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

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.