent parameter. This prediction is tested and verified in a few different systems, including the Kuramoto model with inertia, where the crisis controls the loss of stability of a chimera state.

nlin.AO↗

arXiv2025

Effective grand-canonical description of condensation in negative-temperature regimes

The observation of negative-temperature states in the localized phase of the Discrete Nonlinear Schrödinger (DNLS) equation has challenged statistical mechanics for a long time. For isolated systems, they can emerge as stationary extended states through a large-deviation mechanism occurring for finite sizes, while they are formally unstable in grand-canonical setups, being associated to an unlimited growth of the condensed fraction. Here, we show that negative-temperature states in open setups are metastable and their lifetime $τ$ is exponentially long with the temperature, $τ\approx \exp(λ|T|)$ (for $T<0$). A general expression for $λ$ is obtained in the case of a simplified stochastic model of non-interacting particles. In the DNLS model, the presence of an adiabatic invariant, makes $λ$ even larger because of the resulting freezing of the breather dynamics. This mechanism, based on the existence of two conservation laws, provides a new perspective over the statistical description of condensation processes.

cond-mat.stat-mech↗

arXiv2024

Chaotic synchronization in adaptive networks of pulse-coupled oscillators

Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a robust irregular macroscopic dynamics. The resulting, strongly synchronized, regime is sustained by a homeostatic mechanism induced by the shape of the phase-response curve combined with adaptive coupling strength, included to account for energy dissipated by the pulse emission. The proposed setup mimicks a neural network composed of excitatory and inhibitory neurons.

cond-mat.dis-nn↗

arXiv2024

A robust balancing mechanism for spiking neural networks

Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works also in absence of strong external currents. Biologically, the mechanism exploits the plasticity of excitatory-excitatory synapses induced by short-term depression. Mathematically, the nonlinear response of the synaptic activity is the key ingredient responsible for the emergence of a stable balanced regime. Our claim is supported by a simple self-consistent analysis accompanied by extensive simulations performed for increasing network sizes. The observed regime is essentially fluctuation driven and characterized by highly irregular spiking dynamics of all neurons.

cond-mat.dis-nn↗

arXiv2023

Ultra-slow dynamics of free-running ring lasers: towards a minimal model

The dynamics of a resonant, free-running ring laser, in the common case of a fast relaxation of the atomic polarization, is unexpectedly highly singular. As shown in [Phys. Rev. Research, {\bf 5}, 023059 (2023)], this is due to the closeness to a pure Hamiltonian dynamics ruled by a nonlinear wave equation, herein named Klein-Gordon-Toda model. In this paper, we derive a quasi-Hamiltonian model which allows describing realistic systems. In particular, we identify two nearly conserved, energy-like quantities, which ``naturally" exhibit an ultra-slow dynamics confirmed and highlighted by numerical simulations. A minimal version of the quasi-Hamiltonian model is finally derived, which does not only reproduce the laser thresholds, but also helps understanding the origin of the nearly integrable character of the laser dynamics.

physics.optics↗

arXiv2023

Onsager coefficients in a coupled-transport model displaying a condensation transition

We study nonequilibrium steady states of a one-dimensional stochastic model, originally introduced as an approximation of the Discrete Nonlinear Schrödinger equation. This model is characterized by two conserved quantities, namely mass and energy; it displays a ``normal", homogeneous phase, separated by a condensed (negative-temperature) phase, where a macroscopic fraction of energy is localized on a single lattice site. When steadily maintained out of equilibrium by external reservoirs, the system exhibits coupled transport herein studied within the framework of linear response theory. We find that the Onsager coefficients satisfy an exact scaling relationship, which allows reducing their dependence on the thermodynamic variables to that on the energy density for unitary mass density. We also determine the structure of the nonequilibrium steady states in proximity of the critical line, proving the existence of paths which partially enter the condensed region. This phenomenon is a consequence of the Joule effect: the temperature increase induced by the mass current is so strong as to drive the system to negative temperatures. Finally, since the model attains a diverging temperature at finite energy, in such a limit the energy-mass conversion efficiency reaches the ideal Carnot value.

cond-mat.stat-mech↗

arXiv2023

Nearly Hamiltonian dynamics of laser systems

The Arecchi-Bonifacio (or Maxwell-Bloch) model is the benchmark for the description of active optical media. However, in the presence of a fast relaxation of the atomic polarization, its implementation is a challenging task even in the simple ring-laser configuration, due to the presence of multiple time scales. In this Article we show that the dynamics is nearly Hamiltonian over time scales much longer than those of the cavity losses. More precisely, we prove that it can be represented as a pseudo spatio-temporal pattern generated by a nonlinear wave equation equipped with a Toda potential. The existence of two constants of motion (identified as pseudo energies), thereby, elucidates the reason why it is so hard to simplify the original model: the adiabatic elimination of the polarization must be accurate enough to describe the dynamics correctly over unexpectedly long time scales. Finally, since the nonlinear wave equation with Toda potential can be simulated on much longer times than the previous models, this opens up the route to the numerical (and theoretical) investigation of realistic setups.

physics.optics↗

arXiv2022

Frozen dynamics of a breather induced by an adiabatic invariant

The Discrete Nonlinear Schrödinger (DNLS) equation is a Hamiltonian model displaying an extremely slow relaxation process when discrete breathers appear in the system. In [Iubini S, Chirondojan L, Oppo G L, Politi A and Politi P 2019 Physical Review Letters 122 084102], it was conjectured that the frozen dynamics of tall breathers is due to the existence of an adiabatic invariant (AI). Here, we prove the conjecture in the simplified context of a unidirectional DNLS equation, where the breather is "forced" by a background unaffected by the breather itself. We first clarify that the nonlinearity of the breather dynamics and the deterministic nature of the forcing term are both necessary ingredients for the existence of a frozen dynamics. We then derive perturbative expressions of the AI by implementing a canonical perturbation theory and via a more phenomenological approach based on the estimate of the energy flux. The resulting accurate identification of the AI allows revealing the presence and role of sudden jumps as the main breather destabilization mechanism, with an unexpected similarity with Lévy processes.

cond-mat.stat-mech↗

arXiv2022

Some considerations about reviewing and open-access in scientific publishing

Scientific research changed profoundly over the last 30 years, in all its aspects. Scientific publishing has changed as well, mainly because of the strong increased number of submitted papers and because of the appearance of Open Access journals and publishers. We propose some reflections on these issues.

cs.DL↗

arXiv2021

Spaceless description of active optical media

The acclaimed Maxwell-Bloch (or Arecchi-Bonifacio) equations are a valid dynamical model, effectively describing wave propagation in nonlinear optical media: from the amplification in input-output devices to multimode instabilities arising in laser systems. However, the inherent spatial variability of the physical observables represents an obstacle to fast simulations and analysis, especially whenever networks of active elements have to be considered. In this paper, we propose an approach which, stripping the spatial dependence of its role as a generator of dynamical richness, allows for a compelling simple portrait. It leads to (a few) ordinary differential equations in input-output configurations, complemented by a time-delayed feedback in closed-loop setups. Such scheme reproduces accurately the dynamics, paving the way to a plain treatment of the wealth of phenomena described by the Maxwell-Bloch equations.

physics.optics↗

arXiv2021

Coherent oscillations in balanced neural networks driven by endogenous fluctuations

We present a detailed analysis of the dynamical regimes observed in a balanced network of identical Quadratic Integrate-and-Fire (QIF) neurons with a sparse connectivity for homogeneous and heterogeneous in-degree distribution. Depending on the parameter values, either an asynchronous regime or periodic oscillations spontaneously emerge. Numerical simulations are compared with a mean field model based on a self-consistent Fokker-Planck equation (FPE). The FPE reproduces quite well the asynchronous dynamics in the homogeneous case by either assuming a Poissonian or renewal distribution for the incoming spike trains. An exact self consistent solution for the mean firing rate obtained in the limit of infinite in-degree allows identifying balanced regimes that can be either mean- or fluctuation-driven. A low-dimensional reduction of the FPE in terms of circular cumulants is also considered. Two cumulants suffice to reproduce the transition scenario observed in the network. The emergence of periodic collective oscillations is well captured both in the homogeneous and heterogeneous setups by the mean field models upon tuning either the connectivity, or the input DC current. In the heterogeneous situation we analyze also the role of structural heterogeneity.

q-bio.NC↗

arXiv2021

Chaos and localization in the Discrete Nonlinear Schrödinger Equation

We analyze the chaotic dynamics of a one-dimensional discrete nonlinear Schrödinger equation. This nonintegrable model, ubiquitous in several fields of physics, describes the behavior of an array of coupled complex oscillators with a local nonlinear potential. We explore the Lyapunov spectrum for different values of the energy density, finding that the maximal value of the Kolmogorov-Sinai entropy is attained at infinite temperatures. Moreover, we revisit the dynamical freezing of relaxation to equilibrium, occurring when large localized states (discrete breathers) are superposed to a generic finite-temperature background. We show that the localized excitations induce a number of very small, yet not vanishing, Lyapunov exponents, which signal the presence of extremely long characteristic time-scales. We widen our analysis by computing the related Lyapunov covariant vectors, to investigate the interaction of a single breather with the various degrees of freedom.

nlin.CD↗