# Kardar-Parisi-Zhang equation with spatially correlated noise: a unified picture from nonperturbative renormalization group.

@article{Kloss2013KardarParisiZhangEW, title={Kardar-Parisi-Zhang equation with spatially correlated noise: a unified picture from nonperturbative renormalization group.}, author={Thomas Kloss and L{\'e}onie Canet and Bertrand Delamotte and Nicol{\'a}s Wschebor}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2013}, volume={89 2}, pages={ 022108 } }

We investigate the scaling regimes of the Kardar-Parisi-Zhang (KPZ) equation in the presence of spatially correlated noise with power-law decay D(p) ∼ p(-2ρ) in Fourier space, using a nonperturbative renormalization group approach. We determine the full phase diagram of the system as a function of ρ and the dimension d. In addition to the weak-coupling part of the diagram, which agrees with the results from Europhys. Lett. 47, 14 (1999) and Eur. Phys. J. B 9, 491 (1999), we find the two fixed…

## 24 Citations

### Kardar-Parisi-Zhang equation with temporally correlated noise: A nonperturbative renormalization group approach.

- PhysicsPhysical review. E
- 2019

It is found that for the short-range noise with any finite τ, the symmetries are dynamically restored at large scales, such that the long-distance and long-time properties are governed by the SR-KPZ fixed point, in accordance with previous renormalization group results.

### Sinc noise for the Kardar-Parisi-Zhang equation.

- PhysicsPhysical review. E
- 2018

The study of the one-dimensional Kardar-Parisi-Zhang equation with correlated noise by field-theoretic dynamic renormalization-group techniques suggests that the KPZ dynamics is universal with respect to the exact noise structure, provided the noise correlation length ξ is finite.

### Kardar-Parisi-Zhang universality in discrete two-dimensional driven-dissipative exciton polariton condensates

- PhysicsPhysical Review Research
- 2022

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…

### Dynamic criticality far from equilibrium: One-loop flow of Burgers-Kardar-Parisi-Zhang systems with broken Galilean invariance.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

This work compute the phase diagram and critical exponents of the KPZ equation with 1/f noise (KPZ1/f) in spatial dimensions 1≤d<4 using the dynamic renormalization group with a frequency cutoff technique in a one-loop truncation.

### Fully developed isotropic turbulence: Nonperturbative renormalization group formalism and fixed-point solution.

- PhysicsPhysical review. E
- 2016

This work derives exact flow equations in the large wave-number limit, and shows that the fixed point does not entail the usual scale invariance, thereby identifying the mechanism for the emergence of intermittency within the NPRG framework.

### Probability distributions for kinetic roughening in the Kardar-Parisi-Zhang growth with long-range temporal and spatial correlations

- Physics
- 2022

We investigate numerically the eﬀects of long-range temporal and spatial correlations based on probability distribution of interface width W ( L,t ) in the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ)…

### The nonperturbative functional renormalization group and its applications

- PhysicsPhysics Reports
- 2021

### Functional renormalisation approach to driven dissipative dynamics

- Physics
- 2014

In this thesis we investigate driven-dissipative stationary scaling states of Burgers’ and Gross–Pitaevskii equations (GPE).
The path integral representation of the steady state of the stochastic…

### Static Approach to Renormalization Group Analysis of Stochastic Models with Spatially Quenched Noise

- PhysicsJournal of Statistical Physics
- 2019

A new “static” renormalization group approach to stochastic models of fluctuating surfaces with spatially quenched noise is proposed in which only time-independent quantities are involved. As…

### From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group

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We investigate the transition from unitary to dissipative dynamics in the relativistic O(N) vector model with the λ(φ2)2 interaction using the nonperturbative functional renormalization group in the…

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