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The statistical mechanics of the coagulation-diffusion process with a stochastic reset. (English) Zbl 1293.82016

The paper is a study about a stochastic reset effect in the exactly solvable one-dimensional coagulation-diffusion process. The phenomenon of stochastic resets can occur quite commonly in different situations. Generally, one can understand it as a situation when a network of tidal channels on a beach is washed out by a larger wave from time to time. The same can be said about random walks; if in this process we also assume a possibility to reset most of so far known features, this process will dramatically change; for example in the long-time limit, the stationary distribution of the particle with reset is no longer Gaussian. In this paper, we have considerations about a simple model of interacting particles – the coagulation-diffusion process, which in one spatial dimension is exactly solvable. However, this model is expanded by the stochastic reset basing on Equation (1.2) which becomes the most important one in this new model. In Section 2, this equation is derived in both cases: discrete and continuous. Section 3 gives a further expansion of the proposed model because a possibility of a particle-input on the lattice with fixed rate \(\lambda\) is allowed. This small change shows that input and reset interact in a rather non-intuitive way which can lead to a complex and non-monotonous dependence of the stationary particle density on the used parameters. Section 4 gives visualizations for inter-particle distribution functions.

MSC:

82C22 Interacting particle systems in time-dependent statistical mechanics
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics