Approach to Equilibrium in a Simple Model

Publisher Website
Google Scholar
Abstract
The time evolution of a class of generalized quantum Ising models (with various long‐range interactions, including Dyson's 1/rα) has been studied from the C*‐algebraic point of view. We establish that: (1) All 〈A〉t are weakly almost periodic in time; (2) there exists a unique averaging procedure over time; (3) the time evolution in the thermodynamical limit can be locally implemented by effective Hamiltonians in the algebra of quasilocal observables; (4) there exists a specific connection between the spectral properties of the time evolution of the initial state and the approach to equilibrium; (5) there are examples in which the time evolution is not G‐Abelian.

This publication has 15 references indexed in Scilit: