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Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behavior quite different from that of their equilibrium counterparts. Here we demonstrate a surprising…

Soft Condensed Matter · Physics 2016-08-09 Leiming Chen , Chiu Fan Lee , John Toner

Integrable spin chains with a continuous non-Abelian symmetry, such as the one-dimensional isotropic Heisenberg model, show superdiffusive transport with little theoretical understanding. Although recent studies reported a surprising…

We expand a previous study [Phys. Rev. E 86, 051611 (2012)] on the conditions for occurrence of strong anisotropy (SA) in the scaling properties of two-dimensional surfaces displaying generic scale invariance. There, a natural Ansatz was…

Statistical Mechanics · Physics 2015-06-18 Edoardo Vivo , Matteo Nicoli , Rodolfo Cuerno

Two-dimensional (2D) KPZ growth is usually investigated on substrates of lateral sizes $L_x=L_y$, so that $L_x$ and the correlation length ($\xi$) are the only relevant lengths determining the scaling behavior. However, in cylindrical…

Statistical Mechanics · Physics 2024-05-06 Ismael S. S. Carrasco , Tiago J. Oliveira

In this work we focus on the two-dimensional anisotropic KPZ (aKPZ) equation, which is formally given by \begin{equation*}\partial_t h =\frac{\nu}{2}\Delta h + \lambda((\partial_1 h)^2 - (\partial_2 h)^2) +…

Probability · Mathematics 2019-07-09 G. Cannizzaro , D. Erhard , P. Schönbauer

Logarithmic or Sinai type subdiffusion is usually associated with random force disorder and non-stationary potential fluctuations whose root mean squared amplitude grows with distance. We show here that extremely persistent, macroscopic…

Statistical Mechanics · Physics 2017-11-29 Igor Goychuk , Vasyl O. Kharchenko , Ralf Metzler

Equilibrium and nonequilibrium states of matter can exhibit fundamentally different behavior. A key example is the Kardar-Parisi-Zhang universality class in two spatial dimensions (2D KPZ), where microscopic deviations from equilibrium give…

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

The Kardar-Parisi-Zhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally…

Condensed Matter · Physics 2016-08-31 Michael Lassig

Local Scale-Invariance theory is tested by extensive dynamical simulations of the driven dimer lattice gas model, describing the surface growth of the 2+1 dimensional Kardar-Parisi-Zhang surfaces. Very precise measurements of the universal…

Statistical Mechanics · Physics 2017-02-28 Jeffrey Kelling , Géza Ódor , Sibylle Gemming

We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang equation for the kinetic growth of an interface in higher dimensions. The weak noise approach provides a many body picture of a growing interface in terms of a…

Statistical Mechanics · Physics 2009-11-13 Hans C. Fogedby

We study the simple, linear, Edwards-Wilkinson equation that describes surface growth governed by height diffusion in the presence of spatiotemporally power-law decaying correlated noise. We analytically show that the surface becomes…

Pattern Formation and Solitons · Physics 2020-04-22 Alejandro Alés , Juan M López

The Kardar-Parisi-Zhang (KPZ) equation is a paradigmatic model of nonequilibrium low-dimensional systems with spatiotemporal scale invariance, recently highlighting universal behavior in fluctuation statistics. Its space derivative, namely…

Statistical Mechanics · Physics 2020-05-27 E. Rodriguez-Fernandez , R. Cuerno

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 prove the two dimensional KPZ equation with a logarithmically tuned nonlinearity and a small coupling constant, scales to the Edwards-Wilkinson equation with an effective variance.

Probability · Mathematics 2019-06-06 Yu Gu

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…

In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the Fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that…

Statistical Mechanics · Physics 2008-04-21 Eytan Katzav

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

The effects of a randomly moving environment on a randomly growing interface are studied by the field theoretic renormalization group analysis. The kinetic growth of an interface (kinetic roughening) is described by the Kardar-Parisi-Zhang…

Statistical Mechanics · Physics 2020-01-28 N. V. Antonov , P. I. Kakin , N. M. Lebedev

We study numerically the Kuramoto-Sivashinsky (KS) equation forced by external white noise in two space dimensions, that is a generic model for e.g. surface kinetic roughening in the presence of morphological instabilities. Large scale…

Statistical Mechanics · Physics 2015-06-04 Matteo Nicoli , Edoardo Vivo , Rodolfo Cuerno