Slow relaxation and aging kinetics for the driven lattice gas

Daquila, George L.; Täuber, Uwe C.

doi:10.1103/physreve.83.051107

Cited by 30 publications

(41 citation statements)

References 55 publications

(101 reference statements)

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“…The data are fully compatible with a numerical solution of the KPZ equation and directly test simple ageing (1) in the 1D KPZ class. All this, completely analogous to the EW and MH classes, confirms and strengthens earlier conclusions [23][24][25][26]30].…”

supporting

confidence: 77%

“…For the 1D KPZ class, the exponents z, β are exactly known [1], whereas the relation b = −2ζ/z = −2β follows from dynamical scaling [23,24]. Also, evidence for a growing length L(t) ∼ t 1/z [25,26] and estimates of λ C [23,24] have been reported [27]. However, no systematic test of the ageing scaling has been reported for the space-time correlation function, and no information exists at all for the response function R. These will be provided now.…”

mentioning

confidence: 99%

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Phenomenology of aging in the Kardar-Parisi-Zhang equation

2012

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supporting

confidence: 77%

mentioning

confidence: 99%

Phenomenology of aging in the Kardar-Parisi-Zhang equation

2012

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“…In fact, slow relaxations and aging are amongst the most distinct features of glasses, whose understanding presents an important problem in contemporary condensed matter physics. Much experimental and theoretical attention has been devoted to aging in the past decades, in a variety of fields, such as spin-glass (7-13), colloids (14,15), vortices in superconductors (16,17), and many others (18)(19)(20)(21)(22)(23).…”

mentioning

confidence: 99%

On relaxations and aging of various glasses

Amir

Oreg²,

Imry³

2012

Proc. Natl. Acad. Sci. U.S.A.

127

108

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Slow relaxation occurs in many physical and biological systems. "Creep" is an example from everyday life. When stretching a rubber band, for example, the recovery to its equilibrium length is not, as one might think, exponential: The relaxation is slow, in many cases logarithmic, and can still be observed after many hours. The form of the relaxation also depends on the duration of the stretching, the "waiting time." This ubiquitous phenomenon is called aging, and is abundant both in natural and technological applications. Here, we suggest a general mechanism for slow relaxations and aging, which predicts logarithmic relaxations, and a particular aging dependence on the waiting time. We demonstrate the generality of the approach by comparing our predictions to experimental data on a diverse range of physical phenomena, from conductance in granular metals to disordered insulators and dirty semiconductors, to the low temperature dielectric properties of glasses.nonequilibrium | slow dynamics | memory effects | 1/f noise P hysicists often take for granted that systems relax exponentially. Indeed, when a capacitor discharges, it will discharge exponentially, with a rate independent of the time it has been charged for. However, the relaxation of many systems in nature is far from exponential, as was noticed already in the 19th century by Weber (1). In many cases, the relaxation is logarithmic: Such relaxations have been experimentally observed in the decay of current in superconductors (2), current relaxation in metal-oxidesemiconductor field-effect transistor devices (3), mechanical relaxation of plant roots (4), volume relaxation of crumpling paper (5), and frictional strength (6), to name but a few. Fig. 1 shows experimental data for electron glasses and for crumpling a thin sheet, which are governed by extremely different physical processes, yet they display identical relaxation behavior, which is logarithmic over a strikingly broad time window.In these systems, in contrast to the capacitor example, the relaxation does depend on the time the system has been perturbed for-in the scientific jargon, this is referred to as "aging." In fact, slow relaxations and aging are amongst the most distinct features of glasses, whose understanding presents an important problem in contemporary condensed matter physics. Much experimental and theoretical attention has been devoted to aging in the past decades, in a variety of fields, such as spin-glass (7-13), colloids (14, 15), vortices in superconductors (16,17), and many others (18-23).Here, we study a generic model for aging and discuss several mechanisms yielding a broad distribution of relaxation rates. We demonstrate the generality of the model on four different experimental systems, measuring the dependence of the relaxation both on time t and on the "waiting time" t w , during which an external perturbation has been applied. We show how the following form of relaxations transpires: Sðt;t w Þ ∝ logð1 þ t w ∕tÞ ¼ logðt w ∕tÞ for t ≪ t w ; t w ∕t for t ≫ t w ;where S is the p...

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“…The height model corresponding to the TASEP (b = 0) is known to obey the Kardar-Parisi-Zhang (KPZ) equation [24] for which it is known that the dynamic exponent z = 3/2, the roughness exponent α = 2 − z = 1/2 and the growth exponent β = 1/3 (see also Appendix A), and therefore S(0, t) ∝ t −2/3 for large systems as indeed verified in recent numerical simulations [25]. Our objective here is to study the exclusion process with hole-dependent hop rates at the critical point and determine if the dynamics differ from that in the b = 0 case.…”

Section: Model a Jamming Transitionmentioning

confidence: 87%

“…In a recent work [21], this correlation function was calculated in the fluid phase and at the critical point using an exact expression for it. It was shown that at the critical point, the equal time correlation function decays as a power law with a continuously varying exponent, see (25) below. Here we give a simpler derivation of this result.…”

Section: Equal Time Correlation Function a Density-density Corrmentioning

confidence: 99%

Critical dynamics of the jamming transition in one-dimensional nonequilibrium lattice-gas models

Priyanka

Jain

2016

Phys. Rev. E

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We consider several one-dimensional driven lattice-gas models that show a phase transition in the stationary state between a high-density fluid phase in which the typical length of a hole cluster is of order unity and a low-density jammed phase where a hole cluster of macroscopic length forms in front of a particle. Using a hydrodynamic equation for an interface growth model obtained from the driven lattice-gas models of interest here, we find that in the fluid phase, the roughness exponent and the dynamic exponent that, respectively, characterize the scaling of the saturation width and the relaxation time of the interface with the system size are given by the Kardar-ParisiZhang exponents. However, at the critical point, we show analytically that when the equal time density-density correlation function decays slower than inverse distance, the roughness exponent varies continuously with a parameter in the hop rates but it is one half otherwise. Using these results and numerical simulations for the density-density autocorrelation function, we further find that the dynamic exponent z = 3/2 in all cases.

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Slow relaxation and aging kinetics for the driven lattice gas

Cited by 30 publications

References 55 publications

Phenomenology of aging in the Kardar-Parisi-Zhang equation

Phenomenology of aging in the Kardar-Parisi-Zhang equation

On relaxations and aging of various glasses

Critical dynamics of the jamming transition in one-dimensional nonequilibrium lattice-gas models

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