Exact kinetics of a coagulating system with the kernel \(K = 1\). (English) Zbl 1226.82037
Summary: The time evolution of a system of coagulating particles is studied within the Marcus-Lushnikov scheme. Each state of the system is characterized by the probability of finding a given set of population numbers of the particles with given mass at time \(t\). The generating functional for these probabilities obeys a Schrödinger-type evolution equation which is solved exactly for the coagulation kernel independent of the masses of colliding particles. I also show that the evolution equation is a good starting point for the asymptotic analysis of its solution in the limit of large total particle numbers.
MSC:
82C22 | Interacting particle systems in time-dependent statistical mechanics |
82D60 | Statistical mechanics of polymers |
60H30 | Applications of stochastic analysis (to PDEs, etc.) |
35Q82 | PDEs in connection with statistical mechanics |