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Updated: Jun 1, 2026

Single-Molecule Measurement of Protein Interaction Dynamics Within Biomolecular Condensates

Single-Molecule Measurement of Protein Interaction Dynamics Within Biomolecular Condensates

Published on: January 5, 2024

Bose-Einstein condensation and a two-dimensional walk model.

Farhad H Jafarpour¹

¹Physics Department, Bu-Ali Sina University, 65174-4161 Hamedan, Iran. farhad@ipm.ir

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 24, 2011

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.

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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.