Stationary $1/f^{\alpha}$ noise in discrete models of the Kardar-Parisi-Zhang class

Rahul Chhimpa; Avinash Chand Yadav

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arXiv · 2603.18515

Stationary $1/f^{\alpha}$ noise in discrete models of the Kardar-Parisi-Zhang class

Rahul Chhimpa·Avinash Chand Yadav

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Abstract

In discrete models describing growing rough interfaces of the Kardar-Parisi-Zhang universality class, we examine height fluctuations at a fixed site as a function of time in the monolayer unit. For small systems, we show that it is possible to reach the stationary state. We compute the two-time autocorrelation and power spectra independently. The correlation function remains non-exponential and vanishes after a correlation time that diverges with system size. As a result, the power spectra display a lower cutoff that maintains constant power. In the nontrivial frequency regime, we observe $1/f^{\alpha}$-type scaling with the spectral exponent 5/3. Finite-size scaling reveals that the temporal correlation function follows a dynamic scaling. Our findings, supported by scaling-theoretical arguments, establish that the fluctuations are wide-sense stationary, implying applicability of the Wiener-Khinchin theorem.

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Rahul Chhimpa, Avinash Chand Yadav. 2026-03-19. Stationary $1/f^{\alpha}$ noise in discrete models of the Kardar-Parisi-Zhang class. https://arxiv.org/abs/2603.18515

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