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Conformal Invariance in Driven Diffusive Systems at High Currents.

D Karevski1, G M Schütz1,2

  • 1Institut Jean Lamour, dpt. P2M, Groupe de Physique Statistique, Université de Lorraine, CNRS UMR 7198, B.P. 70239, F-54506 Vandoeuvre les Nancy Cedex, France.

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Summary
This summary is machine-generated.

We reveal how space-time correlations in driven diffusive systems are governed by conformal field theory for high activity. A phase diagram shows this regime and a phase separation region for low activity, with dynamics belonging to Kardar-Parisi-Zhang universality classes.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Driven diffusive systems exhibit complex behaviors, including fluctuations into atypical dynamical regimes.
  • Understanding space-time correlations is crucial for characterizing these systems' dynamics.

Purpose of the Study:

  • To analyze space-time correlations in driven diffusive systems during fluctuations to atypical current or activity regimes.
  • To determine the universality classes and phase diagram governing these dynamics.

Main Methods:

  • Application of conformal field theory (CFT) with central charge c=1 for one-dimensional systems.
  • Analysis of the one-dimensional asymmetric simple exclusion process (ASEP) with periodic and open boundaries.
  • Investigation of phase transitions and dynamical exponents.

Main Results:

  • Spatiotemporal density correlations are determined by CFT (c=1, dynamical exponent z=1) for high activity.
  • A full phase diagram reveals a conformally invariant regime and a phase separation region for low activity.
  • The phase transition line corresponds to Kardar-Parisi-Zhang universality classes (z=3/2), with a diffusive point (z=2).
  • Exact universal dynamical structure functions were obtained for the ASEP in the maximal current limit.

Conclusions:

  • Conformal field theory and Kardar-Parisi-Zhang universality classes precisely describe different regimes of driven diffusive systems.
  • The study provides exact results for universal dynamical properties in one dimension.
  • The findings offer a comprehensive understanding of phase transitions and correlations in these systems.