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Condensation transition in a conserved generalized interacting zero-range process.

Abdul Khaleque¹, Parongama Sen¹

¹Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India.

Physical Review. E

|May 14, 2016

Summary

This summary is machine-generated.

This study analyzes a particle hopping model, revealing distinct system phases based on interaction probability. A condensate phase emerges, showing universal behavior for short-range interactions and nonuniversality for infinite-range interactions.

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Area of Science:

Statistical Mechanics
Many-Body Physics
Non-equilibrium Systems

Background:

The study investigates a conserved generalized zero-range process, a model describing particle interactions between two sites.
Particles hop from a more populated site to a less populated one with a probability p.

Purpose of the Study:

To determine the steady-state particle distribution function P(n) for the described system.
To analyze the different phases the system exhibits as the interaction probability p is varied.
To investigate the behavior of the system in the condensate and noncondensate phases, particularly concerning universality.

Main Methods:

Employed both analytical and numerical methods to obtain the steady-state particle distribution function P(n).
Analyzed the particle distribution function P(n) within the condensate phase using a known scaling form.
Identified distinct regions within the noncondensate phase based on the value of p relative to p_c and 0.5.

Main Results:

The system exhibits several distinct phases as the interaction probability p changes.
A condensate phase is identified for p_l < p < p_c, with phase boundaries dependent on interaction range.
Short-range interactions show universal behavior in the condensate phase, while infinite-range interactions display nonuniversality.
In the noncondensate phase (p > p_c), two regions are observed: p_c < p ≤ 0.5 and p > 0.5.
A scale emerges in the system for p > 0.5, irrespective of the interaction range.

Conclusions:

The generalized zero-range process displays complex phase behavior dependent on interaction probability and range.
Universality is observed in the short-range condensate phase, contrasting with nonuniversality in the infinite-range case.
A distinct scaling behavior emerges in the high-probability noncondensate phase, indicating a different dynamical regime.