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Temporally correlated zero-range process with open boundaries: Steady state and fluctuations
Massimo Cavallaro1, Raúl J Mondragón2, Rosemary J Harris1
1School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS, United Kingdom.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 19, 2015
Summary
This study investigates an open-boundary zero-range process with temporal correlations. Results show memory effects influence particle currents and can induce dynamical phase transitions, differing from memoryless models.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Physics
- Complex Systems
Background:
- The on-off zero-range process models particle dynamics with temporal correlations.
- Real-world systems exhibit particle condensation due to such correlations.
- Understanding non-equilibrium statistical mechanics is crucial for complex systems.
Purpose of the Study:
- To analyze an open-boundary zero-range process with temporal correlations.
- To investigate the impact of memory on particle condensation and current distributions.
- To explore large deviation properties and potential phase transitions.
Main Methods:
- Derivation of the exact steady-state solution for a one-site system.
- Application of a mean-field approximation for one-dimensional lattices.
- Analytical and numerical calculations of particle current properties.
Main Results:
- The particle distribution is accurately described by an effective Markovian solution.
- Rare particle current probabilities deviate significantly from memoryless models.
- Evidence for a memory-induced dynamical phase transition was found.
Conclusions:
- Temporal correlations in the on-off zero-range process can lead to phenomena like particle condensation.
- The system's behavior, particularly rare events, is influenced by memory effects.
- Dynamical phase transitions can emerge due to these memory-induced correlations.
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