Research Advances In Quantum Dynamics

There continue at present many developments in the area of quantum mechanics and quantum dynamics in particular, of a very fundamental nature, all the way from implications for the foundations of physics to the influence of quantum mechanics on emerging technologies, such as the areas of quantum semiconductors and quantum computing, both of which are very important examples. It is hoped that the papers in this volume will be able to provide a much needed resource for researchers with regard to current fields of research in this dynamic area.

This is a rapidly developing field to which the author is a leading contributor New methods in quantum dynamics and computational techniques, with applications to interesting physical problems, are brought together in this book Useful to both students and researchers

This book covers advanced topics in quantum mechanics, including nonrelativistic multi-particle systems, relativistic wave equations, and relativistic fields. Numerous examples for application help readers gain a thorough understanding of the subject. The presentation of relativistic wave equations and their symmetries, and the fundamentals of quantum field theory lay the foundations for advanced studies in solid-state physics, nuclear, and elementary particle physics. The authors earlier book, Quantum Mechanics, was praised for its unsurpassed clarity.

This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schrödinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical physics, PDE, and operator theory. All their material is the fruit of recent studies that have already become a reference in the community. Offering a unified perspective of the mathematics of quantum mechanics, it is a valuable resource for researchers in the field.

Quantum technology has arrived as one of the most important new topics of research, as it is the newest way to create computing power, harness secure communications, and use sensitive measurement methods that surpass the capabilities of modern supercomputers. If successfully developed, quantum computers and technology will be able to perform algorithms at impressively quick rates and solve problems that were previously deemed impossible. This technology will disrupt what is already known about computing and will be able to reach new heights, speeds, and problem-solving capabilities not yet seen. Beyond its inherent benefits comes the fact that quantum technology will create improvements in many everyday gadgets as well, spanning many industries. The Research Anthology on Advancements in Quantum Technology presents the latest discoveries in quantum technology itself along with providing its essential uses, applications, and technologies that will impact computing in modern times and far into the future. Along with this overview comes a look at quantum technology in many different fields such as healthcare, communications, aviation, automotive, forecasting, and more. These industries will be looked at from the perspective of data analytics, pattern matching, cryptography, algorithms, and more. This book is essential for computer scientists, engineers, professionals, researchers, students, and practitioners interested in the latest information on quantum technology.

The Advanced Study Institute on "Quantum Dynamics of Molecules: The New Experimental Challenge to Theorists," which was sponsored by the Scientific Affairs Division of NATO, was held at Trinity Hall, Ca~bridge, England from September 15th till September 29th, 1979. In all, a total of 79 lecturers and students attended the meeting: they had diverse backgrounds in chemistry, physics and mathematics. In my proposal to NATO requesting financial support for an Advanced Study Institute, I suggested that molecular physics was facing a qualitatively new experimental situation in which the exploration of previously inaccessible dynamical phenomena would become of increasing importance. At the same time I was aware that in recent years powerful theoretical techniques, that might prove crucial tools for the interpretation of the new experiments, have been developed in mathematics and theoretical physics. The aim of the ASI was to review at an advanced level these recent developments, juxtaposing new theory with new experimental pos sibilities in the hope that the participants in the-Institute would through their subsequent work increase the awareness of the whole molecular theory community of the changing nature of chemical physics. The recent developments in laser spectroscopy, particle scatter ing experiments and molecular beam technology imply that an entirely new class of phenomena involving molecules in gasses and liquids can now be investigated.

Advances in Quantum Chemistry publishes surveys of current developments in the rapidly developing field of quantum chemistry--a field that falls between the historically established areas of mathematics, physics,chemistry, and biology. With invited reviews written by leading international researchers, each presenting new results, this quality serial provides a single vehicle for following progress in this interdisciplinary area. "Volume 28 collects papers written in honor of Geerd H.F. Diercksen. Diercksen is a pioneer in the field of quantum mechanics whose research includes studies of the structure and stability of hydrogen-bonded and Van der Waals dimers and small clusters, thevibrational and rotational spectra of diatomic and triatomic molecules, on static electric properties in solutions and of molecules absorbed on surfaces. His results are essential in molecular and atomic physics, in astrophysics, and in biochemistry.

The introduction of control theory in quantum mechanics has created a rich, new interdisciplinary scientific field, which is producing novel insight into important theoretical questions at the heart of quantum physics. 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. To advantage students, instructors and practitioners, and since the field is highly interdisciplinary, this book presents an introduction with all the basic notions in the same place. The field has seen a large development in parallel with the neighboring fields of quantum information, computation and communication. The author has maintained an introductory level to encourage course use. 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. Changes to the New Edition: New Chapter 4: Uncontrollable Systems and Dynamical Decomposition New section on quantum control landscapes A brief discussion of the experiments that earned the 2012 Nobel Prize in Physics Corrections and revised concepts are made to improve accuracy Armed with the basics of quantum control and dynamics, readers will invariably use this interdisciplinary knowledge in their mathematics, physics and engineering work.