The Kardar-Parisi-Zhang exponents for the $2+1$ dimensions

Abstract

The Kardar-Parisi-Zhang (KPZ) equation has been connected to a large number of important stochastic processes in physics, chemistry and growth phenomena, ranging from classical to quantum physics. The central quest in this field is the search for ever more precise universal growth exponents. Notably, exact growth exponents are only known for $1+1$ dimensions. In this work, we present physical and geometric analytical methods that directly associate these exponents to the fractal dimension of the rough interface. Based on this, we determine the growth exponents for the $2+1$ dimensions, which are in agreement with the results of thin films experiments and precise simulations. We also make a first step towards a solution in $d+1$ dimensions, where our results suggest the inexistence of an upper critical dimension.

References in corpus (12)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems
• Numerical estimate of the Kardar Parisi Zhang universality class in (2 + 1) dimensions
• Khinchin theorem and anomalous diffusion
• Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections
• Interface fluctuations for deposition on enlarging flat substrates
• Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition
• Entropy, non-ergodicity and non-Gaussian behaviour in ballistic transport
• Growth exponents of the etching model in high dimensions
• Analysis of etching at a solid-solid interface
• The hidden fluctuation-dissipation theorem for growth

Cited by in corpus (13)

• Universality in driven open quantum matter
• The fractal geometry of growth: fluctuation-dissipation theorem and hidden symmetry
• Modeling the diffusion-erosion crossover dynamics in drug release
• Kardar-Parisi-Zhang universality class in ($d+1$)-dimensions
• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Universal scaling relation for growth phenomena
• Restoring the fluctuation-dissipation theorem in Kardar-Parisi-Zhang universality class through a new emergent fractal dimension
• A geometrical interpretation of critical exponents
• Logarithmic or algebraic: roughening of an active Kardar-Parisi-Zhang surface
• Fractality in resistive circuits: The Fibonacci resistor networks
• Random Walk on a Random Surface: Implications of Non-perturbative Concepts and Dynamical Emergence of Galilean Symmetry
• Scaling, Fractal Dynamics and Critical Exponents: Application in a non-integer dimensional Ising model
• Hierarchical deposition and scale-free networks: a visibility algorithm approach