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We study the competitive RSOS-BD model focusing on the validity of the Kardar-Parisi-Zhang (KPZ) ansatz h(t) = v t + (\Gamma t)^{\beta} \chi and the universality of the height distributions (HDs) near the point where the model has…

Statistical Mechanics · Physics 2013-03-14 Tiago J. Oliveira

Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its…

Probability · Mathematics 2011-11-03 Ivan Corwin

We present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class, in d=1+1, for both flat and curved…

Statistical Mechanics · Physics 2013-05-15 Sidiney G. Alves , Tiago J. Oliveira , Silvio C. Ferreira

Inspired by the recent results on totally asymmetric simple exclusion processes on a periodic lattice with short-ranged quenched hopping rates [A. Haldar, A. Basu, Phys Rev Research 2, 043073 (2020)], we study the universal scaling…

Statistical Mechanics · Physics 2021-08-18 Astik Haldar

We study height fluctuations of interfaces in the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) class, growing at different speeds in the left half and the right half of space. Carrying out simulations of the discrete polynuclear growth…

Statistical Mechanics · Physics 2018-04-18 Yasufumi Ito , Kazumasa A. Takeuchi

A recent exponent inequality is applied to a number of dynamical growth models. Many of the known exponents for models such as the Kardar-Parisi-Zhang (KPZ) equation are shown to be consistent with the inequality. In some cases, such as the…

Statistical Mechanics · Physics 2011-09-06 Eytan Katzav , Moshe Schwartz

We study an anisotropic variant of the two-dimensional Kardar-Parisi-Zhang equation, that is relevant to describe growth of vicinal surfaces and has Gaussian, logarithmically rough, stationary states. While the folklore belief (based on…

Statistical Mechanics · Physics 2020-09-29 Giuseppe Cannizzaro , Dirk Erhard , Fabio Toninelli

The nonequilibrium steady state of the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) universality class is studied in-depth by exact solutions, yet no direct experimental evidence of its characteristic statistical properties has been…

Statistical Mechanics · Physics 2020-07-14 Takayasu Iwatsuka , Yohsuke T. Fukai , Kazumasa A. Takeuchi

We investigate Kardar-Parisi-Zhang (KPZ) surface growth in the presence of long-term correlated noise. By means of extensive numerical simulations of models in the KPZ universality class we find that, as the noise correlator range…

Statistical Mechanics · Physics 2019-07-03 Alejandro Alés , Juan M. López

We study the interface dynamics of a discrete model to quantitatively describe electrochemical deposition experiments. Extensive numerical simulations indicate that the interface dynamics is unstable at early times, but asymptotically…

Statistical Mechanics · Physics 2016-08-15 Mario Castro , Rodolfo Cuerno , Angel S\anchez , Francisco Domínguez-Adame

Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it…

Analysis of PDEs · Mathematics 2010-05-31 Pierre Germain

The Kardar-Parisi-Zhang (KPZ) equation defines the main universality class for nonlinear growth and roughening of surfaces. But under certain conditions, a conserved KPZ equation (cKPZ) is thought to set the universality class instead. This…

Statistical Mechanics · Physics 2018-07-18 Fernando Caballero , Cesare Nardini , Frederic van Wijland , Michael E. Cates

Local well-posedness for the Dirac - Klein - Gordon equations is proven in one space dimension, where the Dirac part belongs to H^{-{1/4}+\epsilon} and the Klein - Gordon part to H^{{1/4}-\epsilon} for 0 < \epsilon < 1/4, and global…

Analysis of PDEs · Mathematics 2007-05-23 Hartmut Pecher

A host of spatially extended systems, both in physics and in other disciplines, are well described at a coarse-grained scale by a Langevin equation with multiplicative-noise. Such systems may exhibit non-equilibrium phase transitions, which…

Condensed Matter · Physics 2015-06-24 Miguel A. Munoz , F. de los Santos , A. Achahbar

We investigate the finite-size origin of the emission linewidth of a spatially-extended, one-dimensional non-equilibrium condensate. We show that the well-known Schawlow-Townes scaling of laser theory, possibly including the Henry…

Statistical Mechanics · Physics 2023-03-07 Ivan Amelio , Alessio Chiocchetta , Iacopo Carusotto

We study the one-dimensional nonlinear Klein-Gordon (NLKG) equation with a convolution potential, and we prove that solutions with small $H^s$ norm remain small for long times. The result is uniform with respect to $c \geq 1$, which however…

Analysis of PDEs · Mathematics 2018-02-14 Stefano Pasquali

We review recent progress on the study of the Kardar-Parisi-Zhang (KPZ) equation in a periodic setting, which describes the random growth of an interface in a cylindrical geometry. The main results include central limit theorems for the…

Probability · Mathematics 2025-01-22 Yu Gu , Tomasz Komorowski

To investigate universal behavior and effects of long-range temporal correlations in kinetic roughening, we perform extensive simulations on the Kardar-Parisi-Zhang (KPZ) equation with temporally correlated noise based on pseudospectral…

Statistical Mechanics · Physics 2023-04-18 Xiongpeng Hu , Dapeng Hao , Hui Xia

The dynamics of a particle in an expanding cavity is investigated in the Klein-Gordon framework in a regime in which the single particle picture remains valid. The cavity expansion represents a time-dependent boundary condition for the…

Quantum Physics · Physics 2020-08-26 S. Colin , A. Matzkin

We consider the codimension one asymptotic stability problem for the soliton of the focusing cubic Klein-Gordon equation on the line under even perturbations. The main obstruction to full asymptotic stability on the center-stable manifold…

Analysis of PDEs · Mathematics 2024-03-04 Jonas Luhrmann , Wilhelm Schlag