Category Archives: nonequilibrium physics

Critical behavior of a programmable time-crystal lattice gas

R. Hurtado-Gutiérrez, C. Pérez-Espigares, P.I. Hurtado

Time crystals are many-body systems whose ground state spontaneously breaks time-translation symmetry and thus exhibits long-range spatiotemporal order and robust periodic motion. Using hydrodynamics, we have recently shown how an mth-order external packing field coupled to density fluctuations in driven diffusive fluids can induce the spontaneous emergence of time-crystalline order in the form of m rotating condensates, which can be further controlled and modulated. Here we analyze this phenomenon at the microscopic level in a paradigmatic model of particle diffusion under exclusion interactions, a generalization of the weakly asymmetric simple exclusion process with a configuration-dependent field called the time-crystal lattice gas. Using extensive Monte Carlo simulations, we characterize the nonequilibrium phase transition to these complex time-crystal phases for different values of m, including the order parameter, the susceptibility and the Binder cumulant, from which we measure the critical exponents, which turn out to be within the Kuramoto universality class for oscillator synchronization. We also elucidate the condensates density profiles and velocities, confirming along the way a scaling property predicted for the higher-order condensate shapes in terms of first-order ones, discussing also novel possibilities for this promising route to time crystals.

arXiv:2503.07741

Optimal paths and dynamical symmetry breaking in the current fluctuations of driven diffusive media

Pablo I. Hurtado

Large deviation theory provides a framework to understand macroscopic fluctuations and collective phenomena in many-body nonequilibrium systems in terms of microscopic dynamics. In these lecture notes we discuss the large deviation statistics of the current, a central observable out of equilibrium, using mostly macroscopic fluctuation theory (MFT) but also microscopic spectral methods. Special emphasis is put on describing the optimal path leading to a rare fluctuation, as well as on different dynamical symmetry breaking phenomena that appear at the fluctuating level. We start with a brief overview of the statistics of trajectories in driven diffusive systems as described by MFT. We then discuss the additivity principle, a simplifying conjecture to compute the current distribution in many one-dimensional (1d) nonequilibrium systems, and extend this idea to generic d-dimensional driven diffusive media. Crucially, we derive a fundamental relation which strongly constrains the architecture of the optimal vector current field in $d$ dimensions, making manifest the spatiotemporal nonlocality of current fluctuations. Next we discuss the intriguing phenomenon of dynamical phase transitions (DPTs) in current fluctuations, i.e. possibility of dynamical symmetry breaking events in the trajectory statistics associated to atypical values of the current. We first analyze a discrete particle-hole symmetry-breaking DPT in the transport fluctuations of open channels, working out a Landau-like theory for this DPT as well as the joint statistics of the current and an appropriate order parameter for the transition. Interestingly, Maxwell-like violations of additivity are observed in the non-convex regimes of the joint large deviation function. We then move on to discuss time-translation symmetry breaking DPTs in periodic systems, in which the system of interest self-organizes into a coherent traveling wave that facilitates the current deviation by gathering particles/energy in a localized condensate. We also shed light on the microscopic spectral mechanism leading to these and other symmetry breaking DPTs, which is linked to an emerging degeneracy of the ground state of the associated microscopic generator, with all symmetry-breaking features encoded in the subleading eigenvectors of this degenerate subspace. The introduction of an order parameter space of lower dimensionality allows to confirm quantitatively these spectral fingerprints of DPTs. Using this spectral view on DPTs, we uncover the signatures of the recently discovered time-crystal phase of matter in the traveling-wave DPT found in many periodic diffusive systems. Using Doob’s transform to understand the underlying physics, we propose a packing-field mechanism to build programmable time-crystal phases in driven diffusive systems. We end up these lecture notes discussing some open challenges and future applications in this exciting research field.

arXiv:2501.09629

Lectures on “Current statistics, optimal paths and dynamical symmetry breaking in driven diffusive media” at the 2024 Les Houches Summer School on the Theory of Large Deviations and Applications

The study of large deviations has emerged as a major theme of research in statistical physics over the last two decades, with multiple applications in several inter-disciplinary fields such as nonequilibrium physics, climate science, information theory, disordered systems, etc. This Les Houches Summer School, organized by A. Dhar, J. Krug, S.N. Majumdar, A. Rosso and G. Schehr, has gathered a number of international experts, spanning across disciplines, who provided a broad overview of this rapidly evolving field.

