arXiv subjects

Stefano Ruffo

Publications and source records attributed to Stefano Ruffo.

At least 55 records · Page 3Linked to original sources

arXiv2021

Nonlinearity accelerates the thermalization of the quartic FPUT model with stochastic baths

We investigate the equilibration process of the strongly coupled quartic Fermi-Pasta-Ulam-Tsingou (FPUT) model by adding Langevin baths to the ends of the chain. The time evolution of the system is investigated by means of extensive numerical simulations and shown to match the results expected from equilibrium statistical mechanics in the time-asymptotic limit. Upon increasing the nonlinear coupling, the thermalization of the energy spectrum displays an increasing asymmetry in favour of small-scale, high-frequency modes, which relax significantly faster than the large-scale, low-frequency ones. The global equilibration time is found to scale linearly with system size and shown to exhibit a power-law decay with the strength of the nonlinearity and temperature. Nonlinear interaction adds to energy distribution among modes, thus speeding up the thermalization process.

cond-mat.stat-mech↗

arXiv2020

Self-consistent harmonic approximation with non-local couplings

We derive the self-consistent harmonic approximation for the $2D$ XY model with non-local interactions. The resulting equation for the variational couplings holds for any form of the spin-spin coupling as well as for any dimension. Our analysis is then specialized to power-law couplings decaying with the distance $r$ as $\propto 1/r^{2+σ}$ in order to investigate the robustness, at finite $σ$, of the Berezinskii-Kosterlitz-Thouless (BKT) transition, which occurs in the short-range limit $σ\to \infty$. We propose an ansatz for the functional form of the variational couplings and show that for any $σ>2$ the BKT mechanism occurs. The present investigation provides an upper bound for the lower critical threshold $σ^\ast=2$, above which the traditional BKT transition persists in spite of the LR couplings.

cond-mat.stat-mech↗

arXiv2020

Energetics of critical oscillators in active bacterial baths

We investigate the nonequilibrium energetics near a critical point of a non-linear driven oscillator immersed in an active bacterial bath. At the critical point, we reveal a scaling exponent of the average power $\langle\dot{W}\rangle\sim (D_{\rm a}/τ)^{1/4}$ where $D_{\rm a}$ is the effective diffusivity and $τ$ the correlation time of the bacterial bath described by a Gaussian colored noise. Other features that we investigate are the average stationary power and the variance of the work both below and above the saddle-node bifurcation. Above the bifurcation, the average power attains an optimal, minimum value for finite $τ$ that is below its zero-temperature limit. Furthermore, we reveal a finite-time uncertainty relation for active matter which leads to values of the Fano factor of the work that can be below $2k_{\rm B}T_{\rm eff}$, with $T_{\rm eff}$ the effective temperature of the oscillator in the bacterial bath. We analyze different Markovian approximations to describe the nonequilibrium stationary state of the system. Finally, we illustrate our results in the experimental context by considering the example of driven colloidal particles in periodic optical potentials within an E. Coli bacterial bath.

cond-mat.soft↗

arXiv2020

Quantum-heat fluctuation relations in $3$-level systems under projective measurements

We study the statistics of energy fluctuations in a three-level quantum system subject to a sequence of projective quantum measurements. We check that, as expected, the quantum Jarzynski equality holds provided that the initial state is thermal. The latter condition is trivially satisfied for two-level systems, while this is generally no longer true for $N$-level systems, with $N > 2$. Focusing on three-level systems, we discuss the occurrence of a unique energy scale factor $β_{\rm eff}$ that formally plays the role of an effective inverse temperature in the Jarzynski equality. To this aim, we introduce a suitable parametrization of the initial state in terms of a thermal and a non-thermal component. We determine the value of $β_{\rm eff}$ for a large number of measurements and study its dependence on the initial state. Our predictions could be checked experimentally in quantum optics.

quant-ph↗

arXiv2020

Effective negative specific heat by destabilization of metastable states in dipolar systems

