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Current fluctuations in the symmetric zero-range process below and at critical density.

Tanmoy Chakraborty1, Punyabrata Pradhan1, Kavita Jain2

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Summary

This study analyzes current fluctuations in a symmetric zero-range process near a phase transition. We found that the variance of integrated current grows with time, exhibiting distinct behaviors away from and at the critical point.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Non-equilibrium Systems

Background:

  • Characterizing current fluctuations in steady states is crucial but often limited to non-critical systems.
  • Understanding systems near phase transitions requires advanced analytical techniques.

Purpose of the Study:

  • To analytically calculate transport coefficients for a symmetric zero-range process exhibiting a phase transition.
  • To characterize the time-integrated current fluctuations in both steady states and at criticality.

Main Methods:

  • Analytical calculation of density-dependent transport coefficients (bulk-diffusion, particle mobility).
  • Hydrodynamic scaling analysis.
  • Application of scaling theory at the critical point.

Main Results:

  • Away from criticality, variance of integrated current scales as sqrt(t) at short times and t at long times.
  • A full scaling function for variance is derived, quantifying current fluctuation growth.
  • At criticality, short-time behavior shows anomalous growth exponents varying with model parameters.

Conclusions:

  • The study provides a comprehensive characterization of current fluctuations in a system with a phase transition.
  • Distinct scaling behaviors are identified away from and at the critical point.
  • The findings offer insights into non-equilibrium statistical mechanics and critical phenomena.