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Characteristic Sign Renewals of Kardar-Parisi-Zhang Fluctuations
Statistical Mechanics · Submitted 10 Sep 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Thus, we obtain a new type of ergodicity breaking for such systems with many-body interactions.
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The abstract, sentence by sentence
Tracking the sign of fluctuations governed by the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) universality class, we show, both experimentally and numerically, that its evolution has an unexpected link to a simple stochastic model called the renewal process, studied in the context of aging and ergodicity breaking. Although KPZ and the renewal process are fundamentally different in many aspects, we find remarkable agreement in some of the time correlation properties, such as the recurrence time distributions and the persistence probability, while the two systems can be different in other properties. Moreover, we find inequivalence between long-time and ensemble averages in the fraction of time occupied by a specific sign of the KPZ-class fluctuations. The distribution of its long-time average converges to nontrivial broad functions, which are found to differ significantly from that of the renewal process, but instead be characteristic of KPZ. Thus, we obtain a new type of ergodicity breaking for such systems with many-body interactions. Our analysis also detects qualitative differences in time-correlation properties of circular and flat KPZ-class interfaces, which were suggested from previous experiments and simulations but still remain theoretically unexplained.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Tracking the sign of fluctuations governed by the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) universality class, we show, both experimentally and numerically, that its evolution has an unexpected link to a simple stochastic model called the renewal process, studied in the context of aging and ergodicity breaking. | contribution 0.75 | 0.96 | 0.56 | asserted 1.00 |
| s1 | Although KPZ and the renewal process are fundamentally different in many aspects, we find remarkable agreement in some of the time correlation properties, such as the recurrence time distributions and the persistence probability, while the two systems can be different in other properties. | result 0.99 | 0.94 | 0.20 | asserted 1.00 |
| s2 | Moreover, we find inequivalence between long-time and ensemble averages in the fraction of time occupied by a specific sign of the KPZ-class fluctuations. | result 1.00 | 0.96 | 0.16 | asserted 1.00 |
| s3 | The distribution of its long-time average converges to nontrivial broad functions, which are found to differ significantly from that of the renewal process, but instead be characteristic of KPZ. | result 1.00 | 0.95 | 0.17 | asserted 1.00 |
| s4 | Thus, we obtain a new type of ergodicity breaking for such systems with many-body interactions. | interpretation 0.94 | 0.90 | 0.34 | asserted 1.00 |
| s5 | Our analysis also detects qualitative differences in time-correlation properties of circular and flat KPZ-class interfaces, which were suggested from previous experiments and simulations but still remain theoretically unexplained. | result 0.88 | 0.84 | 0.07 | asserted 0.89 |
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Original abstract
Tracking the sign of fluctuations governed by the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) universality class, we show, both experimentally and numerically, that its evolution has an unexpected link to a simple stochastic model called the renewal process, studied in the context of aging and ergodicity breaking. Although KPZ and the renewal process are fundamentally different in many aspects, we find remarkable agreement in some of the time correlation properties, such as the recurrence time distributions and the persistence probability, while the two systems can be different in other properties. Moreover, we find inequivalence between long-time and ensemble averages in the fraction of time occupied by a specific sign of the KPZ-class fluctuations. The distribution of its long-time average converges to nontrivial broad functions, which are found to differ significantly from that of the renewal process, but instead be characteristic of KPZ. Thus, we obtain a new type of ergodicity breaking for such systems with many-body interactions. Our analysis also detects qualitative differences in time-correlation properties of circular and flat KPZ-class interfaces, which were suggested from previous experiments and simulations but still remain theoretically unexplained.
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3 arXiv papers cite this in 8 sentences
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Cites it as support 1 paper
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Further, other experiments also reveal that time averages of observables such as occupation time and intensity of fluorescence fail to converge to a constant in some non-equilibrium systems [ref] .
Distributional Behavior of Diffusion Coefficients Obtained by Single Trajectories in Annealed Transit Time Model · Introduction · 0.96
What it cites
Cites as background 1 paper
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a prominent nonequilibrium class, ruling diverse kinds of nonlinear fluctuations in growing interfaces [ref] , driven particle systems [ref] , fluctuating hydrodynamics [ref] , and so on.
Fluctuating hydrodynamics approach to equilibrium time correlations for anharmonic chains · Introduction · 0.98
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