Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2008-11-06
Phys. Rev. E, 79, 021109 (2009)
Physics
Condensed Matter
Statistical Mechanics
19 pages, 5 figures included
Scientific paper
10.1103/PhysRevE.79.021109
We investigate the long time behaviour of the one-dimensional ballistic aggregation model that represents a sticky gas of N particles with random initial positions and velocities, moving deterministically, and forming aggregates when they collide. We obtain a closed formula for the stationary measure of the system which allows us to analyze some remarkable features of the final `fan' state. In particular, we identify universal properties which are independent of the initial position and velocity distributions of the particles. We study cluster distributions and derive exact results for extreme value statistics (because of correlations these distributions do not belong to the Gumbel-Frechet-Weibull universality classes). We also derive the energy distribution in the final state. This model generates dynamically many different scales and can be viewed as one of the simplest exactly solvable model of N-body dissipative dynamics.
Majumdar Satya N.
Mallick Kirone
Sabhapandit Sanjib
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