arXiv subjects

Emmanuel Trizac

Publications and source records attributed to Emmanuel Trizac.

At least 19 recordsLinked to original sources

arXiv2026

A strong-coupling theory for polarizable symmetrically charged walls with counterions only

A pair of parallel polarizable planar walls at distance d is considered. The walls are symmetrically charged with a uniform surface charge density, neutralized by mobile point counterions moving between them. The case of repulsive particle images is studied in the strong-coupling (SC) regime. Of interest is the dependence of the effective inter-wall interaction (pressure), mediated by the mobile counterions, as a function of the distance d. It is shown that previous virial SC single-particle theories work well at small d when the dielectric jump is small; for intermediate and large dielectric jumps they are inadequate even in the SC region. Here, we propose a Wigner-type SC theory based on harmonic deviations of particles from their ground-state monolayer or bilayer Wigner structures formed inside the space between the dielectric walls. Our Monte-Carlo simulations are in very good agreement with the Wigner SC predictions, even down to moderate coupling constants ($\Xi > 10$).

cond-mat.soft↗

arXiv2026

Accelerating charging dynamics of electric double-layer capacitors

Electric double-layer capacitors (EDLCs), consisting of an ionic fluid between two metallic electrodes, are electrochemical energy storage devices complementary to batteries, allowing for a faster charge/discharge. The charging dynamics in response to a voltage step features a variety of regimes and relaxation timescales, depending on the applied voltage and the various lengths characterizing the system, most importantly the inter-electrode distance and the Debye length over which electrostatic effects are screened in the electrolyte. Inspired by recent works on "shortcut to adiabaticity" in colloidal systems, here we investigate the possibility to control the charge and discharge of planar EDLCs using time-dependent voltages. Specifically, our aim is to achieve a full charge or discharge within a finite time shorter than their intrinsic relaxation timescales. Within the Poisson-Nernst-Planck model and the small-voltage regime, we derive time-dependent protocols that can eliminate an arbitrary number of relaxation modes. This permits to approach the equilibrium charged state within a finite time, that can be in practice an order of magnitude faster than the natural equilibration time. We illustrate the relevance and efficacy of the method on polynomial drivings and show that the surface charge density, charge-density profiles, and global deviation from equilibrium (quantified by a Kullback-Leibler-like divergence) can all be significantly accelerated, even for driving times comparable to or shorter than the natural RC time of the system.

cond-mat.soft↗

arXiv2024

Optimal control of levitated nanoparticles through finite-stiffness confinement

Optimal control of levitated nanoparticles subjected to thermal fluctuations is a challenging problem, both theoretically and experimentally. In this Letter, we compute the time-dependent harmonic confining potential that steers, in a prescribed time and with the minimum energetic cost, a Brownian particle between two assigned equilibrium states. We take full account of inertial effects, thus addressing the general underdamped dynamics, and, to address actual experimental conditions, the stiffness of the confining potential is required to be bounded. We carry out an experiment realizing the described protocol for an optically confined nanoparticle, which is shown to reach the target state within accuracy -- while spending less energy than other protocols with the same duration, significantly shorter than the characteristic relaxation time. The results presented here are expected to have relevant applications in the design of optimal devices, such as engines at the nanoscale.

cond-mat.stat-mech↗

arXiv2023

Fate of Boltzmann's breathers: Stokes hypothesis and anomalous thermalization

Boltzmann showed that in spite of momentum and energy redistribution through collisions, a rarefied gas confined in a isotropic harmonic trapping potential does not reach equilibrium; it evolves instead into a breathing mode where density, velocity and temperature oscillate. This counter-intuitive prediction is upheld by cold atoms experiments. Yet, are the breathers eternal solutions of the dynamics even in an idealized and isolated system? We show by a combination of hydrodynamic arguments and Molecular Dynamics simulations that an original dissipative mechanism is at work, where the minute and often neglected bulk viscosity eventually thermalizes the system, that thus reaches equilibrium.

