arXiv subjects

Pedro L. Garrido

Publications and source records attributed to Pedro L. Garrido.

At least 19 recordsLinked to original sources

arXiv2026

Convergent Power Series for Anharmonic Chain with Periodic Forcing

We study the propagation of energy in one-dimensional anharmonic chains subject to a periodic, localized forcing. For the purely harmonic case, forcing frequencies outside the linear spectrum produce exponentially localized responses, preventing equi-distribution of energy per degree of freedom. We extend this result to anharmonic perturbations with bounded second derivatives and boundary dissipation, proving that for small perturbations and non-resonant forcing, the dynamics converges to a periodic stationary state with energy exponentially localized uniformly in the system size. The perturbed periodic state is described by a convergent power type expansion in the strength of the anharmonicity. This excludes chaoticity induced by anharmonicity, independently of the size of the system. Our perturbative scheme can also be applied in higher dimensions.

math-ph↗

arXiv2025

Periodically Driven anharmonic chain: Convergent Power Series and Numerics

We investigate the long time behavior of a pinned chain of $2N+1$ oscillators, indexed by $x \in\{-N,\ldots, N\}$. The system is subjected to an external driving force on the particle at $x=0$, of period $θ=2π/ω$, and to frictional damping $γ>0$ at both endpoints $x=-N$ and $N$. The oscillators interact with a pinned and nearest neighbor harmonic plus anharmonic potentials of the form $\frac{ω_0^2 q_x^2}{2}+\frac12 (q_{x}-q_{x-1})^2 +ν\left[V(q_x)+U(q_x-q_{x-1}) \right]$, with $V''$ and $U''$ bounded and $ν\in \mathbb{R}$. We recall the recently proven convergence and the global stability of a perturbation series in powers of $ν$ for $|ν| < ν_0$, yielding the long time periodic state of the system. Here $ν_0$ depends only on the supremum norms of $V''$ and $U''$ and the distance of the set of non-negative integer multiplicities of $ω$ from the interval $[ω_0,\sqrt{ω_0^2+4}]$ - the spectrum of the infinite harmonic chain for $ν=0$. We describe also some numerical studies of this system going beyond our rigorous results.

cond-mat.stat-mech↗

arXiv2022

A ghost perturbation scheme to solve ordinary differential equations

We propose an algebraic method that finds a sequence of functions that exponentially approach the solution of any second-order ordinary differential equation (ODE) with any boundary conditions. We define an extended ODE (eODE) composed of a linear generic differential operator that depends on free parameters, $p$, plus an $ε$ perturbation formed by the original ODE minus the same linear term. After the eODE's formal $ε$ expansion of the solution, we can solve order by order a hierarchy of linear ODEs, and we get a sequence of functions $y_n(x;ε,p)$ where $n$ indicates the number of terms that we keep in the $ε$-expansion. We fix the parameters to the optimal values $p^*(n)$ by minimizing a distance function of $y_n$ to the ODE's solution, $y$, over a given $x$-interval. We see that the eODE's perturbative solution converges exponentially fast in $n$ to the ODE solution when $ε=1$: $\vert y_n(x;ε=1,p^*(n))-y(x)\vert<Cδ^{n+1}$ with $δ<1$. The method permits knowing the number of solutions for Boundary Value Problems just by looking at the number of minima of the distance function at each order in $n$, $p^{*,α}(n)$, where each $α$ defines a sequence of functions $y_n$ that converges to one of the ODE's solutions. We present the method by its application to several cases where we discuss its properties, benefits and shortcomings, and some practical algorithmic improvements.

math.NA↗

arXiv2022

Correlations in non-equilibrium diffusive systems

We study the behavior of stationary non-equilibrium two-body correlation functions for Diffusive Systems with equilibrium reference states (DSe). We describe a DSe at the mesoscopic level by $M$ locally conserved continuum fields that evolve through coupled Langevin equations with white noises. The dynamic is designed such that the system may reach equilibrium states for a set of boundary conditions. In this form, we make the system driven to a non-equilibrium stationary state by changing the equilibrium boundary conditions. We decompose the correlations in a known local equilibrium part and another one that contains the non-equilibrium behavior and that we call {\it correlation's excess} $\bar C(x,z)$. We formally derive the differential equations for $\bar C$. To solve them order by order, we define a perturbative expansion around the equilibrium state. We show that the $\bar C$'s first-order expansion, $\bar C^{(1)}$, is always zero for the unique field case, $M=1$. Moreover $\bar C^{(1)}$ is always long-range or zero when $M>1$. Surprisingly we show that their associated fluctuations, the space integrals of $\bar C^{(1)}$, are always zero. Therefore, fluctuations are dominated by local equilibrium up to second-order in the perturbative expansion around the equilibrium. We derive the behaviors of $\bar C^{(1)}$ in real space for dimensions $d=1$ and $2$ explicitly. Finally, we derive the two first perturbative orders of the correlation's excess for a generic $M=2$ case and a hydrodynamic model.

