Studies of distributions in physics using maximum entropy and scaling methods

Sammanfattning: The maximum entropy method (MEM) is applied in the analysis of equilibrium systems. Some general properties of the MEM and how to choose constraints as well as moments are discussed. A numerically stable algorithm is developed and implemented. Distributions arising from physical processes are studied. In particular, charge-state distributions arising in beam-foil spectroscopy have been studied in detail. The main emphasis lies on finding regularities and systematic behaviour through the MEM. It is shown that in the studied system there is a general Gaussian behaviour and the implications of using only Gaussians are discussed. Extending the MEM to an analysis of non-equilibrium systems requires care when choosing the number of moments. How to use the MEM to examine time-dependent problems is discussed. Time evolution of a distribution can be described on a microscopic level by master equations and on a macroscopic level by Fokker-Planck equations. These approaches can be connected through a scaling method: the large-Omega scaling. The procedure and its applications are thoroughly described . Scaling methods in general have a wide applicability in many fields. The method of dimensional scaling is applied in the calculation of multipole polarizabilities. The result is compared to what is obtained from an exact calculation. Also, a procedure to calculate energies of excited states in atoms or molecules by using dimensional scaling on local pseudopotentials is developed.