Chaos, Scattering and Statistical Mechanics
This book describes advances in the application of chaos theory to classical scattering and nonequilibrium statistical mechanics generally, and to transport by deterministic diffusion in particular. The author presents the basic tools of dynamical systems theory, such as dynamical instability, topological analysis, periodic-orbit methods, Liouvillian dynamics, dynamical randomness and large-deviation formalism. These tools are applied to chaotic scattering and to transport in systems near equilibrium and maintained out of equilibrium. Chaotic Scattering is illustrated with disk scatterers and with examples of unimolecular chemical reactions and then generalized to transport in spatially extended systems. This book will be bought by researchers interested in chaos, dynamical systems, chaotic scattering, and statistical mechanics in theoretical, computational and mathematical physics and also in theoretical chemistry.
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Chapter 1 Dynamical systems and their linear stability
Chapter 2 Topological chaos
Chapter 3 Liouvillian dynamics
Chapter 4 Probabilistic chaos
Chapter 5 Chaotic scattering
Chapter 6 Scattering theory of transport
Chapter 7 Hydrodynamic modes of diffusion
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average billiard boundary conditions calculated cells chaos collision correlation functions corresponding cumulative function decay deﬁned deﬁnition deterministic diffusion coeﬂicient dimension disks distribution domain dynamical instability dynamical systems eigenstates eigenvalue entropy per unit entropy production equation ergodic escape rate evolution exponential ﬁnd ﬁnite ﬁrst ﬁxed points ﬂight ﬂow ﬂuctuations ﬂuid ﬂux fractal repeller Frobenius—Perron operator Gaspard given Hausdorff dimension hydrodynamic modes hyperbolic inﬁnite initial conditions integral invariant measure invariant set KS entropy lattice linear Liouville Liouvillian Liouvillian dynamics Lorentz gas Lyapunov exponents Markov chain matrix motion nonequilibrium steady observe obtained particles partition periodic orbits phase space Pollicott—Ruelle resonances positive Lyapunov exponents pressure function properties quantities random processes Ruelle s-entropy semigroup spectrum stability eigenvalues stable and unstable stationary point statistical ensembles statistical mechanics stochastic subset symbolic dynamics theorem theory thermodynamic topological entropy trajectories transport unstable manifolds vanishes variables vector ﬁeld velocity wavenumber zero Zeta function