In this set of two lectures (1.5h each) I discuss the statistics of current fluctuations in many-body nonequilibrium systems, using both macroscopic fluctuation theory and microscopic spectral methods. Particular emphasis is put on describing the optimal path leading to a rare event, as well as on different dynamical symmetry breaking phenomena that appear at the fluctuating level.

lecture 1, lecture 2

Squeezing light to get non-classical work in quantum engines

A. Tejero, D. Manzano, P.I. Hurtado

Light can be squeezed by reducing the quantum uncertainty of the electric field for some phases. We show how to use this purely-quantum effect to extract net mechanical work from radiation pressure in a simple quantum photon engine. Along the way, we demonstrate that the standard definition of work in quantum systems is not appropriate in this context, as it does not capture the energy leaked to these quantum degrees of freedom. We use these results to design an Otto engine able to produce mechanical work from squeezing baths, in the absence of thermal gradient. Interestingly, while work extraction from squeezing generally improves for low temperatures, there exists a nontrivial squeezing-dependent temperature for which work production is maximal, demonstrating the complex interplay between thermal and squeezing effects.

arXiv:2408.15085

An atom-doped photon engine: Extracting mechanical work from a quantum system via radiation pressure

A. Tejero, D. Manzano, P.I. Hurtado

The possibility of efficiently converting heat into work at the microscale has triggered an intense research effort to understand quantum heat engines, driven by the hope of quantum superiority over classical counterparts. In this work, we introduce a model featuring an atom-doped optical quantum cavity propelling a classical piston through radiation pressure. The model, based on the Jaynes-Cummings Hamiltonian of quantum electrodynamics, demonstrates the generation of mechanical work through thermal energy injection. We establish the equivalence of the piston expansion work with Alicki’s work definition, analytically for quasistatic transformations and numerically for finite time protocols. We further employ the model to construct quantum Otto and Carnot engines, comparing their performance in terms of energetics, work output, efficiency, and power under various conditions. This model thus provides a platform to extract useful work from an open quantum system to generate net motion, and sheds light on the quantum concepts of work and heat.

Phys. Rev. E 108, 014107 (2023); arXiv:2311.15712

Spectral signatures of symmetry-breaking dynamical phase transitions

R. Hurtado-Gutiérrez, P.I. Hurtado, C. Pérez-Espigares

Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. One of the most appealing results within this context are dynamical phase transitions (DPTs), which might occur at the level of trajectories in order to maximize the probability of sustaining a rare event. While the Macroscopic Fluctuation Theory has underpinned much recent progress on the understanding of symmetry-breaking DPTs in driven diffusive systems, their microscopic characterization is still challenging. In this work we shed light on the general spectral mechanism giving rise to continuous DPTs not only for driven diffusive systems, but for any jump process in which a discrete ℤn symmetry is broken. By means of a symmetry-aided spectral analysis of the Doob-transformed dynamics, we provide the conditions whereby symmetry-breaking DPTs might emerge and how the different dynamical phases arise from the specific structure of the degenerate eigenvectors. We show explicitly how all symmetry-breaking features are encoded in the subleading eigenvectors of the degenerate manifold. Moreover, by partitioning configuration space into equivalence classes according to a proper order parameter, we achieve a substantial dimensional reduction which allows for the quantitative characterization of the spectral fingerprints of DPTs. We illustrate our predictions in three paradigmatic many-body systems: (i) the 1D boundary-driven weakly asymmetric exclusion process (WASEP), which exhibits a particle-hole symmetry-breaking DPT for current fluctuations, (ii) the 3 and 4-state Potts model, which displays discrete rotational symmetry-breaking DPT for energy fluctuations, and (iii) the closed WASEP which presents a continuous symmetry-breaking DPT to a time-crystal phase characterized by a rotating condensate.

Phys. Rev. E 108, 014107 (2023); arXiv:2301.10262

Molecular hints of two-step transition to convective flow via streamline percolation

P.L. Garrido, P.I. Hurtado

Convection is a key transport phenomenon important in many different areas, from hydrodynamics and ocean circulation to planetary atmospheres or stellar physics. However its microscopic understanding still remains challenging. Here we numerically investigate the onset of convective flow in a compressible (non-Oberbeck-Boussinesq) hard disk fluid under a temperature gradient in a gravitational field. We uncover a surprising two-step transition scenario with two different critical temperatures. When the bottom plate temperature reaches a first threshold, convection kicks in (as shown by a structured velocity field) but gravity results in hindered heat transport as compared to the gravity-free case. It is at a second (higher) temperature that a percolation transition of advection zones connecting the hot and cold plates triggers efficient convective heat transport. Interestingly, this novel picture for the convection instability opens the door to unknown piecewise-continuous solutions to the Navier-Stokes equations.

Phys. Rev. E 106, 014144 (2022); arXiv:2207.09223

Active interaction switching controls the dynamic heterogeneity of soft colloidal dispersions

