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Kardar-Parisi-Zhang modes in d-dimensional directed polymers
G M Schütz1, B Wehefritz-Kaufmann2
1Institute of Complex Systems II, Forschungszentrum Jülich, 52425 Jülich, Germany.
Physical Review. E
|January 20, 2018
Summary
We introduce a new model for fluctuating directed polymers. Our findings show that fluctuations are limited to Kardar-Parisi-Zhang (KPZ) or diffusive types, excluding Lévy-type fluctuations.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Stochastic Processes
Background:
- Directed polymers in random media are fundamental in statistical mechanics.
- Understanding their dynamics and fluctuations is crucial for various physical systems.
- Previous models often exhibited complex fluctuation behaviors.
Purpose of the Study:
- To define a novel stochastic lattice model for fluctuating directed polymers in d≥2 dimensions.
- To analyze the deterministic large dynamics and stationary fluctuations of this model.
- To investigate the nature of fluctuations and their theoretical underpinnings.
Main Methods:
- Definition of a stochastic lattice model.
- Interpretation as a random path or an asymmetric simple exclusion process.
- Application of nonlinear fluctuating hydrodynamics and mode coupling theory.
- Analysis of coupled Kardar-Parisi-Zhang (KPZ) equations and diffusion equations.
Main Results:
- The deterministic large dynamics are governed by coupled KPZ and diffusion equations.
- Stationary fluctuations in any dimension d are exclusively of KPZ or diffusive type.
- Modes are pure, with only subleading couplings, excluding modified KPZ or Lévy fluctuations.
- Mode-coupling matrices satisfy the trilinear condition.
Conclusions:
- The proposed model provides a simplified yet comprehensive framework for studying directed polymer fluctuations.
- The identified fluctuation types (KPZ and diffusive) offer a clear understanding of the system's behavior.
- The exclusion of Lévy-type fluctuations highlights the model's specific applicability and theoretical constraints.
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