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Classical kinetical Bose gas.

An autocatalytic reaction combined with spontaneous creation and annihilation processes of particles are studied in a quantum formalism of the master equation in a lattice gas representation with unrestricted occupancy. In case the system is activated by a linear coupling to a heat bath the problem can be solved exactly and the stationary particle density follows the Bose distribution. The relation to spin-flip processes with a restricted occupancy is discussed. Different from those processes the relaxation time and the density fluctuation increase in the high-temperature limit. On a small scale the mutual interaction between the particles is relevant. While in case of a repulsive interaction the stationary solution becomes unstable against short wavelength fluctuations, an attractive interaction leads to an instability for long wavelength fluctuations. The system decays in domains, the size of which can be estimated as a function of temperature and interaction strength. The model is also appropriate to study the growth of open bacterial colonies under the influence of a competitive interaction between the species.