arXiv subjects

Christian Maes

Publications and source records attributed to Christian Maes.

At least 55 records · Page 3Linked to original sources

arXiv2022

Photon frequency diffusion process

We introduce a stochastic multi-photon dynamics on reciprocal space. Assuming isotropy, we derive the diffusion limit for a tagged photon to be a nonlinear Markov process on frequency. The nonlinearity stems from the stimulated emission. In the case of Compton scattering with thermal electrons, the limiting process describes the dynamical fluctuations around the Kompaneets equation. More generally, we construct a photon frequency diffusion process which enables to include nonequilibrium effects. Modifications of the Planck Law may thus be explored, where we focus on the low-frequency regime.

cond-mat.stat-mech↗

arXiv2022

On the derivation of the Kompaneets equation

The relaxation of a photon bath to thermal equilibrium via Compton scattering with electrons is described in the Kompaneets equation (1956). The equation is mostly known from studies of astrophysical plasmas, for its convergence to the Planck distribution and for possible corrections to that Planck law in the cosmic microwave background, most notably from the Sunyaev-Zeldovich effect. We revisit its derivation emphasizing its structure as a Kramers-Moyal diffusion approximation to the quantum Boltzmann equation or Master equation with stimulated emission. We do not assume that the Planck law is stationary in performing the continuum approximation but we emphasize the necessity of the flux or Møller factor to arrive at a continuity equation. On the other hand, the structure allows more general assumptions than originally envisioned by Kompaneets.

astro-ph.CO↗

arXiv2022

Inducing a bound state between active particles

We show that two active particles can form a bound state by coupling to a driven nonequilibrium environment. We specifically investigate the case of two mutually noninteracting run-and-tumble probes moving on a ring, each in short-range interaction with driven colloids. Under conditions of time-scale separation, these active probes become trapped in bound states. In fact, the bound state appears at high enough persistence (low effective temperature). From the perspective of a co-moving frame, where colloids are in thermal equilibrium and the probes are active and driven, an appealing analogy appears with Cooper pairing, as electrons can be viewed as run-and-tumble particles in a pilot-wave picture.

cond-mat.soft↗

arXiv2022

Diffraction and interference with run-and-tumble particles

Run-and-tumble particles, frequently considered today for modeling bacterial locomotion, naturally appear outside a biological context as well, e.g. for producing waves in the telegraph process. Here, we use a wave function to drive their propulsion and tumbling. Such quantum-active motion realizes a jittery motion of Dirac electrons (as in the famous Zitterbewegung): the Dirac electron is a run-and-tumble particle, where the tumbling is between chiralities. We visualize the trajectories in diffraction and double slit experiments for electrons. In particular, that yields the time-of-arrival statistics of the electrons at the screen. Finally, we observe that away from pure quantum guidance, run-and-tumble particles with suitable spacetime-dependent parameters produce an interference pattern as well.

cond-mat.stat-mech↗

arXiv2021

Wave mechanics for gravity with point-particles

We consider non-relativistic point-particles coupled to Einstein gravity and their canonical quantization. From the resulting Wheeler-DeWitt wave equation we determine a quantum version of geometrodynamics, where the coupled evolution of particle positions and 3-metric is guided by the wave function. We find that this quantum dynamics implies a quantum extension of the Einstein equations. The conserved energy-momentum tensor now contains a quantum contribution. This conceptually-simple set up is promising both for deriving semiclassical and weak field approximations to the quantum Einstein equations and is thus important for the development of quantum corrections to computational general relativity.

gr-qc↗

arXiv2020

Active gating: rocking diffusion channels

When the contacts of an open system flip between different reservoirs, the resulting nonequilibrium shows increased dynamical activity. We investigate such active gating for one-dimensional symmetric (SEP) and asymmetric (ASEP) exclusion models where the left/right boundary rates for entrance and exit of particles are exchanged at random times. Such rocking makes SEP spatially symmetric and on average there is no boundary driving; yet the entropy production increases in the rocking rate. For ASEP a non-monotone density profile can be obtained with particles clustering at the edges. In the totally asymmetric case, there is a bulk transition to a maximal current phase as the rocking exceeds a finite threshold, depending on the boundary rates. We study the resulting density profiles and current as functions of the rocking rate.

