Creation and annihilation operators for Markov processes
N.T. Lin (TU Delft - Electrical Engineering, Mathematics and Computer Science)
FRANK Redig – Mentor (TU Delft - Applied Probability)
JM Thijssen – Graduation committee member (TU Delft - QN/Thijssen Group)
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Abstract
In this thesis the theory of Markov processes and creation and annihilation operators will be used to derive the time evolution of a discrete reaction-diffusion system. More specifically, we make use of transition rates to construct the generator of a process. We then transform this generator through suitable quantum mechan- ical operators to arrive at our result, namely that the Poisson dis- tribution of a reaction-diffusion system stays Poisson distributed in time with varying rate. This applies for the univariate case, with only a simple birth and death process, as well as the multi- variate case. Furthermore, simulations support this result while also showing that an interacting particle system with pairwise an- nihilation does not evolve according to the Poisson distribution.