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Fibonacci family of dynamical universality classes
Vladislav Popkov1, Andreas Schadschneider2, Johannes Schmidt3
1Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany; Centro Interdipartimentale per lo Studio di Dinamiche Complesse, Università di Firenze, 50019 Sesto Fiorentino, Italy;
Summary
Discover an infinite family of nonequilibrium universality classes, extending beyond diffusive and Kardar-Parisi-Zhang (KPZ) dynamics. These novel classes are characterized by dynamical exponents derived from Fibonacci numbers and Lévy distributions.
Area of Science:
- Non-equilibrium statistical physics
- Complex systems dynamics
- Universality in physical systems
Background:
- Universality is a key concept in equilibrium physics, but principles for systems far from equilibrium are less understood.
- Existing universality classes include diffusive and superdiffusive Kardar-Parisi-Zhang (KPZ) dynamics.
- These classes describe phenomena like low-dimensional dynamics with conservation laws.
Purpose of the Study:
- To identify and characterize new universality classes in systems far from equilibrium.
- To explore the mathematical relationships governing the dynamics of these systems.
- To connect theoretical findings to potential experimental measurements.
Main Methods:
- Theoretical analysis of non-equilibrium systems.
- Identification of scaling behaviors and dynamical exponents.
- Characterization of universal scaling functions.
Main Results:
- Identified an infinite discrete family of nonequilibrium universality classes.
- Demonstrated that dynamical exponents are ratios of neighboring Fibonacci numbers.
- Showed that universal scaling functions are asymmetric Lévy distributions.
- Linked these properties to macroscopic current density and compressibility.
Conclusions:
- The diffusive and KPZ universality classes are specific instances within a broader Fibonacci-based framework.
- These findings provide a deeper, unified understanding of universality in non-equilibrium systems.
- The characterized scaling functions are experimentally measurable, offering avenues for validation.
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