M. Bley, P.I. Hurtado, J. Dzubiella, A. Moncho-Jordá

We employ Reactive Dynamical Density Functional Theory (R-DDFT) and Reactive Brownian Dynamics (R-BD) simulations to investigate the dynamics of a suspension of active soft Gaussian colloids with binary interaction switching, i.e., a one-component colloidal system in which every particle stochastically switches at predefined rates between two interaction states with different mobility. Using R-DDFT we extend a theory previously developed to access the dynamics of inhomogeneous liquids to study the influence of the switching activity on the self and distinct part of the Van Hove function in bulk solution, and determine the corresponding mean squared displacement of the switching particles. Our results demonstrate that, even though the average diffusion coefficient is not affected by the switching activity, it significantly modifies the non-equilibrium dynamics and diffusion coefficients of the individual particles, leading to a crossover from short to long times, with a regime for intermediate times showing anomalous diffusion. In addition, the self-part of the van Hove function has a Gaussian form at short and long times, but becomes non-Gaussian at intermediates ones, having a crossover between short and large displacements. The corresponding self-intermediate scattering function shows the two-step relaxation patters typically observed in soft materials with heterogeneous dynamics such as glasses and gels. We also introduce a phenomenological Continuous Time Random Walk (CTRW) theory to understand the heterogeneous diffusion of this system. R-DDFT results are in excellent agreement with R-BD simulations and the analytical predictions of CTRW theory, thus confirming that R-DDFT constitutes a powerful method to investigate not only the structure and phase behavior, but also the dynamical properties of non-equilibrium active switching colloidal suspensions.

Soft Matter 18, 397 (2022); arXiv:2112.01191

Coupled activity-current fluctuations in open quantum systems under strong symmetries

D. Manzano, M.A. Martínez-García, P.I. Hurtado

Strong symmetries in open quantum systems lead to broken ergodicity and the emergence of multiple degenerate steady states. From a quantum jump (trajectory) perspective, the appearance of multiple steady states is related to underlying dynamical phase transitions (DPTs) at the fluctuating level, leading to a dynamical coexistence of different transport channels classified by symmetry. In this paper, we investigate how strong symmetries affect both the transport properties and the activity patterns of a particular class of Markovian open quantum system, a three-qubit model under the action of a magnetic field and in contact with a thermal bath. We find a pair of twin DPTs in exciton current statistics, induced by the strong symmetry and related by time reversibility, where a zero-current exchange-antisymmetric phase coexists with a symmetric phase of negative exciton current. On the other hand, the activity statistics exhibits a single DPT where the symmetric and antisymmetric phases of different but nonzero activities dynamically coexists. The presence of a strong symmetry under non-equilibrium conditions implies non-analyticities in the dynamical free energy in the dual activity-current plane, including an activity-driven current lockdown phase for activities below some critical threshold. Finally, we also study the effect of a symmetry-breaking, ergodicity-restoring dephasing channel on the coupled activity-current statistics for this model. Interestingly, we observe that while this dephasing noise destroys the symmetry-induced DPTs, the underlying topological symmetry leaves a dynamical fingerprint in the form of intermittent, bursty on/off dynamics between the different symmetry sectors.

New J. Phys. 23, 073044 (2021); arXiv:2104.13176

Simulations of transport in hard particle systems

P. I. Hurtado, P.L. Garrido

Hard particle systems are among the most successful, inspiring and prolific models of physics. They contain the essential ingredients to understand a large class of complex phenomena, from phase transitions to glassy dynamics, jamming, or the physics of liquid crystals and granular materials, to mention just a few. As we discuss in this paper, their study also provides crucial insights on the problem of transport out of equilibrium. A main tool in this endeavour are computer simulations of hard particles. Here we review some of our work in this direction, focusing on the hard disks fluid as a model system. In this quest we will address, using extensive numerical simulations, some of the key open problems in the physics of transport, ranging from local equilibrium and Fourier’s law to the transition to convective flow in the presence of gravity, the efficiency of boundary dissipation, or the universality of anomalous transport in low dimensions. In particular, we probe numerically the macroscopic local equilibrium hypothesis, which allows to measure the fluid’s equation of state in nonequilibrium simulations, uncovering along the way subtle nonlocal corrections to local equilibrium and a remarkable bulk-boundary decoupling phenomenon in fluids out of equilibrium. We further show that the the hydrodynamic profiles that a system develops when driven out of equilibrium by an arbitrary temperature gradient obey universal scaling laws, a result that allows the determination of transport coefficients with unprecedented precision and proves that Fourier’s law remains valid in highly nonlinear regimes. Switching on a gravity field against the temperature gradient, we investigate numerically the transition to convective flow. We uncover a surprising two-step transition scenario with two different critical thresholds for the hot bath temperature, a first one where convection kicks but gravity hinders heat transport, and a second critical temperature where a percolation transition of streamlines connecting the hot and cold baths triggers efficient convective heat transport. We also address numerically the efficiency of boundary heat baths to dissipate the energy provided by a bulk driving mechanism. As a bonus track, we depart from the hard disks model to study anomalous transport in a related hard-particle system, the $1d$ diatomic hard-point gas. We show unambiguously that the universality conjectured for anomalous transport in $1d$ breaks down for this model, calling into question recent theoretical predictions and offering a new perspective on anomalous transport in low dimensions. Our results show how carefully-crafted numerical simulations of simple hard particle systems can lead to unexpected discoveries in the physics of transport, paving the way to further advances in nonequilibrium physics.

J. Stat. Phys. 180, 474 (2020)