cond-mat.stat-mech↗

arXiv2023

Self-diffusion in a strongly coupled non-neutral plasma

We propose a joint experimental and theoretical approach to measure the self-diffusion in a laser-cooled trapped ion cloud where part of the ions are shelved in a long-lived dark state. The role of the self-diffusion coefficient in the spatial organisation of the ions is deciphered, following from the good agreement between the experimental observations and the theoretical predictions. This comparison furthermore allows to deduce the temperature of the sample. Protocols to measure the self-diffusion coefficient are discussed, in regard with the control that can be reached on the relevant time scales through the dressing of the atomic levels by laser fields.

physics.atom-ph↗

arXiv2023

dsDNA persistence length with divalent ions

Finding a theoretical formula for the persistence length of polyelectrolytes for the whole experimental range of salt concentration is a long standing challenge. Using the Tethered Particle Motion technique, the double-stranded DNA persistence length is measured for four monovalent and divalent salts on a three-decade concentration range. The formula proposed by Trizac and Shen [EPL, 116 18007 (2016)] and extended to divalent ions fits the data. This formula mixes the high salt limit solution of the Poisson-Boltzmann equation together with the DNA charge renormalisation. Magnesium ions induce a fitted DNA radius smaller than the geometrical one, consistent with a site-specific binding.

cond-mat.soft↗

arXiv2023

Shortcuts to equilibrium with a levitated particle in the underdamped regime

We report on speeding up equilibrium recovery in the previously unexplored general case of the underdamped regime using an optically levitated particle. We accelerate the convergence towards equilibrium by an order of magnitude compared to the natural relaxation time. We then discuss the efficiency of the studied protocols, especially for a multidimensional system. These results pave the way for optimizing realistic nanomachines with application to sensing and developing efficient nano-heat engines.

cond-mat.stat-mech↗

arXiv2023

Singular relaxation of a random walk in a box with a Metropolis Monte Carlo dynamics

We study analytically the relaxation eigenmodes of a simple Monte Carlo algorithm, corresponding to a particle in a box which moves by uniform random jumps. Moves outside of the box are rejected. At long times, the system approaches the equilibrium probability density, which is uniform inside the box. We show that the relaxation towards this equilibrium is unusual: for a jump length comparable to the size of the box, the number of relaxation eigenmodes can be surprisingly small, one or two. We provide a complete analytic description of the transition between these two regimes. When only a single relaxation eigenmode is present, a suitable choice of the symmetry of the initial conditions gives a localizing decay to equilibrium. In this case, the deviation from equilibrium concentrates at the edges of the box where the rejection probability is maximal. Finally, in addition to the relaxation analysis of the master equation, we also describe the full eigen-spectrum of the master equation including its sub-leading eigen-modes.

cond-mat.stat-mech↗

arXiv2023

Poisson-Nernst-Planck charging dynamics of an electric double layer capacitor: symmetric and asymmetric binary electrolytes

A parallel plate capacitor containing an electrolytic solution is the simplest model of a supercapacitor, or electric double layer capacitor. Using both analytical and numerical techniques, we solve the Poisson-Nernst-Planck equations for such a system, describing the mean-field charging dynamics of the capacitor, when a constant potential difference is abruptly applied to its plates. Working at constant total number of ions, we focus on the physical processes involved in the relaxation and, whenever possible, give its functional shape and exact time constants. We first review and study the case of a symmetric binary electrolyte, where we assume the two ionic species to have the same charges and diffusivities. We then relax these assumptions and present results for a generic strong (i.e. fully dissociated) binary electrolyte. At low electrolyte concentration, the relaxation is simple to understand, as the dynamics of positive and negative ions appear decoupled. At higher electrolyte concentration, we distinguish several regimes. In the linear regime (low voltages), relaxation is multi-exponential, it starts by the build-up of the equilibrium charge profile and continues with neutral mass diffusion, and the relevant time scales feature both the average and the Nernst-Hartley diffusion coefficients. In the purely nonlinear regime (intermediate voltages), the initial relaxation is slowed down exponentially due to increased capacitance, while bulk effects become more and more evident. In the fully nonlinear regime (high voltages), the dynamics of charge and mass are completely entangled and, asymptotically, the relaxation is linear in time. We finally discuss non-ideal behavior in real capacitors and provide conditions for which mean-field is expected to hold.

