We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics. Talk given at the Conference on Fundamental Problems in Quantum Theory Baltimore, June 18–22, 1994 Consider a dilute gas of hard spheres in a box with hard walls. Give the spheres some arbitrary i...

We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic, tries to sketch a theoretical view of chaos. Among the main ideas in this article are the distinction between overall chaos and partial chaos, and the fact th...

The aim of this article is twofold: (1). develop a strategy to prove the existence of chaos in weakly quasilinear systems, (2). strengthen the existing results on chaos in partial differential equations. First, we study a sineGordon equation containing weakly quasilinear terms, and existence of chaos is proved. Then, we study a Ginzburg-Landau equation containing weakly quasilinear terms, and e...

Chaos criterion for quantum field theory is proposed. Its accordance with classical chaos criterion is demonstrated in the semi-classical limit of quantum mechanics. Originally phenomenon of chaos was associated with problems of classical mechanics and statistical physics. Attempt of substantiation of statistical mechanics initiated intensive study of chaos and uncover its basic properties main...

This paper is concerned with invariance (F1,F2)-scrambled sets under iterations. The main results are an extension of the compound invariance of Li–Yorke chaos and distributional chaos. New definitions of (F1,F2)-scrambled sets in non-autonomous discrete systems are given. For a positive integer k, the properties P(k) and Q(k) of Furstenberg families are introduced. It is shown that, for any po...

let (x, d) be a compact metric space and f : x → x be a continuous map. consider the metric space (k(x),h) of all non empty compact subsets of x endowed with the hausdorff metric induced by d. let ¯ f : k(x) → k(x) be defined by ¯ f(a) = {f(a) : a ∈ a} . we show that block-coppels chaos in f implies block-coppels chaos in ¯ f if f is a bijection.

– Temperature chaos is an extreme sensitivity of the equilibrium state to a change of temperature. It arises in several disordered systems that are described by the so called scaling theory of spin glasses, while it seems to be absent in mean field models. We consider a model spin glass on a tree and show that although it has mean field behavior with replica symmetry breaking, it manifestly has...