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Over the past years our understanding of the scaling properties of the solutions to the one-dimensional KPZ equation has advanced considerably, both theoretically and experimentally. In our contribution we export these insights to the case…

Statistical Mechanics · Physics 2016-10-24 Patrik L. Ferrari , Tomohiro Sasamoto , Herbert Spohn

We propose a unified moving boundary problem for surface growth by electrochemical and chemical vapor deposition, which is derived from constitutive equations into which stochastic forces are incorporated. We compute the coefficients in the…

Statistical Mechanics · Physics 2009-11-07 Rodolfo Cuerno , Mario Castro

We extend our 2+1 dimensional discrete growth model (PRE 79, 021125 (2009)) with conserved, local exchange dynamics of octahedra, describing surface diffusion. A roughening process was realized by uphill diffusion and curvature dependence.…

Statistical Mechanics · Physics 2010-05-14 Geza Odor , Bartosz Liedke , Karl-Heinz Heinig

A nonperturbative weak noise scheme is applied to the Kardar-Parisi-Zhang equation for a growing interface in all dimensions. It is shown that the growth morphology can be interpreted in terms of a dynamically evolving texture of localized…

Statistical Mechanics · Physics 2014-10-07 Hans C. Fogedby

The pinning of flux lattices by weak impurity disorder is studied in the absence of free dislocations using both the gaussian variational method and, to $O(\epsilon=4-d)$, the functional renormalization group. We find universal logarithmic…

Condensed Matter · Physics 2009-10-22 T. Giamarchi , P. Le Doussal

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

When a nonequilibrium growing interface in the presence of a wall is considered a nonequilibrium wetting transition may take place. This transition can be studied trough Langevin equations or discrete growth models. In the first case, the…

Statistical Mechanics · Physics 2010-08-24 Andre Cardoso Barato

We study a noisy Kuramoto-Sivashinsky (KS) equation which describes unstable surface growth and chemical turbulence. It has been conjectured that the universal long-wavelength behavior of the equation, which is characterized by…

Statistical Mechanics · Physics 2017-09-13 Yuki Minami , Shin-ichi Sasa

The Kardar-Parisi-Zhang universality class of stochastic surface growth is studied by exact field-theoretic methods. From previous numerical results, a few qualitative assumptions are inferred. In particular, height correlations should…

Condensed Matter · Physics 2009-10-30 Michael Lassig

Through the asymptotic expansion, the large-time behavior of the incompressible Navier-Stokes flow in $n$-dimensional whole space is drawn. In particular, the logarithmic evolution included in the flow velocity is the focus of attention.…

Analysis of PDEs · Mathematics 2025-09-29 Masakazu Yamamoto

In a recent work [Phys. Rev. E 109, L042102 (2024)], interesting dimensional crossovers [from two- to one-dimensional (2D to 1D) scaling] were found in the growth of Kardar-Parisi-Zhang (KPZ) interfaces on rectangular substrates, with…

Statistical Mechanics · Physics 2026-05-08 Ismael S. S. Carrasco , Tiago J. Oliveira

The celebrated Kardar-Parisi-Zhang (KPZ) equation describes the kinetic roughening of stochastically growing interfaces. In one dimension, the KPZ equation is exactly solvable and its statistical properties are known to an exquisite degree.…

Statistical Mechanics · Physics 2023-12-25 Côme Fontaine , Francesco Vercesi , Marc Brachet , Léonie Canet

In order to characterise non-equilibrium growth processes, we study the behaviour of global quantities that depend in a non-trivial way on two different times. We discuss the dynamical scaling forms of global correlation and response…

Statistical Mechanics · Physics 2015-05-19 Yen-Liang Chou , Michel Pleimling

In historical mathematics and physics, the Kardar-Parisi-Zhang equation or a quasilinear stationary version of a time-dependent viscous Hamilton-Jacobi equation in growing interface and universality classes, is also known by the different…

Analysis of PDEs · Mathematics 2019-10-11 Minh-Phuong Tran , Thanh-Nhan Nguyen

A growing interface subject to noise is described by the Kardar-Parisi-Zhang equation or, equivalently, the noisy Burgers equation. In one dimension this equation is analyzed by means of a weak noise canonical phase space approach applied…

Statistical Mechanics · Physics 2014-10-07 Hans C Fogedby

Stochastic motion of a point -- known as Brownian motion -- has many successful applications in science, thanks to its scale invariance and consequent universal features such as Gaussian fluctuations. In contrast, the stochastic motion of a…

Statistical Mechanics · Physics 2011-08-11 Kazumasa A. Takeuchi , Masaki Sano , Tomohiro Sasamoto , Herbert Spohn

We propose Josephson junction arrays as realistic platforms for observing nonequilibrium scaling laws characterizing the Kardar-Parisi-Zhang (KPZ) universality class, and space-time soliton proliferation. Focusing on a two-chain ladder…

Statistical Mechanics · Physics 2025-12-12 Mikheil Tsitsishvili , Reinhold Egger , Karsten Flensberg , Sebastian Diehl

Finite temperature spin transport in integrable isotropic spin chains is known to be superdiffusive, with dynamical spin correlations that are conjectured to fall into the Kardar-Parisi-Zhang (KPZ) universality class. However, integrable…

Quantum Gases · Physics 2023-11-28 Jacopo De Nardis , Sarang Gopalakrishnan , Romain Vasseur

We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and…

Statistical Mechanics · Physics 2014-01-28 Matteo Nicoli , Rodolfo Cuerno , Mario Castro

We study a restricted solid-on-solid (RSOS) model involving deposition and evaporation with probabilities p and 1-p, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang…

Statistical Mechanics · Physics 2014-05-07 T. J. Oliveira , K. Dechoum , J. A. Redinz , F. D. A. Aarao Reis