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

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

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

Sémantique et noémique

La distinción fundamental entre "sème" y noème es la siguiente: = el "sème" es el rasgo distintivo semántico de un "séméme", relativo a un pequeño conjunto de términos realmente disponibles y utilizables probablemente por el hablante en una circunstancia dada de comunicación. El "noéme" es un rasgo de sentido planteado independientemente de cualquier lengua natural. Es absoluto (y no relativo a un conjunto) y su existencia será decidida por el analista. Naturalmente, el lingüista ha creado los "noémes" sobre la base de una experiencia que teine de las lenguas naturales. Pero no obtiene automáticamente los "sémes" genéricos (o de clase), aunque la afinidad sea evidente.The fundamental distinction between "sème" and "noèm" is the following: the "sème" is the hallmark of a "séméme semantic", relating to a small set of terms actually available and usable probably by the speaker in a given circumstance of communication. The "noéme" is a trait of sense raised independently of any natural language. It's absolute and its existence will be determined by the analyst. Naturally, the linguist has created the "noémes" on the basis of an experience that he has of natural languages. But not automatically it obtains the "generic" sémes (or class), although the affinity is evident.notPeerReviewe

The Environment and Directed Technical Change: Comment

This paper discusses the growth model with environmental constraints recently presented in (Acemoglu et al., 2011) which focuses on the redirection of technical change by climate policies with research subsidies and a carbon tax. First, Acemoglu et al.'s model and chosen parameters yield numerical results that do not support the conclusion that ambitious climate policies can be conducted “without sacrificing (much or any) long-run growth”. Second, they select unrealistic key parameters for carbon sinks and elasticity of substitution. We find that more realistic parameters lead to very different results. Third, the model leads to an unrealistic conclusion when used to analyse endogenous growth, suggesting specification problems.Technological Change, Endogenous Growth, Climate, Energy Substitutability