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Stochastic ballistic annihilation and coalescence
1Department of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom.
Physical Review Letters
|October 21, 2000
Summary
We reveal a universal phase diagram for stochastic ballistic models in one dimension. This diagram, derived from an exact density solution, uncovers four distinct regimes, including two novel phases due to stochasticity.
Area of Science:
- Statistical Physics
- Mathematical Physics
- Complex Systems
Background:
- Stochastic models with annihilation and coalescence are crucial for understanding particle dynamics.
- Previous studies focused on ballistic annihilation, leaving stochastic effects in density decay largely unexplored.
- A binary velocity distribution in one dimension presents unique challenges for analytical solutions.
Purpose of the Study:
- To investigate a class of stochastic ballistic annihilation and coalescence models in one dimension.
- To derive an exact solution for particle density and identify a universal phase diagram.
- To characterize the asymptotic density decay and explore the impact of stochasticity.
Main Methods:
- Development of a matrix product approach for solving the model.
- Utilizing properties of q-deformed harmonic oscillator algebra.
- Exact analytical solution for particle density.
Main Results:
- An exact solution for the asymptotic density decay was obtained.
- A universal phase diagram, dependent on two reduced parameters, was revealed.
- Four distinct regimes were identified, including two previously uncharacterized phases arising from stochasticity.
- The findings extend the understanding of ballistic annihilation models.
Conclusions:
- The study provides a comprehensive framework for analyzing stochastic ballistic models.
- The universal phase diagram offers new insights into particle dynamics and density decay.
- The identified novel phases highlight the significant role of stochasticity in these systems.