Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension

Abstract

We obtain the exact solution of the one-loop mode-coupling equations for the dynamical structure function in the framework of non-linear fluctuating hydrodynamics in one space dimension for the strictly hyperbolic case where all characteristic velocities are different. All solutions are characterized by dynamical exponents which are Kepler ratios of consecutive Fibonacci numbers, which includes the golden mean as a limiting case. The scaling form of all higher Fibonacci modes are asymmetric Lévy-distributions. Thus a hierarchy of new dynamical universality classes is established. We also compute the precise numerical value of the Prähofer-Spohn scaling constant to which scaling functions obtained from mode coupling theory are sensitive.

arXiv commentPACS classification: \pacs{05.60.Cd, 05.20.Jj, 05.70.Ln, 47.10.-g}

References in corpus (20)

• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Exact scaling functions for one-dimensional stationary KPZ growth
• A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
• Exact results for anomalous transport in one dimensional Hamiltonian systems
• Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics
• Fibonacci family of dynamical universality classes
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Mode coupling and renormalization group results for the noisy Burgers equation
• Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields
• Coupled Kardar-Parisi-Zhang Equations in One Dimension
• Energy diffusion in hard-point systems
• Passive Sliders on Fluctuating Surfaces: Strong-Clustering States
• Universality classes in two-component driven diffusive systems
• Weak and strong dynamic scaling in a one-dimensional driven coupled-field model: Effects of kinematic waves
• Anomalous fluctuations for a perturbed Hamiltonian system with exponential interactions
• Non-KPZ modes in two-species driven diffusive systems
• Numerical Solution of the Mode-Coupling Equations for the Kardar-Parisi-Zhang Equation in One Dimension
• Large compact clusters and fast dynamics in coupled nonequilibrium systems
• Ballistic and superdiffusive scales in macroscopic evolution of a chain of oscillators
• Tagged particle diffusion in one-dimensional systems with Hamiltonian dynamics - II

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