In this master thesis we present the deterministic dynamical model Box-Ball System (BBS) coupled to a stochastic reservoir. This reservoir represents a boundary condition where balls are stochastically created and enter the system. The dynamics of such a system is different from the classical BBS and because of that we will define the auxiliary space. In the thesis we present the properties of this coupled system and numerical results obtained for observables. The properties and observables included in this thesis are: density, ball current, dynamical matrix, partial matrixes of the dynamical matrix and their recursive properties, spectrums of the steady state, marginal sums of the steady state, Schmidt ranks of bipartitions of non-equilibrium steady state, correlation functions and distributions of balls in the auxiliary space.
With the results gathered in the thesis we can make conjectures about BBS coupled with a stochastic reservoir that further study might prove.
The key conjectures in this thesis are about the spectrum of the steady state, partial matrixes, Schmidt ranks, crystal phase and correlations.
|
