THERMODYNAMIC FORMALISM AND LOCALIZATION IN LORENTZ GASES AND HOPPING MODELS

摘要: The thermodynamic formalism expresses chaotic properties of dynamical systems in terms the Ruelle pressure ψ(β). inverse-temperature-like variable β allows one to scan structure probability distributin dynamic phase space. This is applied here a lorentz lattice gas. where particle moving on sizeLd collides with fixed scatterers placed at random locations. Here we give rigorous arguments that limit infinite has two branches joining slope discontinuity β=1. low- and high-β correspond localization trajectories respectively “most chaotic” (highest density) region deterministic” (lowest region, i.e. ψ(β) completely controlled by rare fluctuations distribution lattice. it dose not carry information global static disorder. As approaches unity from either side, localization-delocalization transition leads state are extended transprot properties. At finiteL narrow around β=1 scales as (InL)−2. α depends sign 1−β, ifd>1, (L InL)−1 ifd=1. result appears be general for diffusive disorder, such walks environments or continuous Lorentz Other models disordered lattices, showing same phenomenon, discussed.