cond-mat.stat-mech↗

arXiv2021

Quasi-potentials in the Nonequilibrium Stationary States or a method to get explicit solutions of Hamilton-Jacobi equations

We assume that a system at a mesoscopic scale is described by a field $ϕ(x,t)$ that evolves by a Langevin equation with a white noise whose intensity is controlled by a parameter $1/\sqrtΩ$. The system stationary state distribution in the small noise limit ($Ω\rightarrow\infty$) is of the form $P_{st}[ϕ]\simeq\exp(-ΩV_0[ϕ])$ where $V_0[ϕ]$ is called the {\it quasipotential}. $V_0$ is the unknown of a Hamilton-Jacobi equation. Therefore, $V_0$ can be written as an action computed along a path that is the solution from Hamilton's equation that typically cannot be solved explicitly. This paper presents a theoretical scheme that builds a suitable canonical transformation that permits us to do such integration by deforming the original path into a straight line. We show that this can be done when a set of conditions on the canonical transformation and the model's dynamics are fulfilled. In such cases, we can get the quasipotential algebraically. We apply the scheme to several one-dimensional nonequilibrium models as the diffusive and reaction-diffusion systems.

cond-mat.stat-mech↗

arXiv2020

Notes about the Macroscopic Fluctuating Theory

The Macroscopic Fluctuating Theory is presented from a practical and self consistent point of view. We take as starting point the assumption that a system at a mesoscopic scale is described by a field $ϕ(x,t)$ that evolves by a Langevin equation that locally either conserves or not the field. Its dynamic behavior may also depend on the action of external agents on the bulk or/and at the system's boundaries. We derive the corresponding Fokker-Planck equation and the probability of a path and we use them to study general properties of the system's stationary state. In particular we focus on the study of the quasi-potential that defines the stationary distribution at the small noise limit. We argue that the system is at equilibrium when it is macroscopic reversible, that is when the most probable path to create a fluctuation from the stationary state is equal to the time reversed path that relaxes it. When this doesn't occur the system is in a nonequilibrium stationary state whose quasi-potential may present some lack of differentiability and/or long range action. We also derive closed equations for the two-body correlations at the stationary state and we apply them to some typical cases. Finally we obtain generalized Green-Kubo class of formulas by using the Large Deviation Principle.

cond-mat.stat-mech↗

arXiv2019

Heat Conduction in a hard disc system with non-conserved momentum

We describe results of computer simulations of steady state heat transport in a fluid of hard discs undergoing both elastic interparticle collisions and velocity randomizing collisions which do not conserve momentum. The system consists of N discs of radius r in a unit square, periodic in the y-direction and having thermal walls at x = 0 with temperature T0 taking values from 1 to 20 and at x = 1 with T1 = 1. We consider different values of the ratio between randomizing and interparticle collision rates and extrapolate results from different N, to N->infinity, r->0 such that rho=1/2. We find that in the (extrapolated) limit N->infinity, the systems local density and temperature profiles are those of local thermodynamic equilibrium (LTE) and obey Fourier's law. The variance of global quantities, such as the total energy, deviates from its local equilibrium value in a form consistent with macroscopic fluctuation theory.

cond-mat.stat-mech↗

arXiv2018

Rayleigh-Benard convection in a hard disk system

We do a generic study of the behavior of a hard disk system under the action of a thermal gradient in presence of an uniform gravity field. We observe the conduction-convection transition and measure the main system observables and fields as the thermal current, global pressure, velocity field, temperature field,... We can highlight two of the main results of this overall work: (1) for large enough thermal gradients and a given gravity, we show that the hydrodynamic fields (density, temperature and velocity) have a natural scaling form with the gradient. And (2) we show that local equilibrium holds if the mechanical pressure and the thermodynamic one are not equal, that is, the Stoke's assumption does not hold in this case. Moreover we observe that the best fit to the data is obtained when the bulk viscosity depends on the mechanical pressure.

