Exponent Inequalities in Dynamical Systems

Abstract

In this letter we derive exponent inequalities relating the dynamic exponent $z$ to the steady state exponent $\Gamma$ for a general class of stochastically driven dynamical systems. We begin by deriving a general exact inequality, relating the response function and the correlation function, from which the various exponent inequalities emanate. We then distinguish between two classes of dynamical systems and obtain different and complementary inequalities relating $z$ and $\Gamma$. The consequences of those inequalities for a wide set of dynamical problems, including critical dynamics and Kardar-Parisi-Zhang-like problems are discussed.

4 pages, 1 figure

References in corpus (10)

• Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation
• Numerical study of the Kardar-Parisi-Zhang equation
• Can non-linear elasticity explain contact-line roughness at depinning?
• Elastic systems with correlated disorder: Response to tilt and application to surface growth
• Growing Surfaces with Anomalous Diffusion - Results for the Fractal Kardar-Parisi-Zhang Equation
• Roughness of moving elastic lines - crack and wetting fronts
• Roughness of tensile crack fronts in heterogenous materials
• Stochastic Model in the Kardar-Parisi-Zhang Universality With Minimal Finite Size Effects
• Dynamical Inequality in Growth Models
• Non-Linear Stochastic Equations with Calculable Steady States

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• Dynamics of Fluctuating Thin Sheets Under Random Forcing
• Thermally driven elastic membranes are quasi-linear across all scales
• Nonlinear field theories during homogeneous spatial dilation
• Nonconserved critical dynamics of the two-dimensional Ising model as a surface kinetic roughening process