Equilibrium and Non-Equilibrium Statistical Mechanics

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Equilibrium and Non-equilibrium Statistical MechanicsAbstract of Proposed ResearchBruno Nachtergaele This project will support research on theoretical issues in equilibrium and non-equilibrium quantum statistical mechanics. The main focus is on quantum spin models that arise in condensed matter physics as models for the magnetic properties of a large variety of materials. Apart from the possible applications in material science, the primary goal of the project is to provide new insights in fundamental problems of quantum statistical mechanics and to find rigorous methods for their solution. In particular, I will investigate methods to obtain qualitative and quantitative information about the spectrum of model Hamiltonians such as the Heisenberg model and derive implications of these spectral properties for the dynamics of the system.The main focus is on quantum spin models that arise in condensed matter physics as models for the magnetic properties of a large variety of materials. Due to the close similarity of the mathematics, however, it is expected that the project will also provide useful results for applications in quantum information theory and quantum computation. New directions to be explored include the dynamics of complex quantumsystems and the development of numerical techniques to simulate such systems.