On model dynamical systems in statistical mechanics

Ya. G. Sinaǐ

Andreas U Schmidt

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.

Marco Baldovin, Giacomo Gradenigo, Angelo Vulpiani +1 more

Vladimir V. Bazhanov, Conrad J. Burden

General principles of statistical mechanics, P.A. Pearce the connection between statistical mechanics and quantum field theory, B.M. McCoy two-dimensional models in statistical mechanics, R.J. Baxter topics in conformal field theory, C. Itzykson quantum gravity as dynamical triangulation, A.A. Migdal lattice gauge theory, C.J. Hamer quantum groups for physicists, M. Gould chaos versus order in Hamiltonian dynamical systems, G.R.W. Quispel quantum and classical integrable systems and statistical mechanics, R.K. Bullough and J.T. Timonen introduction to quantum field theory, R.J. Crewther.

Derek W. Robinson

Leo P. Kadanoff

Fundamentals of statistical physics: the lectures - a survey one particle and many Gaussian distributions quantum mechanics and lattices. Random dynamics: diffusion and hopping from hops to statistical mechanics correlations and response. More statistical mechanics: statistical thermodynamics Fermi, Bose, and other. Phase transitions: overview of phase transitions mean field theory of critical behaviour continuous phase transitions renormalization in one dimension real space renormalization techniques duality planar model and Coulomb systems XY model, renormalization and duality.