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Related papers: KPZ-like scaling on a high-dimensional hypersphere

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The Kardar-Parisi-Zhang (KPZ) universality class describes the coarse-grained behavior of a wealth of classical stochastic models. Surprisingly, it was recently conjectured to also describe spin transport in the one-dimensional quantum…

Using the weak-noise theory, we evaluate the probability distribution $\mathcal{P}(H,t)$ of large deviations of height $H$ of the evolving surface height $h(x,t)$ in the Kardar-Parisi-Zhang (KPZ) equation in one dimension when starting from…

Statistical Mechanics · Physics 2016-02-23 Baruch Meerson , Eytan Katzav , Arkady Vilenkin

The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is derived from various microscopic models, and to establish a robust way to derive the KPZ equation is a fundamental problem both in mathematics and…

Probability · Mathematics 2023-06-08 Kohei Hayashi

Scale-invariant fluctuations of growing interfaces are studied for circular clusters of an off-lattice variant of the Eden model, which belongs to the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class. Statistical properties of…

Statistical Mechanics · Physics 2012-05-15 Kazumasa A. Takeuchi

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 simulated a growth model in 1+1 dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with…

Statistical Mechanics · Physics 2009-11-07 Anna Chame , Fabio D. A. Aarao Reis

The long wavelength diffusion coefficient of a critical fluid confined between two parallel plates separated by a distance L is strongly affected by the finite size. Finite size scaling leads us to expect that the vanishing of the diffusion…

Statistical Mechanics · Physics 2009-11-10 Palash Das , Jayanta K. Bhattacharjee

We study a generalized Kardar-Parisi-Zhang (KPZ) equation [Jana et al., Phys. Rev. E 109, L032104 (2024)] that sets the paradigm for universality in roughening of growing nonequilibrium surfaces without any conservation laws but with…

Statistical Mechanics · Physics 2025-07-29 Debayan Jana , Abhik Basu

We numerically investigate the scaling properties of a one-dimensional driven-dissipative condensate described by a stochastic complex Ginzburg-Landau equation (SCGLE). We directly extract the static and dynamical scaling exponents from the…

Statistical Mechanics · Physics 2015-10-20 Liang He , Lukas M. Sieberer , Ehud Altman , Sebastian Diehl

The following question is the subject of our work: could a two-dimensional random path pushed by some constraints to an improbable "large deviation regime", possess extreme statistics with one-dimensional Kardar-Parisi-Zhang (KPZ)…

Statistical Mechanics · Physics 2019-01-18 Sergei Nechaev , Kirill Polovnikov , Senya Shlosman , Alexander Valov , Alexander Vladimirov

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 present results on tagged particle diffusion in a meso-scale lattice model for sheared amorphous material in athermal quasi-static conditions. We find a short time diffusive regime and a long time diffusive regime whose diffusion…

Soft Condensed Matter · Physics 2018-10-10 Botond Tyukodi , Craig E Maloney , Damien Vandembroucq

We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces with curved and flat initial conditions. We introduce a control parameter p as the…

Statistical Mechanics · Physics 2019-02-15 Abbas Ali Saberi , Hor Dashti-N. , Joachim Krug

The Kardar-Parisi-Zhang (KPZ) equation is accepted as a generic description of interfacial growth. In several recent studies, however, values of the roughness exponent alpha have been reported that are significantly less than that…

Statistical Mechanics · Physics 2016-08-31 R. A. Blythe , M. R. Evans

We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…

Probability · Mathematics 2010-05-14 Martin Hairer , Charles Manson

We study atypically large fluctuations of height $H$ in the 1+1-dimensional Kardar-Parisi-Zhang (KPZ) equation at long times $t$, when starting from a "droplet" initial condition. We derive exact large deviation function of height for…

Statistical Mechanics · Physics 2017-06-13 Pavel Sasorov , Baruch Meerson , Sylvain Prolhac

We identify the key features of Kardar-Parisi-Zhang universality class in the fluctuations of the wave density logarithm, in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit…

Disordered Systems and Neural Networks · Physics 2024-04-24 Sen Mu , Jiangbin Gong , Gabriel Lemarié

There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar-Parisi-Zhang (KPZ) universality class. A proper rescaling of time should introduce a non-trivial temporal dimension to these limiting…

Probability · Mathematics 2012-10-29 Ivan Corwin , P. L. Ferrari , S. Peche

We study the role of the topology of the background space on the one-dimensional Kardar-Parisi-Zhang (KPZ) universality class. To do so, we study the growth of balls on disordered 2D manifolds with random Riemannian metrics, generated by…

Statistical Mechanics · Physics 2017-03-08 Silvia N. Santalla , Javier Rodriguez-Laguna , Alessio Celi , Rodolfo Cuerno

We study phase separation in a system of hard-core particles driven by a fluctuating two-dimensional self-affine potential landscape which evolves through Kardar-Parisi-Zhang (KPZ) dynamics. We find that particles tend to cluster together…

Statistical Mechanics · Physics 2007-05-23 G. Manoj , Mustansir Barma