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Single-Molecule Measurement of Protein Interaction Dynamics Within Biomolecular Condensates

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Instability of condensation in the zero-range process with random interaction.

Stefan Grosskinsky¹, Paul Chleboun, Gunter M Schütz

¹Mathematics and Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom.

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

|October 15, 2008

Summary

Quenched disorder alters the condensation transition in the zero-range process, a particle system. This disorder changes critical exponents and causes density fluctuations with a unique distribution crossover.

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Area of Science:

Statistical physics
Stochastic processes
Condensed matter physics

Background:

The zero-range process is a fundamental stochastic interacting particle system.
This system is known to exhibit a phase transition known as condensation.
Understanding phase transitions in disordered systems is crucial in statistical physics.

Purpose of the Study:

To analyze the effect of quenched disorder on the condensation transition in the zero-range process.
To investigate how disorder modifies the critical behavior and exponents.
To characterize the fluctuations in local critical densities.

Main Methods:

Rigorous probabilistic arguments were employed.
Detailed mathematical analysis of the stochastic process was performed.
The distribution of local critical densities was studied.

Main Results:

Quenched disorder was shown to change the critical exponent of the interaction strength for condensation.
Large fluctuations in local critical densities were observed.
A crossover in the distribution of these densities from exponential to algebraic behavior was identified.

Conclusions:

Disorder significantly impacts the condensation transition in the zero-range process.
The findings provide new insights into the role of disorder in interacting particle systems.
The observed crossover in density distributions offers a novel characteristic of disordered phase transitions.