Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation

Abstract

The one-dimensional Kardar-Parisi-Zhang (KPZ) equation is becoming an overarching paradigm for the scaling of nonequilibrium, spatially extended, classical and quantum systems with strong correlations. Recent analytical solutions have uncovered a rich structure regarding its scaling exponents and fluctuation statistics. However, the zero surface tension or zero viscosity case eludes such analytical solutions and has remained ill-understood. Using numerical simulations, we elucidate a well-defined universality class for this case that differs from that of the viscous case, featuring intrinsically anomalous kinetic roughening, despite previous expectations for systems with local interactions and time-dependent noise and ballistic dynamics. The latter may be relevant to recent quantum spin chain experiments which measure KPZ and ballistic relaxation under different conditions. We identify the ensuing set of scaling exponents in previous discrete interface growth models related with isotropic percolation, and show it to describe the fluctuations of additional continuum systems related with the noisy Korteweg-de Vries equation. Along this process, we additionally elucidate the universality class of the related inviscid stochastic Burgers equation.

arXiv comment9 pages, 8 figures, Physical Review E (in press, 2022)

References in corpus (31)

• Quantum Entanglement Growth Under Random Unitary Dynamics
• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• The one-dimensional KPZ equation: an exact solution and its universality
• Growing interfaces uncover universal fluctuations behind scale invariance
• Generic Dynamic Scaling in Kinetic Roughening
• A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
• An exact solution for the KPZ equation with flat initial conditions
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
• An appetizer to modern developments on the Kardar-Parisi-Zhang universality class
• Super-roughening versus intrinsic anomalous scaling of surfaces
• Scaling Approach to Calculate Critical Exponents in Anomalous Surface Roughening
• Effects of Particle Shape on Growth Dynamics at Edges of Evaporating Colloidal Drops
• Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics
• Scaling of Local Slopes, Conservation Laws and Anomalous Roughening in Surface Growth
• Stability of superdiffusion in nearly integrable spin chains
• Surprising mappings of 2D polar active fluids to 2D soap and 1D sandblasting
• Renormalization Group Analysis of a Noisy Kuramoto-Sivashinsky Equation
• Superdiffusivity of the 1D lattice Kardar-Parisi-Zhang equation
• Universality of cauliflower-like fronts: from nanoscale thin films to macroscopic plants
• Topology and the Kardar-Parisi-Zhang universality class
• Random geometry and the Kardar-Parisi-Zhang universality class
• Intermittency of Height Fluctuations and Velocity Increment of The Kardar-Parisi-Zhang and Burgers Equations with infinitesimal surface tension and Viscosity in 1+1 Dimensions
• The derivative of the Kardar-Parisi-Zhang equation is not in the KPZ universality class
• Transition between chaotic and stochastic universality classes of kinetic roughening
• Strong anisotropy in two-dimensional surfaces with generic scale invariance: Non-linear effects
• Anomalous Hydrodynamics in One Dimensional Electronic Fluid
• Gaussian statistics as an emergent symmetry of the stochastic Burgers equation
• Zero tension Kardar-Parisi-Zhang equation in (d+1)- Dimensions

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• Numerical Integration of the KPZ and Related Equations on Networks: The Case of the Cayley Tree
• The stochastic porous medium equation in one dimension
• The non-perturbative sides of the Kardar-Parisi-Zhang equation
• Nonconserved critical dynamics of the two-dimensional Ising model as a surface kinetic roughening process
• Universal interface fluctuations in the contact process
• Unveiling the different scaling regimes of the one-dimensional Kardar-Parisi-Zhang--Burgers equation using the functional renormalisation group