joint BCAM-UPV/EHU Analysis and PDE seminar: Applications of Catastrophe Theory to the Study of Phase Transitions in Quantum Statistical Mechanics.

Seminar

BCAM, Wednesday, October 11th, 2023, 17:00-18:00

Title: Applications of Catastrophe Theory to the Study of Phase Transitions in Quantum Statistical Mechanics. 

Kauê Rodrigues (he/him) - BCAM

Abstract

In both classical and quantum statistical mechanics, mean-field interactions are generally used to model phase transitions, by obtaining a variational problem over the pressure where the phase diagram of the system can be computed. The aim of this talk is to demonstrate that it is possible to analyze this variational problem —for certain fermionic systems with mean-field interactions— by means of catastrophe theory, and to show that catastrophe theory can be a useful tool for obtaining a qualitative description of the phase diagram of a quantum system.