cond-mat.soft↗

arXiv2023

Charging dynamics of electric double layer nanocapacitors in mean-field

An electric double layer capacitor (EDLC) stores energy by modulating the spatial distribution of ions in the electrolytic solution that it contains. We determine the mean-field time scales for planar EDLC relaxation to equilibrium, after a potential difference is applied. We tackle first the fully symmetric case, where positive and negative ionic species have same valence and diffusivity, and then the general, more complex, asymmetric case. Depending on applied voltage and salt concentration, different regimes appear, revealing a remarkably rich phenomenology relevant for nanocapacitors.

physics.chem-ph↗

arXiv2022

Control of Active Brownian Particles: An exact solution

Control of stochastic systems is a challenging open problem in statistical physics, with potential applications in a wealth of systems from biology to granulates. Unlike most cases investigated so far, we aim here at controlling a genuinely out-of-equilibrium system, the two dimensional Active Brownian Particles model in a harmonic potential, a paradigm for the study of self-propelled bacteria. We search for protocols for the driving parameters (stiffness of the potential and activity of the particles) bringing the system from an initial passive-like stationary state to a final active-like one, within a chosen time interval. The exact analytical results found for this prototypical system of self-propelled particles brings control techniques to a wider class of out-of-equilibrium systems.

cond-mat.stat-mech↗

arXiv2022

Ordered ground state configurations of the asymmetric Wigner bilayer system -- revisited: an unsupervised clustering algorithm analysis

We have re-analysed the rich plethora of ground state configurations of the asymmetric Wigner bilayer system that we had recently published in a related diagram of states [M. Antlanger \textit{et al.}, Phys. Rev. Lett. \textbf{117}, 118002 (2016)], comprising roughly 60~000 state points in the phase space spanned by the distance between the plates and the charge asymmetry parameter of the system. In contrast to this preceding contribution where the classification of the emerging structures was carried out ``by hand'', we have used this time machine learning concepts, notably based on a principal component analysis and a $k$-means clustering approach: using a 30-dimensional feature vector for each emerging structure (containing relevant information, such as the composition of the configuration as well as the most relevant order parameters) we were able to re-analyse these ground state configurations in a considerably more systematic and comprehensive manner than we could possibly do in the previously published classification scheme. Indeed we were now able to identify new structures in previously unclassified regions of the parameter space and could considerably refine the previous classification scheme, identifying thereby a rich wealth of new emerging ground state configurations. Thorough consistency checks confirm the validity of the newly defined diagram of states.

cond-mat.soft↗

arXiv2022

Metropolis Monte Carlo sampling: convergence, localization transition and optimality

Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis scheme. Analysing the relaxation properties of some model algorithms sufficiently simple to enable analytic progress, we show that the deviations from the target steady-state distribution can feature a localization transition as a function of the characteristic length of the attempted jumps defining the random walk. While the iteration of the Monte Carlo algorithm converges to equilibrium for all choices of jump parameters, the localization transition changes drastically the asymptotic shape of the difference between the probability distribution reached after a finite number of steps of the algorithm and the target equilibrium distribution. We argue that the relaxation before and after the localisation transition is respectively limited by diffusion and rejection rates.