cond-mat.stat-mech↗

arXiv2020

On a possible nonequilibrium imprint in the cosmic background at low frequencies

The cosmic background radiation has been observed to deviate from the Planck law expected from a blackbody at $\sim$ 2.7 K at frequencies below $\sim 3$ GHz. We discuss the abundance of the low-energy photons from the perspective of nonequilibrium statistical mechanics. We propose a mechanism of stochastic frequency-diffusion, the counterpart to stochastic acceleration for charged particles in a turbulent plasma, to modify the standard Kompaneets equation. The resulting violation of the Einstein relation allows to take advantage of low-frequency localization and finally leads to photon cooling. The new equation predicts a frequency distribution in agreement with the absolute temperature measurements of the cosmic background radiation down to about 20 MHz, for which we offer here an updated compilation. In that sense, the so called 'space roar' we observe today is interpreted as a nonequilibrium echo of the early universe, and of nonequilibrium conditions in the primordial plasma more specifically.

astro-ph.CO↗

arXiv2020

Local detailed balance

We review the physical meaning and mathematical implementation of the condition of local detailed balance for a class of nonequilibrium mesoscopic processes. A central concept is that of fluctuating entropy flux for which the steady average gives the mean entropy production rate. We repeat how local detailed balance is essentially equivalent to the widely discussed fluctuation relations for that entropy flux and hence is at most "only half of the story."

cond-mat.stat-mech↗

arXiv2020

Pushing run-and-tumble particles through a rugged channel

We analyze the case of run-and-tumble particles pushed through a rugged channel both in the continuum and on the lattice. The current characteristic is non-monotone in the external field with (1) the appearance of a current and nontrivial density profile even at zero field for asymmetric obstacles, (2) the current decreasing with persistence at small field and increasing with persistence at large field. Activity in terms of self-propulsion increases the maximal current and postpones dying. We give an effective theoretical description with wider validity.

cond-mat.stat-mech↗

arXiv2020

Fluctuating motion in an active environment

We derive the fluctuation dynamics of a probe in weak coupling with a "living" medium, modeled as particles undergoing an active Ornstein-Uhlenbeck dynamics. Nondissipative corrections to the fluctuation-dissipation relation are written out explicitly in terms of time-correlations in the active medium. A first term changes the inertial mass of the probe, as a consequence of the persistence of the active medium. A second correction modifies the friction kernel. The resulting generalized Langevin equation benchmarks the motion induced on probes immersed in active versus passive media. The derivation uses nonequilibrium response theory.

cond-mat.soft↗

arXiv2020

Statistical mechanical foundation of Weber-Fechner laws

Even though the phenomenological relations between perception and stimulus have been firmly established, a theoretical argument for Weber's and Fechner's law in terms of relevant models or from statistical physics is largely missing. We present such a discussion in terms of response theory for nonequilibrium systems, where the induced displacement or current, which stands for the perceived stimulus, crucially depends on the change in time-symmetric reactivities. Stationary nonequilibria may indeed generate extra currents by changing the dynamical activity. The argument finishes by understanding how the extra dynamical activity logarithmically encodes the actual stimulus.

