Physics

A - Knowledge and understanding OF 1) To know the fundamentals of the theory of stochastic processes, discrete and continuous, and thier formal framework in terms of resolution of Chapman-Kolmogorov, Fokker-Planck and master equations. OF 2) To understand the similarities with the properties of equations already known to the students (like Schroedinger equation) and to learn equation resolution methods using operational calculus. OF 3) To know the formalism of stochastic integration of stochastic differential equations and the connection to the Fokker-Planck partial differential equation. B - Application skills OF 4) To deduce physical properties of systems from the analysis of the stochastic equations. OF 5) To apply newly learned methods to the estimate of first passage times and to the consequences of Arrhenius law on relaxation towards equilibrium in systems with rough potential landscapes. OF 6) To apply methods and techniques to systems of different nature at and off equilibrium (viscous liquids, wave systmes, glassy systems, lasers). C - Autonomy of judgment OF 7) To be able to integrate acquired knwoledge and apply it also to cases not explicitly treated in the course. OF 8) To be able to connect acquired knowledge to previous one, formalizing known concepts and connetcing them to more complex cases. D - Communication skills OF 9) To know how to orally present a demonstration procedure or an application assessing the most relevant and clarifying steps and their meaning. E - Ability to learn OF 10) To be able to consult diferrent textbooks and scientifc papers to the aim of autonomously deepening some of the arguments covered by the course. OF 11) To be able to evaluate the effectiveness of the various studied approaches in relation to the treated problems.