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Bose-Einstein condensation and a two-dimensional walk model
1Physics Department, Bu-Ali Sina University, 65174-4161 Hamedan, Iran. farhad@ipm.ir
Summary
We developed a 2D walk model confined to a plane quadrant, revealing a phase transition. Its partition function matches a driven-diffusive system, hinting at Bose-Einstein condensation phenomena.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Mathematical Physics
Background:
- Random walks are fundamental models in statistical physics.
- Phase transitions are critical phenomena observed in many physical systems.
- Driven-diffusive systems model transport phenomena with external forces.
Purpose of the Study:
- To introduce and analyze a novel two-dimensional walk model.
- To investigate the phase transition behavior of this model.
- To establish connections between different statistical physics models.
Main Methods:
- Calculation of the partition function using the transfer matrix method.
- Analysis of a driven-diffusive system on a discrete lattice.
- Mapping the driven-diffusive system to a zero-range process.
Main Results:
- The two-dimensional walk model exhibits a phase transition.
- The partition function of the walk model is identical to that of a specific driven-diffusive system.
- The driven-diffusive system shows particle accumulation, resembling Bose-Einstein condensation.
Conclusions:
- The studied two-dimensional walk model provides a new perspective on phase transitions.
- The exact equivalence to a driven-diffusive system highlights unexpected connections between models.
- The observed phenomena suggest potential links to real-space Bose-Einstein condensation.
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