The purpose of the course is to provide the student with a wide vision on how theoretical physics can contribute to understand phenomena in a variety of fields ranging from “classical” subjects like diffusion, quantum mechanics and, more in general, to the physics of complex systems. Particular emphasis will be placed on the relationships between different topics allowing for a unified mathematical approach where the concept of universality will play an important role. The course will deal with a series of paradigmatic physical systems that have marked the evolution of theoretical physics in the last century including the most recent challenges posed by disordered systems with applications to machine learning and neural networks. Each physical problem, the modeling and the solution thereof, will be described in detail using powerful mathematical techniques.

The first part of the course will provide the basic mathematical tools necessary to deal with most of the subjects of our interest. The second part of the course will be concerned with the key concepts of universality, stochastic processes and emergent phenomena, which justify the use of field theoretical models of interacting systems. In the third part it will be shown how solutions of quantum systems can be mapped in solutions of diffusion problems and vice versa using common mathematical techniques. The last part will deal with the most advanced theoretical challenges related to non-homogenous/disordered systems, which find applications even outside the physical context in which they arose.

Category: A.A. 2018 - 2019 / Corsi di laurea magistrale / SC2443 - PHYSICS OF DATA