We study dipolarly coupled three dimensional spin systems in both the microcanonical and the canonical ensembles by introducing appropriate numerical methods to determine the microcanonical temperature and by realizing a canonical model of heat bath. In the microcanonical ensemble, we show the existence of a branch of stable antiferromagnetic states in the low energy region. Other metastable ferromagnetic states exist in this region: by externally perturbing them, an effective negative specific heat is obtained. In the canonical ensemble, for low temperatures, the same metastable states are unstable and reach a new branch of more robust metastable states which is distinct from the stable one. Our statistical physics approach allows us to put some order in the complex structure of stable and metastable states of dipolar systems.

cond-mat.stat-mech↗

arXiv2019

Many-body synchronisation in a classical Hamiltonian system

We study synchronisation between periodically driven, interacting classical spins undergoing a Hamiltonian dynamics. In the thermodynamic limit there is a transition between a regime where all the spins oscillate synchronously for an infinite time with a period twice as the driving period (synchronized regime) and a regime where the oscillations die after a finite transient (chaotic regime). We emphasize the peculiarity of our result, having been synchronisation observed so far only in driven-dissipative systems. We discuss how our findings can be interpreted as a period-doubling time crystal and we show that synchronisation can appear both for an overall regular and an overall chaotic dynamics.

cond-mat.stat-mech↗

arXiv2019

Phase transitions in the unconstrained ensemble

The unconstrained ensemble describes completely open systems in which energy, volume and number of particles fluctuate. Here we show that not only equilibrium states can exist in this ensemble, but also that completely open systems can undergo first-order phase transitions. This is shown by studying a modified version of the Thirring model with attractive and repulsive interactions and with particles of finite size. The model exhibits first-order phase transitions in the unconstrained ensemble, at variance with the analogous model with point-like particles. While unconstrained and grand canonical ensembles are equivalent for this model, we found inequivalence between the unconstrained and isothermal-isobaric ensembles. By comparing the thermodynamic phase diagram in the unconstrained case with that obtained in the isothermal-isobaric ensemble, we show that phase transitions under completely open conditions for this model are different from those in which the number of particles is fixed, highlighting the inequivalence of ensembles.

cond-mat.stat-mech↗

arXiv2019

Pulse solutions of the fractional effective models of the Fermi-Pasta-Ulam lattice with long-range interactions

We study analytical solutions of the Fractional Boussinesq Equation (FBE), which is an effective model for the Fermi-Pasta-Ulam (FPU) one-dimensional lattice with long-range couplings. The couplings decay as a power-law with exponent s, with 1 < s < 3, so that the energy density is finite, but s is small enough to observe genuine long-range effects. The analytic solutions are obtained by introducing an ansatz for the dependence of the field on space and time. This allows to reduce the FBE to an ordinary differential equation, which can be explicitly solved. The solutions are initially localized and they delocalize progressively as time evolves. Depending on the value of s the solution is either a pulse (meaning a bump) or an anti-pulse (i.e., a hole) on a constant field for 1 < s < 2 and 2 < s < 3, respectively.

cond-mat.stat-mech↗

arXiv2019

Criticality of Spin Systems with Weak Long-Range Interactions

The study of critical properties of systems with long-range interactions has attracted in the last decades a continuing interest and motivated the development of several analytical and numerical techniques, in particular in connection with spin models. From the point of view of the investigation of their criticality, a special role is played by systems in which the interactions are long-range enough that their universality class is different from the short-range case and, nevertheless, they maintain the extensivity of thermodynamical quantities. Such interactions are often called weak long-range. In this paper we focus on the study of the critical behaviour of spin systems with weak-long range couplings using renormalization group, and we review their remarkable properties. For the sake of clarity and self-consistency, we start from the classical $O(N)$ spin models and we then move to quantum spin systems.

cond-mat.stat-mech↗

arXiv2019

Ising chains with competing interactions in presence of long-range couplings

In this paper we study an Ising spin chain with short-range competing interactions in presence of long-range ferromagnetic interactions in the canonical ensemble. The simultaneous presence of the frustration induced by the short-range couplings together with their competition with the long-range term gives rise to a rich thermodynamic phase diagram. We compare our results with the limit in which one of two local interactions is turned off, which was previously studied in the literature. Eight regions of parameters with qualitatively distinct properties are featured, with different first- and second-order phase transition lines and critical points.

