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Burgers-Kardar-Parisi-Zhang (KPZ) scaling has recently (re-) surfaced in a variety of physical contexts, ranging from anharmonic chains to quantum systems such as open superfluids, in which a variety of random forces may be encountered…

Statistical Mechanics · Physics 2015-03-24 Philipp Strack

We develop the hydrodynamic theory for number conserving asymmetric exclusion processes with short-range random quenched disordered hopping rates, which is one-dimensional Kardar-Parisi- Zhang (KPZ) equation with quenched columnar disorder.…

Statistical Mechanics · Physics 2020-10-16 Astik Haldar , Abhik Basu

We consider an infinite interface in $d>2$ dimensions, governed by the Kardar-Parisi-Zhang (KPZ) equation with a weak Gaussian noise which is delta-correlated in time and has short-range spatial correlations. We study the probability…

Statistical Mechanics · Physics 2018-05-02 Baruch Meerson , Pavel V. Sasorov , Arkady Vilenkin

The statistics of the average height fluctuation of the one-dimensional Kardar-Parisi-Zhang(KPZ)-type surface is investigated. Guided by the idea of local stationarity, we derive the scaling form of the characteristic function in the…

Statistical Mechanics · Physics 2009-11-11 Deok-Sun Lee , Doochul Kim

We show that several aspects of the low-temperature hydrodynamics of a discrete Gross-Pitaevskii equation (GPE) can be understood by mapping it to a nonlinear version of fluctuating hydrodynamics. This is achieved by first writing the GPE…

Quantum Gases · Physics 2015-10-21 Manas Kulkarni , David A. Huse , Herbert Spohn

We study the fluctuations of discretized versions of the stochastic heat equation (SHE) and the Kardar-Parisi-Zhang (KPZ) equation in spatial dimensions $d\geq 3$ in the weak disorder regime. The discretization is defined using the directed…

Probability · Mathematics 2025-10-22 Stefan Junk , Shuta Nakajima

The Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension dynamically develops sharply connected valley structures within which the height derivative {\it is not} continuous. There are two different regimes before and after creation of the…

Statistical Mechanics · Physics 2016-08-31 A. A. Masoudi , F. Shahbazi , J. Davoudi , M. Reza Rahimi Tabar

For stationary interface growth, governed by the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions, typical fluctuations of the interface height at long times are described by the Baik-Rains distribution. Recently Chhita et al. [1]…

Statistical Mechanics · Physics 2017-11-22 Baruch Meerson , Johannes Schmidt

In this article we will present a study of the well-known Kardar-Parisi-Zhang(KPZ) model. Under certain conditions we have found analytic self-similar solutions for the underlying equation. The results are strongly related to the error…

Adaptation and Self-Organizing Systems · Physics 2011-12-14 Imre Ferenc Barna , Laszlo Matyas

We present a systematic discretization scheme for the Kardar-Parisi-Zhang (KPZ) equation, which correctly captures the strong-coupling properties of the continuum model. In particular we show that the scheme contains no finite-time…

Condensed Matter · Physics 2009-10-28 T. J. Newman , A. J. Bray

We study the synchronization physics of 1D and 2D oscillator lattices subject to noise and predict a dynamical transition that leads to a sudden drastic increase of phase diffusion. Our analysis is based on the widely applicable…

Statistical Mechanics · Physics 2017-08-02 Roland Lauter , Aditi Mitra , Florian Marquardt

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 consider the Kardar-Parisi-Zhang (KPZ) equation for a circular interface in two dimensions, unconstrained by the standard small-slopes and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate…

Statistical Mechanics · Physics 2014-01-14 Silvia N. Santalla , Javier Rodriguez-Laguna , Rodolfo Cuerno

We have considered three different "one-body" statistical systems involving Brownian excursions, which possess for fluctuations Kardar-Parisi-Zhang scaling with the critical exponent $\nu=\frac{1}{3}$. In all models imposed external…

Statistical Mechanics · Physics 2020-05-07 Alexander Gorsky , Sergei Nechaev , Alexander Valov

The continuum Kardar-Parisi-Zhang equation in one dimension is lattice discretized in such a way that the drift part is divergence free. This allows to determine explicitly the stationary measures. We map the lattice KPZ equation to a…

Mathematical Physics · Physics 2015-05-13 Tomohiro Sasamoto , Herbert Spohn

The Kardar-Parisi-Zhang (KPZ) fixed point is a Markov process, recently introduced by Matetski, Quastel, Remenik (arXiv:1701.00018), that describes the limit fluctuations of the height function associated to the totally asymmetric simple…

Probability · Mathematics 2019-12-18 Leandro P. R. Pimentel

For suitably discretized versions of the Kardar-Parisi-Zhang equation in one space dimension exact scaling functions are available, amongst them the stationary two-point function. We explain one central piece from the technology through…

Disordered Systems and Neural Networks · Physics 2009-11-11 Herbert Spohn

We study the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) interfaces growing inward from ring-shaped initial conditions, experimentally and numerically, using growth of a turbulent state in liquid-crystal electroconvection and an…

Statistical Mechanics · Physics 2017-08-14 Yohsuke T. Fukai , Kazumasa A. Takeuchi

We study the continuum space-time limit of a periodic one dimensional array of deterministic logistic maps coupled diffusively. First, we analyse this system in connection with a stochastic one dimensional Kardar-Parisi-Zhang (KPZ) equation…

Disordered Systems and Neural Networks · Physics 2007-05-23 Eytan Katzav , Leticia F. Cugliandolo

The Kardar-Parisi-Zhang (KPZ) fixed point is a Markov process that is conjectured to be at the core of the KPZ universality class. In this article we study two aspects the KPZ fixed point that share the same Brownian limiting behaviour: the…

Probability · Mathematics 2019-12-30 Leandro P. R. Pimentel