cond-mat.stat-mech↗

arXiv2018

Diffusion equations from kinetic models with non-conserved momentum

We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that conserves energy and momentum such as the Boltzmann equation and an external randomization of the particle velocity directions that breaks the momentum conservation. Rescaling space and time by epsilon and epsilon square respectively and carrying out a Hilbert expansion in epsilon around a local equilibrium Maxwellian yields coupled diffusion equations with specified Onsager coefficients for the particle and energy density. Our analysis includes a system of hard disks at intermediate densities by using the Enskog equation for the collision kernel.

cond-mat.stat-mech↗

arXiv2016

A violation of universality in anomalous Fourier's law

Since the discovery of long-time tails, it has been clear that Fourier's law in low dimensions is typically anomalous, with a size-dependent heat conductivity, though the nature of the anomaly remains puzzling. The conventional wisdom, supported by renormalization-group arguments and mode-coupling approximations within fluctuating hydrodynamics, is that the anomaly is universal in 1d momentum-conserving systems and belongs in the Levy/Kardar-Parisi-Zhang universality class. Here we challenge this picture by using a novel scaling method to show unambiguously that universality breaks down in the paradigmatic 1d diatomic hard-point fluid. Hydrodynamic profiles for a broad set of gradients, densities and sizes all collapse onto an universal master curve, showing that (anomalous) Fourier's law holds even deep into the nonlinear regime. This allows to solve the macroscopic transport problem for this model, a solution which compares flawlessly with data and, interestingly, implies the existence of a bound on the heat current in terms of pressure. These results question the renormalization-group and mode-coupling universality predictions for anomalous Fourier's law in 1d, offering a new perspective on transport in low dimensions.

cond-mat.stat-mech↗

arXiv2016

Weak additivity principle for current statistics in d-dimensions

The additivity principle (AP) allows to compute the current distribution in many one-dimensional (1d) nonequilibrium systems. Here we extend this conjecture to general d-dimensional driven diffusive systems, and validate its predictions against both numerical simulations of rare events and microscopic exact calculations of three paradigmatic models of diffusive transport in d=2. Crucially, the existence of a structured current vector field at the fluctuating level, coupled to the local mobility, turns out to be essential to understand current statistics in d>1. We prove that, when compared to the straightforward extension of the AP to high-d, the so-called weak AP always yields a better minimizer of the macroscopic fluctuation theory action for current statistics.

cond-mat.stat-mech↗

arXiv2013

Thermodynamics of currents in nonequilibrium diffusive systems: theory and simulation

Understanding the physics of nonequilibrium systems remains as one of the major challenges of theoretical physics. This problem can be cracked in part by investigating the macroscopic fluctuations of the currents characterizing nonequilibrium behavior, their statistics and associated structures. This fundamental line of research has been severely hampered by the overwhelming complexity of this problem. However, during the last years two new general methods have appeared to investigate fluctuating behavior that are changing radically our understanding of nonequilibrium physics: a powerful macroscopic fluctuation theory (MFT) and a set of advanced computational techniques to measure rare events. In this work we study the statistics of current fluctuations in nonequilibrium diffusive systems, using macroscopic fluctuation theory as theoretical framework, and advanced Monte Carlo simulations of several stochastic lattice gases as a laboratory to test the emerging picture. Our quest will bring us from (1) the confirmation of an additivity conjecture in one and two dimensions, which considerably simplifies the MFT complex variational problem to compute the thermodynamics of currents, to (2) the discovery of novel isometric fluctuation relations, which opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations, and to (3) the observation of coherent structures in fluctuations, which appear via dynamic phase transitions involving a spontaneous symmetry breaking event at the fluctuating level. The clear-cut observation, measurement and characterization of these unexpected phenomena, well described by MFT, strongly support this theoretical scheme as the natural theory to understand the thermodynamics of currents in nonequilibrium diffusive media, opening new avenues of research in nonequilibrium physics.

cond-mat.stat-mech↗

arXiv2012

Dynamical phase transition for current statistics in a simple driven diffusive system