cond-mat.stat-mech↗

arXiv2022

Shortcuts To Adiabaticity for L\'evy processes in harmonic traps

L\'evy stochastic processes, with noise distributed according to a L\'evy stable distribution, are ubiquitous in science. Focusing on the case of a particle trapped in an external harmonic potential, we address the problem of finding "shortcuts to adiabaticity": after the system is prepared in a given initial stationary state, we search for time-dependent protocols for the driving external potential, such that a given final state is reached in a given, finite time. These techniques, usually used for stochastic processes with additive Gaussian noise, are typically based on a inverse-engineering approach. We generalise the approach to the wider class of L\'evy stochastic processes, both in the overdamped and in the underdamped regime, by finding exact equations for the relevant characteristic functions in Fourier space.

cond-mat.stat-mech↗

arXiv2022

Accelerating the heat diffusion: fast thermal relaxation of a microcantilever

In most systems, thermal diffusion is intrinsically slow with respect to mechanical relaxation. We devise here a generic approach to accelerate the relaxation of the temperature field of a 1D object, in order to beat the mechanical time scales. This approach is applied to a micro-meter sized silicon cantilever, locally heated by a laser beam. A tailored driving protocol for the laser power is derived to quickly reach the thermal stationary state. The model is implemented experimentally yielding a significant acceleration of the thermal relaxation, up to a factor 30. An excellent agreement with the theoretical predictions is reported. This strategy allows a thermal steady state to be reached significantly faster than the natural mechanical relaxation.

physics.app-ph↗

arXiv2022

Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics

Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic equations of motion, introduces time into the description of thermodynamic processes -- which opens the way to fine control them. As a result, the field of finite-time thermodynamics of mesoscopic systems has blossomed. In this article, after introducing a few concepts of control for isolated mechanical systems evolving according to deterministic equations of motion, we review the different strategies that have been developed to realize finite-time state-to-state transformations in both over and underdamped regimes, by the proper design of time-dependent control parameters/driving. The systems under study are stochastic, epitomized by a Brownian object immersed in a fluid; they are thus strongly coupled to their environment playing the role of a reservoir. Interestingly, a few of those methods (inverse engineering, counterdiabatic driving, fast-forward) are directly inspired by their counterpart in quantum control. The review also analyzes the control through reservoir engineering. Besides the reachability of a given target state from a known initial state, the question of the optimal path is discussed. Optimality is here defined with respect to a cost function, a subject intimately related to the field of information thermodynamics and the question of speed limit. Another natural extension discussed deals with the connection between arbitrary states or non-equilibrium steady states. This field of control in stochastic thermodynamics enjoys a wealth of applications, ranging from optimal mesoscopic heat engines to population control in biological systems.

cond-mat.stat-mech↗

arXiv2022

Like-charge attraction at the nanoscale: ground-state correlations and water destructuring

Like-charge attraction, driven by ionic correlations, challenges our understanding of electrostatics both in soft and hard matter. For two charged planar surfaces confining counterions and water, we prove that even at relatively low correlation strength, the relevant physics is the ground-state one, oblivious of fluctuations. Based on this, we derive a simple and accurate interaction pressure, that fulfills known exact requirements and can be used as an effective potential. We test this equation against implicit-solvent Monte Carlo simulations and against explicit-solvent simulations of cement and several types of clays. We argue that water destructuring under nanometric confinement drastically reduces dielectric screening, enhancing ionic correlations. Our equation of state at reduced permittivity therefore explains the exotic attractive regime reported for these materials, even in absence of multivalent counterions.

cond-mat.soft↗

arXiv2021

One-dimensional Monte Carlo dynamics at zero temperature

We investigate, both analytically and with numerical simulations, a Monte Carlo dynamics at zero temperature, where a random walker evolving in continuous space and discrete time seeks to minimize its potential energy, by decreasing this quantity at each jump. The resulting dynamics is universal in the sense that it does not depend on the underlying potential energy landscape, as long as it admits a unique minimum; furthermore, the long time regime does not depend on the details of the jump distribution, but only on its behaviour for small jumps. We work out the scaling properties of this dynamics, as embodied by the walker probability density. Our analytical predictions are in excellent agreement with direct Monte Carlo simulations.

cond-mat.stat-mech↗