Boundary conditions and KMS states

• Grant number: 20/14563-0
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate (Direct)
• Start date: June 01, 2021
• End date: May 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Rodrigo Bissacot Proença
• Grantee: Lucas Affonso Silva Pereira
• Supervisor: Marcelo Laca
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: University of Victoria (UVic), Canada
• Associated to the scholarship: 17/18152-2 - Phase transitions on Quantum Ising Models, BP.DD

Abstract

The notion of equilibrium is central in statistical mechanics. In the classical case, the DLR equations describe all the possible equilibrium states for a spin lattice system. In the quantum case, where the appropiate notion of equilibrium is the KMS condition, the very notion of boundary condition is not well understood, even though some proposals already exist. In this project, using the groupoid picture, we intend to solve this problem by introducing an appropriate notion of boundary condition and proving that the KMS condition may be described by a set of equations closely related to the DLR equation. (AU)