cond-mat.stat-mech↗

arXiv2020

Response theory: a trajectory-based approach

We collect recent results on deriving useful response relations also for nonequilibrium systems. The approach is based on dynamical ensembles, determined by an action on trajectory space. (Anti)Symmetry under time-reversal separates two complementary contributions in the response, one entropic the other frenetic. Under time-reversal invariance of the unperturbed reference process, only the entropic term is present in the response, giving the standard fluctuation-dissipation relations in equilibrium. For nonequilibrium reference ensembles, the frenetic term contributes essentially and is responsible for new phenomena. We discuss modifications in the Sutherland-Einstein relation, the occurence of negative differential mobilities and the saturation of response. We also indicate how the Einstein relation between noise and friction gets violated for probes coupled to a nonequilibrium environment. We end with some discussion on the situation for quantum phenomena, but the bulk of the text concerns classical mesoscopic (open) systems. The choice of many simple examples is trying to make the notes pedagogical, to introduce an important area of research in nonequilibrium statistical mechanics.

cond-mat.stat-mech↗

arXiv2020

Active velocity processes with suprathermal stationary distributions and long-time tails

When a particle moves through a spatially-random force field, its momentum may change at a rate which grows with its speed. Suppose moreover that a thermal bath provides friction which gets weaker for large speeds, enabling high-energy localization. The result is a unifying framework for the emergence of heavy tails in the velocity distribution, relevant for understanding the power-law decay in the electron velocity distribution of space plasma or more generally for explaining non-Maxwellian behavior of driven gases. We also find long-time tails in the velocity autocorrelation, indicating persistence at large speeds for a wide range of parameters and implying superdiffusion of the position variable.

cond-mat.stat-mech↗

arXiv2020

Cosmic acceleration from quantum Friedmann equations

We consider a simplified model of quantum gravity using a mini-superspace description of an isotropic and homogeneous universe with dust. We derive the corresponding Friedmann equations for the scale factor, which now contain a dependence on the wave function. We identify wave functions for which the quantum effects lead to a period of accelerated expansion that is in agreement with the apparent evolution of our universe, without introducing a cosmological constant.

gr-qc↗

arXiv2019

Nonequilibrium calorimetry

We consider stationary driven systems in contact with a thermal equilibrium bath. There is a constant (Joule) heat dissipated from the steady system to the environment as long as all parameters are unchanged. As a natural generalization from equilibrium thermodynamics, the nonequilibrium heat capacity measures the excess in that dissipated heat when the temperature of the thermal bath is changed. To improve experimental accessibility we show how the heat capacity can also be obtained from the response of the instantaneous heat flux to small periodic temperature variations.

cond-mat.stat-mech↗

arXiv2019

Frenesy: time-symmetric dynamical activity in nonequilibria

We review the concept of dynamical ensembles in nonequilibrium statistical mechanics as specified from an action functional or Lagrangian on spacetime. There, under local detailed balance, the breaking of time-reversal invariance is quantified via the entropy flux, and we revisit some of the consequences for fluctuation and response theory. Frenesy is the time-symmetric part of the path-space action with respect to a reference process. It collects the variable quiescence and dynamical activity as function of the system's trajectory, and as has been introduced under different forms in studies of nonequilibria. We discuss its various realizations for physically inspired Markov jump and diffusion processes and why it matters a good deal for nonequilibrium physics. This review then serves also as an introduction to the exploration of frenetic contributions in nonequilibrium phenomena.

cond-mat.stat-mech↗

arXiv2019

Nonequilibrium corrections to gradient flow

The force on a probe induced by a nonequilibrium medium is in general nongradient. We detail the mechanism of that feature via nonequilibrium response theory. The emergence of nongradient forces is due to a systematic "twist" of the excess frenesy with respect to the entropy flux, in response to changes in the coupling or in the position of the probe in the nonequilibrium medium.

cond-mat.stat-mech↗

arXiv2019

Glassy states: the free Ising model on a tree

We consider the ferromagnetic Ising model on the Cayley tree and we investigate the decomposition of the free state into extremal states below the spin glass temperature. We show that this decomposition has uncountably many components. The tail observable showing that the free state is not extremal is related to the Edwards-Anderson parameter, measuring the variance of the (random) magnetization obtained from drawing boundary conditions from the free state.

cond-mat.stat-mech↗