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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
PubMed
Summary
This summary is machine-generated.

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.

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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.