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 properties 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.

Description-Table Of Contents

1. Introduction: a summary of mathematical and physical background for one-particle quantum mechanics -- 2. Spreading and asymptotic decay of free wave packets: the method of stationary phase and van der Corput's approach -- 3. The relation between time-like decay and spectral properties. 3.1. Decay on the average sense. 3.2. Decay in the L[symbol]-sense. 3.3. Pointwise decay. 3.4. Quantum dynamical stability -- 4. Time decay for a class of models with sparse potentials. 4.1. Spectral transition for sparse models in d = 1. 4.2. Decay in the average. 4.3. Pointwise decay -- 5. Resonances and quasi-exponential decay. 5.1. Introduction. 5.2. The model system. 5.3. Generalities on Laplace-Borel transform and asymptotic expansions. 5.4. Decay for a class of model systems after Costin and Huang: Gamow vectors and dispersive part. 5.5. The role of Gamow vectors. 5.6. A first example of quantum instability: ionization. 5.7. Ionization: study of a simple model. 5.8. A second example of multiphoton ionization: the work of M. Huang. 5.9. The reason for enhanced stability at resonances: connection with the Fermi golden rule -- 6. Aspects of the connection between quantum mechanics and classical mechanics: quantum systems with infinite number of degrees of freedom. 6.1. Introduction. 6.2. Exponential decay and quantum Anosov systems. 6.3. Approach to equilibrium. 6.4. Interlude: systems with an infinite number of degrees of freedom. 6.5. Approach to equilibrium and related problems in quantum systems with an infinite number of degrees of freedom.