Zeno Dynamics in Quantum Statistical Mechanics

TL;DR

This paper investigates the quantum Zeno effect in quantum statistical mechanics using operator algebra, providing conditions for its occurrence, explicit Zeno generators, and demonstrating macroscopic effects in the X-Y model.

Contribution

It introduces a condition for the quantum Zeno effect in operator algebraic systems and constructs the associated Zeno dynamics and equilibrium states.

Findings

The condition effectively predicts the Zeno effect in quantum spin systems.

Explicit form of the Zeno generator is derived.

Frequent microscopic measurements can alter macroscopic equilibrium states.

Abstract

We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Further, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium.