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Zeno dynamics in quantum statistical mechanics

: Schmidt, A.U.


Journal of Physics. A, Mathematical and general 36 (2003), No.4, pp.1135-1148
ISSN: 0301-0015
ISSN: 0305-4470
ISSN: 0022-3689
Journal Article
Fraunhofer SIT ()

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. Furthermore, 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.