cond-mat.stat-mech↗

arXiv2018

Concavity, Response Functions and Replica Energy

In nonadditive systems, like small systems or like long-range interacting systems even in the thermodynamic limit, ensemble inequivalence can be related to the occurrence of negative response functions, this in turn being connected with anomalous concavity properties of the thermodynamic potentials associated to the various ensembles. We show how the type and number of negative response functions depend on which of the quantities E, V and N (energy, volume and number of particles) are constrained in the ensemble. In particular, we consider the unconstrained ensemble in which E, V and N fluctuate, physically meaningful only for nonadditive systems. In fact, its partition function is associated to the replica energy, a thermodynamic function that identically vanishes when additivity holds, but that contains relevant information in nonadditive systems.

cond-mat.stat-mech↗

arXiv2018

Reconstructing quantum entropy production to probe irreversibility and correlations

One of the major goals of quantum thermodynamics is the characterization of irreversibility and its consequences in quantum processes. Here, we discuss how entropy production provides a quantification of the irreversibility in open quantum systems through the quantum fluctuation theorem. We start by introducing a two-time quantum measurement scheme, in which the dynamical evolution between the measurements is described by a completely positive, trace-preserving (CPTP) quantum map (forward process). By inverting the measurement scheme and applying the time-reversed version of the quantum map, we can study how this backward process differs from the forward one. When the CPTP map is unital, we show that the stochastic quantum entropy production is a function only of the probabilities to get the initial measurement outcomes in correspondence of the forward and backward processes. For bipartite open quantum systems we also prove that the mean value of the stochastic quantum entropy production is sub-additive with respect to the bipartition (except for product states). Hence, we find a method to detect correlations between the subsystems. Our main result is the proposal of an efficient protocol to determine and reconstruct the characteristic functions of the stochastic entropy production for each subsystem. This procedure enables to reconstruct even others thermodynamical quantities, such as the work distribution of the composite system and the corresponding internal energy. Efficiency and possible extensions of the protocol are also discussed. Finally, we show how our findings might be experimentally tested by exploiting the state-of-the-art trapped-ion platforms.

quant-ph↗

arXiv2018

Spontaneous synchronization and nonequilibrium statistical mechanics of coupled phase oscillators

Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously exhibit collective oscillations at a common frequency. The Kuramoto model provides the basic analytical framework to study spontaneous synchronization. The model comprises limit-cycle oscillators with distributed natural frequencies interacting through a mean-field coupling. Although more than forty years have passed since its introduction, the model continues to occupy the centre-stage of research in the field of non-linear dynamics, and is also widely applied to model diverse physical situations. In this brief review, starting with a derivation of the Kuramoto model and the synchronization phenomenon it exhibits, we summarize recent results on the study of a generalized Kuramoto model that includes inertial effects and stochastic noise. We describe the dynamics of the generalized model from a different yet a rather useful perspective, namely, that of long-range interacting systems driven out of equilibrium by quenched disordered external torques. A system is said to be long-range interacting if the inter-particle potential decays slowly as a function of distance. Using tools of statistical physics, we highlight the equilibrium and nonequilibrium aspects of the dynamics of the generalized Kuramoto model, and uncover a rather rich and complex phase diagram that it exhibits, which underlines the basic theme of intriguing emergent phenomena that are exhibited by many-body complex systems.

nlin.AO↗

arXiv2018

Non-equilibrium quantum-heat statistics under stochastic projective measurements

In this paper we aim at characterizing the effect of stochastic fluctuations on the distribution of the energy exchanged by a quantum system with an external environment under sequences of quantum measurements performed at random times. Both quenched and annealed averages are considered. The information about fluctuations is encoded in the quantum-heat probability density function, or equivalently in its characteristic function, whose general expression for a quantum system with arbitrary Hamiltonian is derived. We prove that, when a stochastic protocol of measurements is applied, the quantum Jarzynski equality is obeyed. Therefore, the fluctuation relation is robust against the presence of randomness in the times intervals between measurements. Then, for the paradigmatic case of a two-level system, we analytically characterize the quantum-heat transfer. Particular attention is devoted to the limit of large number of measurements and to the effects caused by the stochastic fluctuations. The relation with the stochastic Zeno regime is also discussed.

quant-ph↗

arXiv2017

Equilibration in the Nosé-Hoover isokinetic ensemble: Effect of inter-particle interactions

