Experimental study of the fluctuation dissipation relation during an aging process

Bellon, Ludovic; Ciliberto, S.

doi:10.1016/s0167-2789(02)00520-1

Cited by 73 publications

(100 citation statements)

References 23 publications

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“…The origin of this discrepancy is presently unclear. Other recent experiments by Ciliberto and coworkers [343,344] on Laponite, a synthetic clay of charged particles that have the shape of a disc, show strong FD violations. If let evolve inside water, Laponite generates a colloid glass consisting of a packed irregular structure of disks due to the complex pattern of quadrupolar interactions.…”

Section: Qfdt: the Experimental Evidencementioning

confidence: 85%

Violation of the fluctuation–dissipation theorem in glassy systems: basic notions and the numerical evidence

Crisanti

Ritort

2003

J. Phys. A: Math. Gen.

359

595

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Abstract. This review reports on the research done during the past years on violations of the fluctuation-dissipation theorem (FDT) in glassy systems. It is focused on the existence of a quasi-fluctuation-dissipation theorem (QFDT) in glassy systems and the currently supporting knowledge gained from numerical simulation studies.It covers a broad range of non-stationary aging and stationary driven systems such as structural-glasses, spin-glasses, coarsening systems, ferromagnetic models at criticality, trap models, models with entropy barriers, kinetically constrained models, sheared systems and granular media. The review is divided into four main parts: 1) An introductory section explaining basic notions related to the existence of the FDT in equilibrium and its possible extension to the glassy regime (QFDT), 2) A description of the basic analytical tools and results derived in the framework of some exactly solvable models, 3) A detailed report of the current evidence in favour of the QFDT and 4) A brief digression on the experimental evidence in its favour. This review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the QFDT as well as for the more expert readers who may be interested in more specific results.

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Section: Qfdt: the Experimental Evidencementioning

confidence: 85%

Violation of the fluctuation–dissipation theorem in glassy systems: basic notions and the numerical evidence

Crisanti

Ritort

2003

J. Phys. A: Math. Gen.

359

595

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“…In other cases, for instance when the diffusing particle evolves in an aging medium such as a glassy colloidal suspension of Laponite [1]- [3], another equation of motion has to be used. We shall derive such an equation…”

Section: Equation Of Motion Of a Particle Linearly Coupled To An Out mentioning

confidence: 99%

Anomalous diffusion of a particle in an aging medium

Pottier

Mauger

2004

Physica A: Statistical Mechanics and its Applications

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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 |ω| δ−1 at small frequencies, with 0 < δ < 2. The aging properties of the medium are encoded in a frequency dependent effective temperature T eff. (ω). The latter is modelized by a function proportional to |ω| α at small frequencies, with α < 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 δ as it would be the case in a thermal bath, but also to the exponent α characterizing the density of slow modes.

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“…This second linear regime has a slope reduced by a violation factor, X , relative to equilibrium, and is described as having an effective temperature, T eff = T /X . Thus far, experiments studying the breakdown of the FDR in structural and soft colloidal glasses have focused on the quasi-equilibrium regime with t w > t − t w , and have given a range of results that have found strong [18][19][20] , weak 21 or nonexistent 22 FDR violations. The strong-ageing regime has been difficult to access in these systems, owing largely to instrumental and statistical challenges of measuring thermal noise at the very low frequencies required.…”

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confidence: 99%

Nanoscale non-equilibrium dynamics and the fluctuation–dissipation relation in an ageing polymer glass

Oukris

Israeloff

2009

Nature Phys

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Response functions 1 and fluctuations 2 measured locally in complex materials should equally well characterize mesoscopic-scale dynamics. The fluctuation-dissipation relation (FDR) relates the two in equilibrium, a fact used regularly, for example, to infer mechanical properties of soft matter from the fluctuations in light scattering 3 . In slowly evolving non-equilibrium systems, such as ageing spin 4,5 and structural glasses 6,7 , sheared soft matter 8 and active matter 9 , a form of FDR has been proposed in which an effective temperature 10 , T eff , replaces the usual temperature, and universal behaviour is found in mean-field models 10,11 and simulations 6-8,12 . Thus far, only experiments on spin-glasses 13 and liquid crystals 14 have succeeded in accessing the strong-ageing regime, where T eff > T and possible scaling behaviour are expected. Here we test these ideas through measurements of local dielectric response and polarization noise in an ageing structural glass, polyvinyl acetate. The relaxation-time spectrum, as measured by noise, is compressed, and by response, is stretched, relative to equilibrium, requiring an effective temperature with a scaling behaviour similar to that of certain mean-field spin-glass models.The FDR expresses the equilibrium thermal fluctuations of an observable, O, in terms of available thermal energy, k B T (where k B is the Boltzmann constant), and the linear response of that observable to an applied field, F (ref. 10). It also relates the time (t ) dependence of the fluctuations, found in the autocorrelation function, C(t ) = δO(t + t )δO(t ) t , and the time-dependent susceptibility, χ (t ) = O(t )/F , where F is applied at t = 0. In equilibrium, C(t ) should contain the same information about the dynamics that is found in χ (t ), such as the spectrum of relaxation times. This is seen clearly in plotting χ (t ) versus C(t ) and obtaining a straight line, with a negative slope inversely proportional to temperature 10 . Deviations from the FDR have been intensively studied theoretically in ageing or driven glassy systems, both on the macroscale 8,10 and nanoscale 12 . Ageing occurs in glassy materials that have been quenched from high to low temperature. During ageing, the response functions depend both on time, t , and on the age of the system since the quench, t w . However, χ (t , t w ) and C(t , t w ) need not have the same dependence. This can be understood conceptually by viewing ageing dynamics as hopping on a tilted energy landscape 11 : energy-lowering transitions cause more rapid decorrelation than is possible by thermal energy alone. Prominent glass-transition models 15 place fragile structural glasses 6,16 in the same universality class as mean-field p-spin models with single-step replica symmetry breaking 17 . In such models 10 and simulations of structural glasses 7 , the χ (t ,t w ) versus C(t ,t w ) asymptotically collapse (with increasing t w ) to a single scaling Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA. *e-mail: n...

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Experimental study of the fluctuation dissipation relation during an aging process

Cited by 73 publications

References 23 publications

Violation of the fluctuation–dissipation theorem in glassy systems: basic notions and the numerical evidence

Violation of the fluctuation–dissipation theorem in glassy systems: basic notions and the numerical evidence

Anomalous diffusion of a particle in an aging medium

Nanoscale non-equilibrium dynamics and the fluctuation–dissipation relation in an ageing polymer glass

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