Periodic orbit theory of strongly anomalous transport

Periodic orbit theory of strongly anomalous transport

We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical appearance of phase transitions in the spectrum of transport exponents is explained. PACS numbers: 05.45.-a † also at Istituto Nazionale Fisica Nucleare, Se...

Periodic orbit theory of anomalous diffusion.

We introduce a novel technique to find the asymptotic time behaviour of deterministic systems exhibiting anomalous diffusion. The procedure is tested for various classes of simple but physically relevant 1–D maps and possible relevance of our findings for more complicated problems is briefly discussed. In the last few years the phenomenon of deterministic diffusion has been widely investigated:...

Periodic Orbit Theory

Beyond the periodic orbit theory

The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated Fredholm determinants are of particularly simple polynomial form. The theory developed suggests an alternative to the conventional periodic orbit theory appr...

Periodic{orbit Theory of the Number Variance of Strongly Chaotic Systems

We discuss the number variance 2 (L) and the spectral form factor F() of the energy levels of bound quantum systems whose classical counterparts are strongly chaotic. Exact periodic{orbit representations of 2 (L) and F() are derived which explain the breakdown of universality, i. e., the deviations from the predictions of random{matrix theory. The relation of the exact spectral form factor F() ...