The Rise of the Shi

Pines, Yuri

doi:10.21313/hawaii/9780824832759.003.0006

Cited by 3 publications

(6 citation statements)

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“…This power law approach to stationarity in reversible reaction-diffusion systems was later verified through more elaborated approaches [20,21,22,23], through numerical simulations [24,25], and through some exactly solved models [26,27,28,29]. In addition, this power law behavior has been observed experimentally in excited-state proton transfer reactions [30,31,32]. All these studies demonstrate that the most important ingredient for aging, namely slow dynamics, is typically encountered in reversible reaction-diffusion systems.…”

Section: Introductionmentioning

confidence: 75%

Aging processes in reversible reaction-diffusion systems

Elgart

Pleimling

2008

Phys. Rev. E

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Reversible reaction-diffusion systems display anomalous dynamics characterized by a power-law relaxation toward stationarity. In this paper we study in the aging regime the nonequilibrium dynamical properties of some model systems with reversible reactions. Starting from the exact Langevin equations describing these models, we derive expressions for two-time correlation and autoresponse functions and obtain a simple aging behavior for these quantities. The autoresponse function is thereby found to depend on the specific nature of the chosen perturbation of the system.

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Section: Introductionmentioning

confidence: 75%

Aging processes in reversible reaction-diffusion systems

Elgart

Pleimling

2008

Phys. Rev. E

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“…All this points to a high degree of universality, suggesting that systems with reversible reactions form excellent candidates for the experimental study of aging properties in reaction-diffusion systems. No fine-tuning of the system parameters is needed in order to have slow dynamics, as demonstrated in experimental studies of excited-state proton transfer reactions [27,28,29]. As our theoretical findings point to a high robustness of the reported results, a future experimental verification of our predictions can be envisioned.…”

Section: Resultsmentioning

confidence: 57%

“…As discussed in many theoretical studies [16,17,18,19,20,21,22,23,24,25,26] and as verified in some experiments [27,28,29], systems with reversible chemical reactions are characterized by slow dynamics such that the particle densities approach their steadystate values with a power-law in time. More specifically, for the exactly solvable models without site restriction studied in [23,30] one finds that particle densities asymptotically behave like…”

Section: Particle Densitiesmentioning

confidence: 87%

“…This is, however, different for systems with reversible reactions, as these systems generically display power-law relaxation, independent of the values of the reaction and diffusion rates [16,17,18,19,20,21,22,23,24,25,26]. Studies of excited-state proton transfer reactions provided experimental verifications of this theoretically predicted behavior [27,28,29]. This of course makes the diffusion-limited systems with reversible reactions very attractive for a study of aging processes.…”

Section: Introductionmentioning

confidence: 99%

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Ageing processes in reversible reaction–diffusion systems: Monte Carlo simulations

Afzal¹,

Waugh²,

Pleimling³

2011

J. Stat. Mech.

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Reaction-diffusion systems with reversible reactions generically display power-law relaxation towards chemical equilibrium. In this work we investigate through numerical simulations aging processes that characterize the non-equilibrium relaxation. Studying a model which excludes multiple occupancy of a site, we find that the scaling behavior of the two-time correlation and response functions are similar to that discovered previously in an exactly solvable version with no restrictions on the occupation numbers. Especially, we find that the scaling of the response depends on whether the perturbation conserves a certain quantity or not. Our results point to a high degree of universality in relaxation processes taking place in diffusion-limited systems with reversible reactions.

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“…For a colloidal particle in a thermal environment, it is known that the velocity (and position, for a particle in a generic confining potential) equilibrates to the Maxwell-Boltzmann distribution and the relaxation occurs exponentially in time. However, there are many examples where a slower nonexponential relaxation is observed, such as in sub-diffusive processes [1], glassy dynamics, systems with initial condition drawn from heavy-tailed distributions [2], processes with resetting [3], reversible diffusion-controlled chemical reactions [4,5,6,7], and diffusion in a logarithmic potential [8]. In the present work, we consider another example where the system is connected to a heat bath localised in space.…”

Section: Introductionmentioning

confidence: 99%

Unusual equilibration of a particle in a potential with a thermal wall

Bhat¹,

Sabhapandit²,

Kundu³

et al. 2017

J. Stat. Mech.

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Abstract. We consider a particle in a one-dimensional box of length L with a Maxwell bath at one end and a reflecting wall at the other end. Using a renewal approach, as well as directly solving the master equation, we show that the system exhibits a slow power law relaxation with a logarithmic correction towards the final equilibrium state. We extend the renewal approach to a class of confining potentials of the form U (x) ∝ x α , x > 0, where we find that the relaxation is ∼ t −(α+2)/(α−2) for α > 2, with a logarithmic correction when (α + 2)/(α − 2) is an integer. For α < 2 the relaxation is exponential. Interestingly for α = 2 (harmonic potential) the localised bath can not equilibrate the particle. Unusual equilibration of a particle in a potential with a thermal wall 2 Figure 1. A point particle moves between a thermal reservoir kept at x = 0 and a reflecting wall at x = L. Whenever particle approaches the reservoir it renews its velocity and comes with velocity chosen from Rayleigh distribution while it gets reflected once it approaches the wall. Arrows with solid and dashed lines respectively indicate the velocity of the particle before and after collision, either with the reservoir on the left end or with the reflecting wall on right end of the cylinder.

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The Rise of the Shi

Cited by 3 publications

References 0 publications

Aging processes in reversible reaction-diffusion systems

Aging processes in reversible reaction-diffusion systems

Ageing processes in reversible reaction–diffusion systems: Monte Carlo simulations

Unusual equilibration of a particle in a potential with a thermal wall

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