Spontaneous Relaxation in Generalized Oscillator Models with Glassy Dynamics

Ritort, Fèlix

doi:10.1021/jp037991y

Cited by 15 publications

(40 citation statements)

References 28 publications

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“…For example, glassy systems age in time driven by spontaneous heat fluxes to the environment, after being prepared in a metastable configuration [8]. Although several extensions of the FT [9][10][11][12] and generalized fluctuation-dissipation relations (GFDRs) [2][3][4]6] have been formulated for relaxing systems, the comparison between theory and experiments still lacks a clear interpretation.…”

mentioning

confidence: 99%

Fluctuations, linear response and heat flux of an aging system

Gomez-Solano¹,

Petrosyan²,

Ciliberto³

2012

EPL

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We measure the fluctuations of the position of a Brownian particle confined by an optical trap in an aging gelatin droplet after a fast quench. Its linear response to an external perturbation is also measured. We compute the spontaneous heat flux from the particle to the bath due to the nonequilibrium formation of the gel. We show that the mean heat flux is quantitatively related to the violation of the equilibrium fluctuation-dissipation theorem as a measure of the broken detailed balance during the aging process.

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confidence: 99%

Fluctuations, linear response and heat flux of an aging system

Gomez-Solano¹,

Petrosyan²,

Ciliberto³

2012

EPL

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“…Therefore, for a given asymptotic waiting time s the FD plot gives a straight line with negative slope equal to the inverse of the asymptotic effective temperature (27). In Fig.6 we represent the resulting asymptotic FD plot which has also been obtained before in the OM model 36 as a particular case. Straight FD plots are characteristic of the one-step behavior of structural glasses.…”

Section: Mode Effective Temperaturesmentioning

confidence: 65%

“…For this particular example we note that equation (39) is only defined for ǫ = ǫ 1 , ǫ 2 so it does not have a well defined threshold solution ǫ * . However, as we have already mentioned earlier, we can distinguish the two regions (35) and (36) corresponding to different signs of ∂w(ǫ,t) ∂t . This is shown in Fig.4 where we show the time evolution of w(ǫ, t) at zero temperature (30).…”

Section: A Mode-energy Density Relaxationmentioning

confidence: 69%

“…To investigate how different energy modes relax to equilibrium we introduce the mode-energy density (28), the mode-magnetization (44) and the mode-correlations and mode-responses (41,45). From the dynamical equations equations (30) we can prove the existence of time-dependent threshold located at ǫ * (s) separating two regions (I and II) characterized by the sign of the time derivative of the mode-energy density (35,36,37). Only the modes in region I satisfy the equipartition relation at the effective temperature Θ(s) (40).…”

Section: Summary Of Resultsmentioning

confidence: 99%

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Mode-dependent nonequilibrium temperature in aging systems

Garriga

Ritort

2005

Phys. Rev. E

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We introduce an exactly solvable model for glassy dynamics with many relaxational modes, each one characterized by a different relaxational time scale. Analytical solution of the aging dynamics at low temperatures shows that a nonequilibrium or effective temperature can be associated to each time scale or mode. The spectrum of effective temperatures shows two regions that are separated by an age-dependent boundary threshold. Region I is characterized by partially equilibrated modes that relax faster than the modes at the threshold boundary. Thermal fluctuations and time correlations for modes in region I show that those modes are in mutual thermal equilibrium at a unique age-dependent effective temperature ⍜͑s͒. In contrast, modes with relaxational time scales longer than that of modes at the threshold ͑region II͒ show diffusive properties and do not share the common temperature ⍜͑s͒. The shift of the threshold toward lower energy modes as the system ages, and the progressive shrinking of region II, determines how the full spectrum of modes equilibrates. As is usually done in experiments, we have defined a frequency-dependent effective temperature and we have found that all modes in region I are mutually equilibrated at the temperature ⍜͑s͒ independently of the probing frequency. The present model aims to explain transport anomalies observed in supercooled liquids in terms of a collection of structurally disordered and cooperative rearranging mesoscopic regions.

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“…The results for the leading parameters α, β, γ of the oscillator potential and for the energy eigenvalue of the first excited state are given by α = −0.899165, β = −0.003268, γ = 0.0000405, λ = 0.364335 (23) and the square distance from the minimum is l = 9.9 10 −7 . The minimum was found by employing the Minimizefunction implemented in Mathematica.…”

Section: B Construction Of An Anharmonic Hamiltonian and Functional mentioning

confidence: 99%

Non-analytic quantum oscillator image of complete replica symmetry breaking

Oppermann

Schenck

2012

Philosophical Magazine

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We describe the effect of replica symmetry breaking in the field distribution function P (h) of the T = 0 SK-model as the difference between a split Gaussian and the first excited state ψ1 of a weakly anharmonic oscillator with nonanalytic shift by means of the analogy P (h) ↔ |ψ 1 (x)|.New numerical calculations of the leading 100 orders of replica symmetry breaking (RSB) were performed in order to obtain P (h), employing the exact mapping between density of states ρ(E) of the fermionic SK-model and P (h) of the standard model, as derived by Perez-Castillo and Sherrington. Fast convergence towards a fixed point function ρ(E) for infinite steps of RSB is observed. A surprisingly small number of harmonic oscillator wave-functions suffices to represent this fixed point function. This allows to determine an anharmonic potential V (x) with nonanalytic shift, whose first excited state represents ρ(E) and hence P (h). The harmonic potential with unconventional shift V2(x) ∼ (|x| − x0) 2 = (x − x0 sign(x)) 2 yields already a very good approximation, since anharmonic couplings of V (x) − V2(x) ∼ |x| m , m > 2, decay rapidly with increasing m.We compare the pseudogap-forming effect of replica symmetry breaking, hosted by the fermionic SK-model, with the analogous effect in the Coulomb glass as designed by Davies-Lee-Rice and described by Müller-Pankov.PACS numbers: I. INTRODUCTIONThe Sherrington-Kirkpatrick (SK-) model 1 has been an extraordinary stimulating source for analytical and numerical studies in the physics of frustrated magnetism and in numerous interdisciplinary applications. Many relevant properties of the SK-model have been explored since its discovery 2-6 .Near the zero temperature limit and at T = 0, the model displays rather simple features but also analytically still unresolved behavior, and therefore remains challenging in our point of view.Along a particular line of theoretical analysis, on which the present article evolves, we searched for explicit analytical solutions deep in the ordered phase and particularly at zero temperature. The limit of zero temperature was recently described to accommodate two critical points related to the criticality of the hierarchical scheme of replica symmetry breaking (RSB) hosted by the SK-model 7-10 . In order to reveal this type of criticality, the finite-step discrete-RSB was utilized. Extreme high order calculations up to 200 orders and Padé-approximants allowed to analyze the limit towards infinite breaking analyzed by means of high-precision numerical work, renormalization group ideas, and scaling theory in addition. 7-10 . The scaling theory allowed to resolve the puzzle of noncommuting zero temperature limit and infinite-step limit of replica symmetry breaking 10 .In this article we present new numerical calculations which led us to a surprisingly simple modeling of the distribution of internal magnetic fields.Pioneering work on this local magnetic field distribution by Thomsen et al 4 presented various analytical limits and numerical studies (TAP theory, simula...

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Spontaneous Relaxation in Generalized Oscillator Models with Glassy Dynamics

Cited by 15 publications

References 28 publications

Fluctuations, linear response and heat flux of an aging system

Fluctuations, linear response and heat flux of an aging system

Mode-dependent nonequilibrium temperature in aging systems

Non-analytic quantum oscillator image of complete replica symmetry breaking

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