Anomalous diffusion of a particle in an aging medium

We report new results about the anomalous diffusion of a particle in an aging medium. For each given age, the quasi-stationary particle velocity is governed by a generalized Langevin equation with a frequency-dependent friction coefficient proportional to $|\omega|^{\delta-1}$ at small frequencies, with $0<\delta<2$. The aging properties of the medium are encoded in a frequency dependent effective temperature $T_{\rm eff.}(\omega)$. The latter is modelized by a function proportional to $|\omega|^\alpha$ at small frequencies, with $\alpha<0$, thus allowing for the medium to have a density of slow modes proportionally larger than in a thermal bath. Using asymptotic Fourier analysis, we obtain the behaviour at large times of the velocity correlation function and of the mean square displacement. As a result, the anomalous diffusion exponent in the aging medium appears to be linked, not only to $\delta$ as it would be the case in a thermal bath, but also to the exponent $\alpha$ characterizing the density of slow modes

Aging properties of an anomalously diffusing particle

We report new results about the two-time dynamics of an anomalously diffusing classical particle, as described by the generalized Langevin equation with a frequency-dependent noise and the associated friction. The noise is defined by its spectral density proportional to $\omega^{\delta-1}$ at low frequencies, with $0<\delta<1$ (subdiffusion) or $1<\delta<2$ (superdiffusion). Using Laplace analysis, we derive analytic expressions in terms of Mittag-Leffler functions for the correlation functions of the velocity and of the displacement. While the velocity thermalizes at large times (slowly, in contrast to the standard Brownian motion case $\delta=1$), the displacement never attains equilibrium: it ages. We thus show that this feature of normal diffusion is shared by a subdiffusive or superdiffusive motion. We provide a closed form analytic expression for the fluctuation-dissipation ratio characterizing aging.Comment: 15 page

Quantum fluctuation-dissipation theorem: a time domain formulation

A time-domain formulation of the equilibrium quantum fluctuation-dissipation theorem (FDT) in the whole range of temperatures is presented. In the classical limit, the FDT establishes a proportionality relation between the dissipative part of the linear response function and the derivative of the corresponding equilibrium correlation function. At zero temperature, the FDT takes the form of Hilbert transform relations between the dissipative part of the response function and the corresponding symmetrized equilibrium correlation function, which allows to establish a connection with analytic signal theory. The time-domain formulation of the FDT is especially valuable when out-of-equilibrium dynamics is concerned, as it is for instance the case in the discussion of aging phenomena.Comment: 18 TeX pages, 1 Postscript figure, submitted to Physica

Out of equilibrium generalized Stokes-Einstein relation: determination of the effective temperature of an aging medium

We analyze in details how the anomalous drift and diffusion properties of a particle evolving in an aging medium can be interpreted in terms of an effective temperature of the medium. From an experimental point of view, independent measurements of the mean-square displacement and of the mobility of a particle immersed in an aging medium such as a colloidal glass give access to an out of equilibrium generalized Stokes-Einstein relation, from which the effective temperature of the medium can eventually be deduced. We illustrate the procedure on a simple model with power-law behaviours.Comment: 15 page

Le climato-scepticisme Réflexions sur la confusion des genres

International audienceThe analysis examines the socio-psychological mechanisms underlying the dimate-sceptical position. Pottier distinguishes between two elements in the debate on climate change: a "diagnostic" component, induding the observation of the warming of the planet, its causes (the emission of greenhouse gases) and its possible consequences (a scenario tending towards large-scale dimatic upheavals), and a "prescriptive" part which, taking account of the diagnosis, proposes political measures and relates not to scientific observations but to a moral evaluation of the situation. After reminding us of what "fuels" the debate (the element of uncertainty which, Pottier argues, can relate only to the vision of the likely future that emerges from the observation of the facts, not to the description of the facts observed), he shows us that dimate-sceptical arguments arise out of a confusion between diagnosis and prescription: it is because they reject the need for, or the content of, climate policies that they corne to deny the scientific reality of climate change, shifting the ground of the debate and veering deeper into error. This posture is ail the more harmful for being widely echoed in the media, tending to add a touch more confusion to the information available to the public: "Citizens' perceptions of contemporary issues are skewed in favour of those interests that would be seriously impacted by a campaign against greenhouse emissions.".L'analyse examine les ressorts sociopsychologiques du discours climato-sceptique. L'auteur distingue deux éléments dans le débat sur le changement climatique : une partie " diagnostic " comprenant l'observation du réchauffement de la planète, ses causes (l'émission de gaz à effet de serre) et ses conséquences possibles (scénario tendanciel de bouleversements climatiques de grande ampleur) ; et une partie " prescription " qui, tenant compte du diagnostic, propose des mesures politiques et relève non plus d'observations scientifiques mais d'une appréciation morale. Après un rappel de ce qui alimente le débat (la part d'incertitude qui ne peut concerner que la vision prospective découlant de l'observation des faits, et non la qualification des faits observés), Antonin Pottier montre bien que les thèses climato-sceptiques relèvent d'une confusion entre le diagnostic et la prescription : c'est parce qu'ils refusent la nécessité ou le contenu des politiques climatiques qu'ils en viennent à dénier la réalité scientifique du changement climatique, déplaçant le débat et s'enfonçant dans l'erreur. Une posture d'autant plus dommageable qu'elle trouve un écho médiatique important tendant à embrouiller un peu plus les informations à la disposition de l'opinion publique : " La perception des enjeux contemporains par le citoyen est entravée, au profit des intérêts que fragiliserait une lutte contre les émissions de gaz à effet de serre.

Aging effects in the quantum dynamics of a dissipative free particle: non-ohmic case

We report new results related to the two-time dynamics of the coordinate of a quantum free particle, damped through its interaction with a fractal thermal bath (non-ohmic coupling $\sim\omega^\delta$ with $0<\delta<1$ or $1<\delta<2)$. When the particle is localized, its position does not age. When it undergoes anomalous diffusion, only its displacement may be defined. It is shown to be an aging variable. The finite temperature aging regime is self-similar. It is described by a scaling function of the ratio ${t_w/\tau}$ of the waiting time to the observation time, as characterized by an exponent directly linked to $\delta$.Comment: 4 pages, 3 figures, submitted to PR

Grammaire, lexique et typologie

Enunciators have a wide range of solutions available when they wish to express something in their language. Some of the categorisations they wish to produce take the form of bound morphemes (affixes: as in French re-diffus-ion-s) or morphologies that are free-standing to some extent (French: a chanté, aurait pu chanter). This onomasiological approach is essential in the study of language mechanisms and evolutionary processes. The semasiological approach —the one that brings the receiver into play— tends rather towards studying how to settle issues of interpretative choice, with less impact on typological considerations