Decoherence has been hailed as the solution to long-standing foundational problems dating back to the beginnings of quantum mechanics. It has been cursed as the key obstacle to next-generation technologies, such as quantum computers (another se- ingly omnipresent ?eld of research). And while decoherence has been directly observed in various experiments, its scope and meaning have often been m- understood and misrepresented. Decoherence makes a fantastic subject of research, as it touches upon many di?erent facets of physics, from phi- sophically inclined questions of interpretation all the way to down-to-earth problems in experimental settings and engineering applications. This book will introduce the reader, in an accessible and self-contained manner, to these various fascinating aspects of decoherence. It will focus in particularontherelationofdecoherencetotheso-calledquantum-to-classical transition, i. e., the question of how decoherence may explain the emergence of the classical appearance of the macroscopic world around us from the underlying quantum substrate. Thescopeofthisbookisrelativelybroadinordertofamiliarizethereader withthemanyfacetsofdecoherence, inboththetheoreticalandexperimental domains. Throughout the book, I have sought to maintain a healthy balance betweentheconceptualideasassociatedwiththedecoherenceprogramonthe one hand and the formal and mathematical details on the other hand. This book will establish a proper understanding of decoherence as a pure quantum phenomenon and will emphasize the importance of the correct interpretation of the consequences and achievements of decoherence.

    In the last century these classical concepts were found inadequate. In the new quantum mechanics theory, conscious experiences enter into the dynamics in specified ways not fixed by physically described aspects alone.

    Exploring this emerging subject, Introduction to Quantum Control and Dynamics presents the mathematical concepts and fundamental physics behind the analysis and control of quantum dynamics, emphasizing the application of Lie algebra and Lie group theory.After introducing the basics of quantum mechanics, the book derives a class of models for quantum control systems from fundamental physics. It examines the controllability and observability of quantum systems and the related problem of quantum state determination and measurement. The author also uses Lie group decompositions as tools to analyze dynamics and to design control algorithms. In addition, he describes various other control methods and discusses topics in quantum information theory that include entanglement and entanglement dynamics. The final chapter covers the implementation of quantum control and dynamics in several fields.Armed with the basics of quantum control and dynamics, readers will invariably use this interdisciplinary knowledge in their mathematical, physics, and engineering work.