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The term 'KPZ' stands for the initials of three physicists, namely Kardar, Parisi and Zhang, which, in 1986 conjectured the existence of universal scaling behaviours for many random growth processes in the plane. A process is said to belong…

Probability · Mathematics 2024-10-11 Pantelis Tassopoulos

We compute the non-universal constants in the KPZ equation in one dimension, in terms of the thermodynamical quantities associated to the underlying microscopic dynamics. In particular, we derive the second-order Einstein relation $\lambda…

Probability · Mathematics 2015-06-22 Patricia Gonçalves , Milton Jara

The power spectrum of interface fluctuations in the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) universality class is studied both experimentally and numerically. The $1/f^\alpha$-type spectrum is found and characterized through a set of…

Statistical Mechanics · Physics 2017-06-09 Kazumasa A. Takeuchi

Revealing universal behaviors is a hallmark of statistical physics. Phenomena such as the stochastic growth of crystalline surfaces, of interfaces in bacterial colonies, and spin transport in quantum magnets all belong to the same…

The short-time evolution of a growing interface is studied analytically and numerically for the Kadar-Parisi-Zhang (KPZ) universality class. The scaling behavior of response and correlation functions is reminiscent of the ``initial slip''…

Statistical Mechanics · Physics 2009-10-30 M. Krech

We study fluctuations of interfaces in the Kardar-Parisi-Zhang (KPZ) universality class with curved initial conditions. By simulations of a cluster growth model and experiments of liquid-crystal turbulence, we determine the universal…

Statistical Mechanics · Physics 2020-02-13 Yohsuke T. Fukai , Kazumasa A. Takeuchi

We elucidate the universal spatio-temporal scaling properties of the time-dependent correlation functions in a class of two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion process. By…

Statistical Mechanics · Physics 2024-06-17 Pritha Dolai , Aditi Simha , Abhik Basu

We investigate growing interfaces of topological-defect turbulence in the electroconvection of nematic liquid crystals. The interfaces exhibit self-affine roughening characterized by both spatial and temporal scaling laws of the…

Statistical Mechanics · Physics 2010-06-15 Kazumasa A. Takeuchi , Masaki Sano

We consider a model of first passage percolation (FPP) where the nearest-neighbor edges of the standard two-dimensional Euclidean lattice are equipped with random variables. These variables are i.i.d.\, nonnegative, continuous, and have a…

Probability · Mathematics 2021-05-06 Ujan Gangopadhyay

The statistics of the fluctuations of quantum many-body systems are highly revealing of their nature. In driven-dissipative systems displaying macroscopic quantum coherence, as exciton polariton condensates under incoherent pumping, the…

For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behaviour at criticality. Our…

Statistical Mechanics · Physics 2008-12-08 Axel Kammerer , Felix Höfling , Thomas Franosch

It is not known (and even physicists disagree) whether first passage percolation (FPP) on $\mathbb{Z}^d$ has an upper critical dimension $d_c$, such that the fluctuation exponent $\chi=0$ in dimensions $d>d_c$. In part to facilitate study…

Probability · Mathematics 2023-04-19 Kenneth S. Alexander

We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We…

Disordered Systems and Neural Networks · Physics 2018-12-19 Aurelio W. T. de Noronha , André A. Moreira , André P. Vieira , Hans J. Herrmann , José S. Andrade , Humberto A. Carmona

We have studied front dynamics for the discrete $A+A \leftrightarrow A$ reaction-diffusion system, which in the continuum is described by the (stochastic) Fisher-Kolmogorov-Petrovsky-Piscunov equation. We have revisited this discrete model…

Statistical Mechanics · Physics 2023-11-30 B. G. Barreales , J. J. Melendez , R. Cuerno , J. J. Ruiz-Lorenzo

The determination of the exact exponents of the KPZ class in any substrate dimension $d$ is one of the most important open issues in Statistical Physics. Based on the behavior of the dimensional variation of some exact exponent differences…

Statistical Mechanics · Physics 2022-12-21 Tiago J. Oliveira

Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies…

Statistical Mechanics · Physics 2012-10-23 Michael T Gastner , Beata Oborny

We study the first-passage time (FPT) problem for widespread recurrent processes in confined though large systems and present a comprehensive framework for characterizing the FPT distribution over many time scales. We find that the FPT…

Statistical Mechanics · Physics 2025-03-21 Talia Baravi , David A. Kessler , Eli Barkai

Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal the scaling behaviors of higher-order gaps in the largest…

Statistical Mechanics · Physics 2024-11-01 Sheng Fang , Qing Lin , Jun Meng , Bingsheng Chen , Jan Nagler , Youjin Deng , Jingfang Fan

This work investigates the origin of Kardar-Parisi-Zhang (KPZ) scaling in the phase dynamics of one-dimensional and two-dimensional polariton condensates. We demonstrate that the key mechanism leading to the observed power laws for the…

Mesoscale and Nanoscale Physics · Physics 2026-04-14 Denis Novokreschenov , Alexey Kavokin

We study universal aspects of polymer conformations and transverse fluctuations for a single swollen chain characterized by a contour length $L$ and a persistence length $\ell_p$ in two dimensions (2D) and in three dimensions (3D) in the…

Soft Condensed Matter · Physics 2023-06-07 Jacob Bair , Swarnadeep Seth , Aniket Bhattacharya