edited by Sandro Graffi (Università di Bologna, Italy) & André Martinez (Università di Bologna, Italy)

This book is centered on the two minicourses conducted by C Liverani (Rome) and J Sjoestrand (Paris) on the return to equilibrium in classical statistical mechanics and the location of quantum resonances via semiclassical analysis, respectively. The other contributions cover related topics of classical and quantum mechanics, such as scattering theory, classical and quantum statistical mechanics, dynamical localization, quantum chaos, ergodic theory and KAM techniques.

• Return to Equilibrium in Classical and Quantum Systems (C Liverani)
• Quantum Resonances and Trapped Trajectories (J Sjöstrand)
• Return to Thermal Equilibrium in Quantum Statistical Mechanics (V Bach)
• Small Oscillations in Some Nonlinear PDE's (D Bambusi & S Paleari)
• The Semi-Classical Van-Vleck Formula. Application to the Aharonov–Bohm Effect (J-M Bily & D Robert)
• Fractal Dimensions and Quantum Evolution Associated with Sparse Potential Jacobi Matrices (J-M Combes & G Mantica.)
• Infinite Step Billiards (M D Esposti)
• Semiclassical Expansion for the Thermodynamic Limit of the Ground State Energy of Kac's Operator (B Helffer & T Ramond)
• Asymptotics of Scattering Poles for Two Strictly Convex Obstacles (M Ikawa)
• Parabolic Dynamical Systems and Inducing (S Isola)
• QFT for Scalar Particles in External Fields on Riemannian Manifolds (H Isozaki)
• Existence and Born-Oppenheimer Asymptotics of the Total Scattering Cross-Section in Ion–Atom Collisions (T Jecko et al.)
• On Asymptotic Perturbation Theory for Quantum Mechanics (G Nenciu)
• Destruction of the Beating Effect in a Periodically Driven Double-Well (A Sacchetti)
• Berezin–Toeplitz Quantization and Berezin Transform (M Schlichenmaier)