We consider fluctuations of the time-averaged current in the one-dimensional weakly-asymmetric exclusion process on a ring. The optimal density profile which sustains a given fluctuation exhibits an instability for low enough currents, where it becomes time-dependent. This instability corresponds to a dynamical phase transition in the system fluctuation behavior: while typical current fluctuations result from the sum of weakly-correlated local events and are still associated with the flat, steady-state density profile, for currents below a critical threshold the system self-organizes into a macroscopic jammed state in the form of a coherent traveling wave, that hinders transport of particles and thus facilitates a time-averaged current fluctuation well below the average current. We analyze in detail this phenomenon using advanced Monte Carlo simulations, and work out macroscopic fluctuation theory predictions, finding very good agreement in all cases. In particular, we study not only the current large deviation function, but also the critical current threshold, the associated optimal density profiles and the traveling wave velocity, analyzing in depth finite-size effects and hence providing a detailed characterization of the dynamical transition.

cond-mat.stat-mech↗

arXiv2011

Spontaneous Symmetry Breaking at the Fluctuating Level

Phase transitions not allowed in equilibrium steady states may happen however at the fluctuating level. We observe for the first time this striking and general phenomenon measuring current fluctuations in an isolated diffusive system. While small fluctuations result from the sum of weakly-correlated local events, for currents above a critical threshold the system self-organizes into a coherent traveling wave which facilitates the current deviation by gathering energy in a localized packet, thus breaking translation invariance. This results in Gaussian statistics for small fluctuations but non-Gaussian tails above the critical current. Our observations, which agree with predictions derived from hydrodynamic fluctuation theory, strongly suggest that rare events are generically associated with coherent, self-organized patterns which enhance their probability.

cond-mat.stat-mech↗

arXiv2011

Symmetries in Fluctuations Far from Equilibrium

Fluctuations arise universally in Nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. In order to sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation which links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulae. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields.

cond-mat.stat-mech↗

arXiv2011

Paradoxical Reflection in Quantum Mechanics

This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This phenomenon is suggested by non-normalizable solutions to the time-independent Schroedinger equation, and we present evidence, numerical and mathematical, that it is also indeed predicted by the time-dependent Schroedinger equation. Furthermore, this paradoxical reflection effect suggests, and we confirm mathematically, that a quantum particle can be trapped for a long time (though not forever) in a region surrounded by downward potential steps, that is, on a plateau.

quant-ph↗

arXiv2010

Large Fluctuations of the Macroscopic Current in Diffusive Systems: A Confirmation of the Additivity Principle

Most systems, when pushed out of equilibrium, respond by building up currents of locally-conserved observables. Understanding how microscopic dynamics determines the averages and fluctuations of these currents is one of the main open problems in nonequilibrium statistical physics. The additivity principle is a theoretical proposal that allows to compute the current distribution in many one-dimensional nonequilibrium systems. Using simulations, we confirm this conjecture in a simple and general model of energy transport, both in the presence of a temperature gradient and in canonical equilibrium. In particular, we show that the current distribution displays a Gaussian regime for small current fluctuations, as prescribed by the central limit theorem, and non-Gaussian (exponential) tails for large current deviations, obeying in all cases the Gallavotti-Cohen fluctuation theorem. In order to facilitate a given current fluctuation, the system adopts a well-defined temperature profile different from that of the steady state, and in accordance with the additivity hypothesis predictions. System statistics during a large current fluctuation is independent of the sign of the current, which implies that the optimal profile (as well as higher-order profiles and spatial correlations) are invariant upon currenst inversion. We also demonstrate that finite-time joint fluctuations of the current and the profile are well described by the additivity functional. These results confirm the additivity hypothesis as a general and powerful tool to compute current distributions in many nonequilibrium systems.

cond-mat.stat-mech↗

arXiv2009

Test of the Additivity Principle for Current Fluctuations in a Model of Heat Conduction

The additivity principle allows to compute the current distribution in many one-dimensional (1D) nonequilibrium systems. Using simulations, we confirm this conjecture in the 1D Kipnis-Marchioro-Presutti model of heat conduction for a wide current interval. The current distribution shows both Gaussian and non-Gaussian regimes, and obeys the Gallavotti-Cohen fluctuation theorem. We verify the existence of a well-defined temperature profile associated to a given current fluctuation. This profile is independent of the sign of the current, and this symmetry extends to higher-order profiles and spatial correlations. We also show that finite-time joint fluctuations of the current and the profile are described by the additivity functional. These results suggest the additivity hypothesis as a general and powerful tool to compute current distributions in many nonequilibrium systems.

cond-mat.stat-mech↗