Probabilistic modelling of classical and quantum systems

Abstract

While probabilistic modelling has been widely used in the last decades, the quantitative prediction in stochastic modelling of real physical problems remains a great challenge and requires sophisticated mathematical models and advanced numerical algoritms. In this study, we developed the mathematical tools for the quantitative prediction of three applications in Polymer Science and Quantum Measurements theory. In particular, we addressed a stochastic approach for the quantitative modelling of Controlled Radical Polymerization. Then, a Population Balance Equations based framework was derived for the on-the-fly prediction of Multi-phase Polymers Morphology. Finally, we designed a stochastic simulation framework for measurements performed on quantum systems, which helped us to re-examine the "continuous fuzzy measurements" theory by Audretsch and Mensky (1997).