Weber, Markus Felix (2016): Master equations: from path integrals, to bosons, to bacteria. Dissertation, LMU München: Faculty of Physics 

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Abstract
The dynamics of a complex physical, biological, or chemical systems can often be modelled in terms of a continuoustime Markov process. The governing equations of these processes are the FokkerPlanck and the master equation. Both equations assume that the future of a system depends only on its current state, memories of its past having been wiped out by randomizing forces. Whereas the FokkerPlanck equation describes a system that evolves continuously from one state to another, the master equation models a system that performs jumps between its states. In this thesis, we focus on master equations. We first present a comprehensive mathematical framework for the analytical and numerical analysis of master equations in chapter I. Special attention is given to their representation by path integrals. In the subsequent chapters, master equations are applied to the study of physical and biological systems. In chapter II, we study the stochastic and deterministic evolution of zerosum games and thereby explain a condensation phenomenon expected in drivendissipative bosonic quantum systems. Afterwards, in chapter III, we develop a coarsegrained model of microbial range expansions and use it to predict which of three strains of Escherichia coli survive such an expansion.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  Stochastic processes, Markov processes, master equations, path integrals, path summation, spectral analysis, rare event probabilities, condensation, bosonic systems, bacterial range expansions 
Subjects:  500 Natural sciences and mathematics 500 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date of oral examination:  27. October 2016 
1. Referee:  Frey, Erwin 
MD5 Checksum of the PDFfile:  c8b9874e2e7d698dbc03ee7408dd929a 
Signature of the printed copy:  0001/UMC 24463 
ID Code:  20380 
Deposited On:  13. Feb 2017 10:07 
Last Modified:  13. Feb 2017 10:07 