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Related papers: KPZ equation correlations in time

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Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems has been reported. Inspired by these results, we explore the KPZ scaling in…

High Energy Physics - Theory · Physics 2024-06-06 Alexander Gorsky , Sergei Nechaev , Alexander Valov

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

We show that the multicomponent Kardar-Parisi-Zhang equation describes the low-energy theory for phase fluctuations in a $\mathbb{Z}_{2}$ degenerate non-equilibrium driven-dissipative condensate with global $U(1)\times U(1)$ symmetry. Using…

Quantum Gases · Physics 2024-11-12 Harvey Weinberger , Paolo Comaron , Marzena H. Szymańska

We study Kardar-Parisi-Zhang equation in spatial dimension 3 or larger driven by a Gaussian space-time white noise with a small convolution in space. When the noise intensity is small, it is known that the solutions converge to a random…

Probability · Mathematics 2020-05-20 Francis Comets , Clement Cosco , Chiranjib Mukherjee

In its original version the KPZ equation models the dynamics of an interface bordering a stable phase against a metastable one. Over past years the corresponding two-dimensional field theory has been applied to models with different…

Statistical Mechanics · Physics 2020-06-24 Herbert Spohn

Kardar-Parisi-Zhang (KPZ) equation is a quasilinear stochastic partial differential equation(SPDE) driven by a space-time white noise. In recent years there have been several works directed towards giving a rigorous meaning to a solution of…

Probability · Mathematics 2014-06-24 Sergio A. Almada Monter , Amarjit Budhiraja

Time correlations for KPZ growth in 1+1 dimensions are reconsidered. We discuss flat, curved, and stationary initial conditions and are interested in the covariance of the height as a function of time at a fixed point on the substrate. In…

Mathematical Physics · Physics 2016-07-27 Patrik L. Ferrari , Herbert Spohn

We define a stochastic lattice model for a fluctuating directed polymer in $d\geq 2$ dimensions. This model can be alternatively interpreted as a fluctuating random path in 2 dimensions, or a one-dimensional asymmetric simple exclusion…

Statistical Mechanics · Physics 2017-09-20 G. M. Schütz , B. Wehefritz-Kaufmann

We investigate space-time coherence in one-dimensional lattices of exciton-polariton condensates formed by fully reconfigurable non-resonant optical pumping. Starting from an open-dissipative Gross-Pitaevskii equation with deterministic…

Mesoscale and Nanoscale Physics · Physics 2025-12-15 D. Novokreschenov , V. Neplokh , M. Misko , N. Starkova , T. Cookson , A. Kudlis , A. Nalitov , I. A. Shelykh , A. V. Kavokin , P. Lagoudakis

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

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

Growth of interfaces during vapor deposition are analyzed on a discrete lattice. Foe a rough surface, relation between the roughness exponent alpha, and corresponding step-step (slope-slope) couplings is obtained in (1+1) and (2+1)…

Soft Condensed Matter · Physics 2007-05-23 S. V. Ghaisas

We investigate the scaling regimes of the Kardar-Parisi-Zhang equation in the presence of spatially correlated noise with power law decay $D(p) \sim p^{-2\rho}$ in Fourier space, using a nonperturbative renormalization group approach. We…

Statistical Mechanics · Physics 2014-02-11 Thomas Kloss , Léonie Canet , Bertrand Delamotte , Nicolás Wschebor

We present an exact solution of the {\it deterministic} Kardar-Parisi-Zhang (KPZ) equation under the influence of a local driving force $f$. For substrate dimension $d \le 2$ we recover the well-known result that for arbitrarily small…

Condensed Matter · Physics 2009-10-28 T. J. Newman , Harald Kallabis

We study the spatial decorrelation of the solution to the KPZ equation with narrow wedge initial data. For fixed $t>0$, we determine the decay rate of the spatial covariance function, showing that ${\rm Cov}[h(t,x),h(t,0)]\sim \frac{t}{x}$…

Probability · Mathematics 2025-07-01 Yu Gu , Fei Pu

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 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…

We prove that the stochastic Burgers equation, which is related to the Kardar-Parisi-Zhang/KPZ equation via weak derivative, is a "critical" scaling limit for density fluctuations for a family of non-integrable and non-stationary…

Probability · Mathematics 2022-03-01 Kevin Yang

We consider the stochastic six-vertex (S6V) model and asymmetric simple exclusion process (ASEP) under general initial conditions which are bounded below lines of arbitrary slope at $\pm\infty$. We show under Kardar-Parisi-Zhang (KPZ)…

Probability · Mathematics 2024-12-25 Amol Aggarwal , Ivan Corwin , Milind Hegde

We perform a numerical study on the two-dimensional nonequilibrium exciton-polariton systems driven by incoherent pumping based on the stochastic generalized Gross-Pitaevskii equation. We calculate the density fluctuation, coherence…

Quantum Gases · Physics 2021-01-13 Quanyu Mei , Kai Ji , Michiel Wouters