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Cluster-factorized steady states in finite-range processes
Amit Chatterjee1, Punyabrata Pradhan2, P K Mohanty1,3
1Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064, India.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2015
Summary
This study introduces a finite-range process (FRP) model for particle hopping on a ring. The research reveals conditions for a factorized steady state (FSS) and a transfer-matrix formulation for analyzing nonequilibrium lattice models.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Theoretical Physics
Background:
- Nonequilibrium lattice models are crucial for understanding complex systems.
- The zero-range process (ZRP) is a foundational model with a factorized steady state (FSS).
- Extending ZRP to finite-range interactions (FRP) presents new analytical challenges.
Purpose of the Study:
- To investigate a class of nonequilibrium lattice models on a ring with finite-range particle hopping.
- To determine the conditions under which FRP exhibits a factorized steady state (FSS).
- To develop analytical tools for calculating correlation functions and mass distributions in FRP.
Main Methods:
- Analysis of a finite-range process (FRP) model on a ring.
- Derivation of conditions for a cluster-factorized steady state.
- Application of finite-dimensional transfer-matrix formulation.
- Investigation of criteria for condensation transitions.
Main Results:
- The steady state of FRP can be factorized into a product of cluster-weight functions under specific hop rate conditions.
- A finite-dimensional transfer-matrix formulation is established for a large class of cluster-weight functions.
- Exact calculation of spatial correlation functions and subsystem mass distributions is enabled.
- A criterion for the condensation transition in FRP is discussed.
Conclusions:
- The study provides a framework for analyzing complex nonequilibrium lattice models beyond the ZRP.
- The developed transfer-matrix method offers powerful tools for exact calculations in statistical physics.
- Understanding factorized steady states and condensation transitions is key for predicting system behavior.
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