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Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport [article]

Stefano Iubini, Stefano Lepri, Roberto Livi, Antonio Politi, Paolo Politi
2019 arXiv   pre-print
This Chapter contains an overview of the effects of nonlinear interactions in selected problems of non-equilibrium statistical mechanics. Most of the emphasis is put on open setups, where energy is exchanged with the environment. With reference to a few models of classical coupled anharmonic oscillators, we review anomalous but general properties such as extremely slow relaxation processes, or non-Fourier heat transport.
arXiv:1911.06017v1 fatcat:yedllsfqqna2pbf33qh35nu3zy

Nonequilibrium discrete nonlinear Schrödinger equation

Stefano Iubini, Stefano Lepri, Antonio Politi
2012 Physical Review E  
We study nonequilibrium steady states of the one-dimensional discrete nonlinear Schroedinger equation. This system can be regarded as a minimal model for stationary transport of bosonic particles like photons in layered media or cold atoms in deep optical traps. Due to the presence of two conserved quantities, energy and norm (or number of particles), the model displays coupled transport in the sense of linear irreversible thermodynamics. Monte Carlo thermostats are implemented to impose a
more » ... temperature and chemical potential at the chain ends. As a result, we find that the Onsager coefficients are finite in the thermodynamic limit, i.e. transport is normal. Depending on the position in the parameter space, the "Seebeck coefficient" may be either positive or negative. For large differences between the thermostat parameters, density and temperature profiles may display an unusual nonmonotonic shape. This is due to the strong dependence of the Onsager coefficients on the state variables.
doi:10.1103/physreve.86.011108 pmid:23005369 fatcat:b3a3sxu3lbffxerru2lamviomq

Energy and magnetisation transport in non-equilibrium macrospin systems [article]

Simone Borlenghi, Stefano Iubini, Stefano Lepri, Jonathan Chico, Lars Bergqvist, Anna Delin, Jonas Fransson
2015 arXiv   pre-print
We investigate numerically the magnetisation dynamics of an array of nano-disks interacting through the magneto-dipolar coupling. In the presence of a temperature gradient, the chain reaches a non-equilibrium steady state where energy and magnetisation currents propagate. This effect can be described as the flow of energy and particle currents in an off-equilibrium discrete nonlinear Schr\"odinger (DNLS) equation. This model makes transparent the transport properties of the system and allows
more » ... a precise definition of temperature and chemical potential for a precessing spin. The present study proposes a novel setup for the spin-Seebeck effect, and shows that its qualitative features can be captured by a general oscillator-chain model
arXiv:1503.00461v1 fatcat:bdnwaqth3vftbk3nmgypd4bpde

Hydrodynamics and transport in the long-range-interacting φ^4 chain [article]

Stefano Iubini, Stefano Lepri, Stefano Ruffo
2022 arXiv   pre-print
We present a simulation study of the one-dimensional φ^4 lattice theory with long-range interactions decaying as an inverse power r^-(1+σ) of the intersite distance r, σ>0. We consider the cases of single and double-well local potentials with both attractive and repulsive couplings. The double-well, attractive case displays a phase transition for 0<σ≤ 1 analogous to the Ising model with long-range ferromagnetic interactions. A dynamical scaling analysis of both energy structure factors and
more » ... s energy correlations shows that the effective hydrodynamics is diffusive for σ>1 and anomalous for 0<σ<1 where fluctuations propagate superdiffusively. We argue that this is accounted for by a fractional diffusion process and we compare the results with an effective model of energy transport based on Lévy flights. Remarkably, this result is fairly insensitive on the phase transition. Nonequilibrium simulations with an applied thermal gradient are in quantitative agreement with the above scenario.
arXiv:2112.02046v2 fatcat:ip7emlkj4remxouh4vp5b3m72i

Aging of living polymer networks [article]

Stefano Iubini, Marco Baiesi, Enzo Orlandini
2020 arXiv   pre-print
Supplemental material for "Aging of living polymer networks" Stefano Iubini, Marco Baiesi, and Enzo Orlandini MODEL AND PHYSICAL UNITS Model.  ... 
arXiv:2001.10739v1 fatcat:5hut36qg6rc5nklftiolofn3pq

Dephasing-Assisted Macrospin Transport

Stefano Iubini, Simone Borlenghi, Anna Delin, Stefano Lepri, Francesco Piazza
2020 Entropy  
Transport phenomena are ubiquitous in physics, and it is generally understood that the environmental disorder and noise deteriorates the transfer of excitations. There are, however, cases in which transport can be enhanced by fluctuations. In the present work, we show, by means of micromagnetics simulations, that transport efficiency in a chain of classical macrospins can be greatly increased by an optimal level of dephasing noise. We also demonstrate the same effect in a simplified model, the
more » ... issipative Discrete Nonlinear Schrödinger equation, subject to phase noise. Our results point towards the realization of a large class of magnonics and spintronics devices, where disorder and noise can be used to enhance spin-dependent transport efficiency.
doi:10.3390/e22020210 pmid:33285985 fatcat:6e5ciadw5vew3nfstwam2e44ha

Negative-temperature Fourier transport in one-dimensional systems [article]

Marco Baldovin, Stefano Iubini
2021 arXiv   pre-print
We thank Stefano Lepri for a critical reading of the manuscript. M.  ... 
arXiv:2102.00307v1 fatcat:n63zzbjm5rexbno5nazwwsvas4

Boundary-Induced Instabilities in Coupled Oscillators

Stefano Iubini, Stefano Lepri, Roberto Livi, Antonio Politi
2014 Physical Review Letters  
A novel class of nonequilibrium phase-transitions at zero temperature is found in chains of nonlinear oscillators.For two paradigmatic systems, the Hamiltonian XY model and the discrete nonlinear Schr\"odinger equation, we find that the application of boundary forces induces two synchronized phases, separated by a non-trivial interfacial region where the kinetic temperature is finite. Dynamics in such supercritical state displays anomalous chaotic properties whereby some observables are
more » ... nsive and transport is superdiffusive. At finite temperatures, the transition is smoothed, but the temperature profile is still non-monotonous.
doi:10.1103/physrevlett.112.134101 pmid:24745424 fatcat:aw75devxvzfbvb4zrdng5d4ife

A Chain, a Bath, a Sink, and a Wall

Stefano Iubini, Stefano Lepri, Roberto Livi, Gian-Luca Oppo, Antonio Politi
2017 Entropy  
Author Contributions: Stefano Iubini performed the numerical simulations. All Authors contributed to the research work and to writing the paper.  ...  Stefano Lepri acknowledges hospitality of the Institut Henri Poincaré-Centre Emile Borel during the trimester Stochastic Dynamics Out of Equilibrium where part of this work was elaborated.  ... 
doi:10.3390/e19090445 fatcat:bhalslbeargo3iswiaq4zl2lgi

Entropy production for complex Langevin equations

Simone Borlenghi, Stefano Iubini, Stefano Lepri, Jonas Fransson
2017 Physical review. E  
We study irreversible processes for nonlinear oscillators networks described by complex-valued Langevin equations that account for coupling to different thermo-chemical baths. Dissipation is introduced via non-Hermitian terms in the Hamiltonian of the model. We apply the stochastic thermodynamics formalism to compute explicit expressions for the entropy production rates. We discuss in particular the non-equilibrium steady states of the network characterised by a constant production rate of
more » ... py and flows of energy and particle currents. For two specific examples, a one-dimensional chain and a dimer, numerical calculations are presented. The role of asymmetric coupling among the oscillators on the entropy production is illustrated.
doi:10.1103/physreve.96.012150 pmid:29347077 fatcat:vfwfky2yercohihrzc7gmbns5u

Chaos and localization in the Discrete Nonlinear Schrödinger Equation [article]

Stefano Iubini, Antonio Politi
2021 arXiv   pre-print
We analyze the chaotic dynamics of a one-dimensional discrete nonlinear Schr\"odinger 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
more » ... o 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.
arXiv:2103.11041v1 fatcat:vnj3xlx3a5ckpamtdxhqrjbwvi

Finite-size localization scenarios in condensation transitions [article]

Gabriele Gotti, Stefano Iubini, Paolo Politi
2021 arXiv   pre-print
We consider the phenomenon of condensation of a globally conserved quantity H=∑_i=1^N ϵ_i distributed on N sites, occurring when the density h= H/N exceeds a critical density h_c. We numerically study the dependence of the participation ratio Y_2=⟨ϵ_i^2⟩/(Nh^2) on the size N of the system and on the control parameter δ = (h-h_c), for various models: (i) a model with two conservation laws, derived from the Discrete NonLinear Schrödinger equation; (ii) the continuous version of the Zero Range
more » ... ess class, for different forms of the function f(ϵ) defining the factorized steady state. Our results show that various localization scenarios may appear for finite N and close to the transition point. These scenarios are characterized by the presence or the absence of a minimum of Y_2 when plotted against N and by an exponent γ≥ 2 defined through the relation N^* ≃δ^-γ, where N^* separates the delocalized region (N≪ N^*, Y_2 vanishes with increasing N) from the localized region (N≫ N^*, Y_2 is approximately constant). We finally compare our results with the structure of the condensate obtained through the single-site marginal distribution.
arXiv:2010.11138v3 fatcat:tyrcixalvrhndpm2imc42wu3ty

Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model [article]

Pierfrancesco Di Cintio, Stefano Iubini, Stefano Lepri, Roberto Livi
2019 arXiv   pre-print
We present a numerical study of dynamical correlations (structure factors) of the long-range generalization of the Fermi-Pasta-Ulam oscillator chain, where the strength of the interaction between two lattice sites decays as a power α of the inverse of their distance. The structure factors at finite energy density display distinct peaks, corresponding to long-wavelength propagating modes, whose dispersion relation is compatible with the predictions of the linear theory. We demonstrate that
more » ... cal scaling holds, with a dynamical exponent z that depends weakly on α in the range 1<α<3. The lineshapes have a non-trivial functional form and appear somehow independent of α. Within the accessible time and size ranges, we also find that the short-range limit is hardly attained even for relatively large values of α.
arXiv:1901.04601v1 fatcat:twmue7tm55cf7lyc2w63uwvc4m

Frozen dynamics of a breather induced by an adiabatic invariant [article]

Antonio Politi, Paolo Politi, Stefano Iubini
2022 arXiv   pre-print
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  ... 
arXiv:2201.02529v2 fatcat:53dqss524vgc5j4qwg6w7ynjdq

Transport in perturbed classical integrable systems: The pinned Toda chain

Pierfrancesco Di Cintio, Stefano Iubini, Stefano Lepri, Roberto Livi
2018 Chaos, Solitons & Fractals  
Nonequilibrium and thermal transport properties of the Toda chain, a prototype of classically integrable system, subject to additional (nonintegrable) terms are considered. In particular, we study via equilibrium and nonequilibrium simulations, the Toda lattice with a power-law pinning potential, recently analyzed by Lebowitz and Scaramazza [ArXiv:1801.07153]. We show that, according to general expectations, even the case with quadratic pinning is genuinely non-integrable, as demonstrated by
more » ... puting the Lyapunov exponents, and displays normal (diffusive) conductivity for very long chains. However, the model has unexpected dynamical features and displays strong finite-size effects and slow decay of correlations to be traced back to the propagation of soliton-like excitations, weakly affected by the harmonic pinning potential. Some novel results on current correlations for the standard integrable Toda model are also reported.
doi:10.1016/j.chaos.2018.11.003 fatcat:lfufm745wbdorlmoect52s3iza
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