The 1+1 dimensional Kardar-Parisi-Zhang equation: more surprises

Abstract

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 physics. Out of a wide choice, the spin-spin time correlations for the Heisenberg chain will be discussed at some length, also the equilibrium time-correlations of the conserved fields for 1D fluids. An interesting recent theoretical advance is the construction of the scale-invariant asymptotic theory, the so-called KPZ fixed point.

15 pages, 5 figures, StatPhys27, added references, typos

References in corpus (10)

• Exact scaling functions for one-dimensional stationary KPZ growth
• Fluctuation properties of the TASEP with periodic initial configuration
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• The one-dimensional KPZ equation and its universality class
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• A determinantal formula for the GOE Tracy-Widom distribution
• Reflected Brownian motions in the KPZ universality class
• Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension
• Mutually avoiding paths in random media and largests eigenvalues of random matrices

Cited by in corpus (5)

• Finite-temperature transport in one-dimensional quantum lattice models
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Kinetic roughening and nontrivial scaling in the Kardar-Parisi-Zhang growth with long-range temporal correlations
• Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation
• The Two Scaling Regimes of the Thermodynamic Uncertainty Relation for the KPZ-Equation