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Zero-range process with finite compartments: Gentile's statistics and glassiness
1Charles University in Prague, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Prague, Czech Republic.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 30, 2014
Summary
This study explores condensation dynamics in limited-size compartments. It reveals self-blocking dynamics that slow down relaxation, particularly in asymmetric systems and Bose-Einstein-like condensations.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Stochastic Processes
Background:
- Investigating condensation phenomena in statistical physics is crucial for understanding emergent collective behaviors.
- Previous models often assumed infinite compartments, limiting applicability to finite systems.
Purpose of the Study:
- To analyze the statics and dynamics of condensation in a zero-range process with finite-sized compartments.
- To understand the conditions under which stationary states factorize for both symmetric and asymmetric dynamics.
- To explore the impact of limited compartment sizes on condensation dynamics and relaxation times.
Main Methods:
- Utilizing a zero-range process model with compartments of limited sizes.
- Analyzing both symmetric and asymmetric dynamics, including special hopping rules.
- Employing grand canonical analysis in the limit of large system sizes.
- Illustrating general features with an inhomogeneous system exhibiting Bose-Einstein-like condensation.
Main Results:
- For symmetric dynamics, the stationary state exhibits a factorized form.
- Asymmetric dynamics factorize only for specific hopping rules allowing compartment overjumps.
- Grand canonical analysis remains accurate in condensed phases for large systems, even with finite compartments.
- Dynamical self-blocking significantly increases relaxation times during condensation.
Conclusions:
- Limited compartment sizes introduce unique condensation behaviors, including dynamical self-blocking.
- The findings extend the applicability of grand canonical analysis to finite systems.
- The study provides insights into Bose-Einstein-like condensations in inhomogeneous systems.
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