Zeno Dynamics in Quantum Statistical Mechanics

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.

15 pages, AMSLaTeX; typos corrected, references updated and added, acknowledgements added, style polished; revised version contains corrections from published corrigenda

References in corpus (4)

• Quantum Zeno subspaces
• Zeno dynamics yields ordinary constraints
• Zeno Dynamics of von Neumann Algebras
• Quantum Zeno effects with "pulsed" and "continuous" measurements

Cited by in corpus (7)

• Quantum Zeno dynamics: mathematical and physical aspects
• Control of decoherence: analysis and comparison of three different strategies
• Quantum Zeno effect and dynamics
• Zeno dynamics and constraints
• Mathematics of the Quantum Zeno Effect
• Approximation of the Semigroup generated by the Robin Laplacian in terms of the Gaussian Semigroup
• The semiclassical limit of a quantum Zeno dynamics