We investigate the stationary and dynamic properties of the celebrated Nosé-Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short- and long-range interactions. The Nosé-Hoover dynamics aims to generate the canonical equilibrium distribution of a system at a desired temperature by employing a set of time-reversible, deterministic equations of motion. A signature of canonical equilibrium is a single-particle momentum distribution that is Gaussian. We find that the equilibrium properties of the system within the Nosé-Hoover dynamics coincides with that within the canonical ensemble. Moreover, starting from out-of-equilibrium initial conditions, the average kinetic energy of the system relaxes to its target value over a {\it size-independent} timescale. However, quite surprisingly, our results indicate that under the same conditions and with only long-range interactions present in the system, the momentum distribution relaxes to its Gaussian form in equilibrium over a scale that {\it diverges with the system size}. On adding short-range interactions, the relaxation is found to occur over a timescale that has a much weaker dependence on system size. This system-size dependence of the timescale vanishes when only short-range interactions are present in the system. An implication of such an ultra-slow relaxation when only long-range interactions are present in the system is that macroscopic observables other than the average kinetic energy when estimated in the Nosé-Hoover dynamics may take an unusually long time to relax to its canonical equilibrium value. Our work underlines the crucial role that interactions play in deciding the equivalence between Nosé-Hoover and canonical equilibrium.

cond-mat.stat-mech↗

arXiv2017

Criticality and Phase Diagram of Quantum Long-Range $\text{O(N)}$ models

Several recent experiments in atomic, molecular and optical systems motivated a huge interest in the study of quantum long-range %spin systems. Our goal in this paper is to present a general description of their critical behavior and phases, devising a treatment valid in $d$ dimensions, with an exponent $d+σ$ for the power-law decay of the couplings in the presence of an $O(N)$ symmetry. By introducing a convenient ansatz for the effective action, we determine the phase diagram for the $N$-component quantum rotor model with long-range interactions, with $N=1$ corresponding to the Ising model. The phase diagram in the $σ-d$ plane shows a non trivial dependence on $σ$. As a consequence of the fact that the model is quantum, the correlation functions are anisotropic in the spatial and time coordinates for $σ$ smaller than a critical value and in this region the isotropy is not restored even at criticality. Results for the correlation length exponent $ν$, the dynamical critical exponent $z$ and a comparison with numerical findings for them are presented.

cond-mat.quant-gas↗

arXiv2017

Traveling Solitons in Long-Range Oscillator Chains

We investigate the existence and propagation of solitons in a long-range extension of the quartic Fermi-Pasta-Ulam (FPU) chain of anharmonic oscillators. The coupling in the linear term decays as a power-law with an exponent greater than 1 and less than 3. We obtain an analytic perturbative expression of traveling envelope solitons by introducing a Non Linear Schrodinger (NLS) equation for the slowly varying amplitude of short wavelength modes. Due to the non analytic properties of the dispersion relation, it is crucial to develop the theory using discrete difference operators. Those properties are also the ultimate reason why kink-solitons may exist but are unstable, at variance with the short-range FPU model. We successfully compare these approximate analytic results with numerical simulations.

nlin.PS↗

arXiv2017

Ensemble inequivalence and absence of quasi-stationary states in long-range random networks

Ensemble inequivalence has been previously displayed only for long-range interacting systems with non-extensive energy. In order to perform the thermodynamic limit, such systems require an unphysical, so-called, Kac rescaling of the coupling constant. We here study models defined on long-range random networks, which avoid such a rescaling. The proposed models have an extensive energy, which is however non-additive. For such long-range random networks, pairs of sites are coupled with a probability decaying with the distance $r$ as $1/r^δ$. In one dimension and with $0 \leq δ<1$, surface energy scales linearly with the network size, while for $δ>1$ it is $O(1)$. By performing numerical simulations, we show that a negative specific heat region is present in the microcanonical ensemble of a Blume-Capel model, in correspondence with a first-order phase transition in the canonical one. This proves that ensemble inequivalence is a consequence of $non$-$additivity$ rather than $non$-$extensivity$. Moreover, since a mean-field coupling is absent in such networks, relaxation to equilibrium takes place on an intensive time scale and quasi-stationary states are absent.

cond-mat.stat-mech↗