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Published on: September 26, 2016
Equivalence of a one-dimensional driven-diffusive system and an equilibrium two-dimensional walk model
Farhad H Jafarpour1, Somayeh Zeraati
1Physics Department, Bu-Ali Sina University, 65174-4161 Hamedan, Iran. farhad@ipm.ir
Summary
We found a direct connection between equilibrium and nonequilibrium systems. The transfer matrix of a one-transit walk model relates to the algebra of driven-diffusive models, linking their physical quantities.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Mathematical Physics
Background:
- Driven-diffusive systems with nearest-neighbor interactions exhibit shock dynamics.
- Nonequilibrium steady states can be described by matrix-product methods.
- Shock measures in these systems can resemble random walkers on lattices.
Purpose of the Study:
- To present an equilibrium two-dimensional one-transit walk model.
- To find the partition function of this model using the transfer matrix method.
- To establish a connection between this equilibrium model and driven-diffusive systems.
Main Methods:
- Transfer matrix method to calculate the partition function.
- Matrix-product representation for driven-diffusive systems.
- Similarity transformation to relate the two models.
Main Results:
- The partition function of the one-transit walk model was derived.
- A direct connection between the partition functions of the two systems was established.
- The transfer matrix of the one-transit walk model is related to the driven-diffusive model's algebra via similarity transformation.
Conclusions:
- The study reveals a deep connection between equilibrium and nonequilibrium statistical mechanics models.
- Physical quantities in both systems are linked through a similarity transformation.
- This work provides a new perspective on analyzing complex many-body systems.
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