ASYMPTOTIC TIME DECAY IN QUANTUM PHYSICS

Time decays form the basis of a multitude of important and interesting phenomena in quantum physics that range from spectral properties, resonances, return and approach to equilibrium, to quantum mixing, dynamical stability preperties and irreversibility and the "arrow of time." This monograph is devoted to a clear and precise, yet pedagogical account of the associated concepts and methods.

Introduction; Spreading and Method of Stationary Phase; The Relation Between Time-Decay and Spectral Properties; Pointwise Decay for a Class of Sparse Models and Anderson-Like Models in Dimensions D>2; Quantum Anosov Systems and Exponential Decay: Relation to Classical Mechanics and "Quantum Chaos"; Quasi-Exponential Decay and Resonances: Gamow Vectors; Interlude: Systems with Infinite Number of Degrees of Freedom; Approach to Equilibrium and Mixing for Systems with Infinite Number of Degrees of Freedom: Irreversibility and the "Arrow of Time".