Some Applications in Physics and Chemistry

In this chapter we will apply the derived solution methods of Chap. 4 to some important applications out of the field of physics and chemistry in order to demonstrate the high potential of the Master equation approach in the field of natural sciences. Chemical reactions are typical examples of discrete dynamic processes obeying the mass action law. Since the single chemical reactions are considered as independent of each other a multinomial Poisson distribution is usually expected. However, in case of nonlinear chemical reactions we demonstrate that although the transition rates obey combinatorial mass-action law kinetics a more complicated statistical distribution is obtained. The investigation of the dynamics of spin-systems, especially the kinetic Ising model with physically motivated transition rates, is of fundamental interest in statistical non-equilibrium physics. The phase transition from an initially disordered state to a ferromagnetic state and the calculation of the escape rate, in other words, the probability of a possible spin flip in their conceptual simplicity will be investigated. The derivation of the photon statistics of the Laser-light is selected as a further typical quantum mechanical example out of the field of physics. The photon statistics of the Laser shows a phase transition at the so-called Laser threshold. The atoms of the Laser active material seem to be slaved: all atoms behave in a coordinated way and emit wave tracks in phase. They emit giant wave tracks with a dramatically increased light intensity. This example will be used to apply the already introduced methods and to learn more about how complicated discrete difference equations can be handled.