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A concise and accessible account of the dynamical properties of one-dimensional quantum systems, for graduate students and new researchers.
The present level of experimental sophistication in quantum physics allows physicists to explore domains unimaginable just a decade ago and to test the most fundamental laws of quantum mechanics. This has led to renewed interest in devising new tests, experiments, and devices where it is possible to observe the interaction and localization of just a few atoms or photons. These techniques have been used to reveal new nonclassical effects, to question the limit of the principle of correspondence, and to force quantum behavior in semiconductors. With contributions from leading experts in quantum systems, Quantum Dynamics of Simple Systems provides an overview of the present range of quantum dynamics, exploring their use and exotic behaviors. It covers specific subjects of quantum dynamics in a competent and detailed way with emphasis on simple systems where few atoms or electrons are involved. This volume will prove to be a useful tool for graduate students as well as experienced physicists.
This thesis addresses the intriguing topic of the quantum tunnelling of many-body systems such as Bose-Einstein condensates. Despite the enormous amount of work on the tunneling of a single particle through a barrier, we know very little about how a system made of several or of many particles tunnels through a barrier to open space. The present work uses numerically exact solutions of the time-dependent many-boson Schrödinger equation to explore the rich physics of the tunneling to open space process in ultracold bosonic particles that are initially prepared as a Bose-Einstein condensate and subsequently allowed to tunnel through a barrier to open space. The many-body process is built up from concurrently occurring single particle processes that are characterized by different momenta. These momenta correspond to the chemical potentials of systems with decreasing particle number. The many-boson process exhibits exciting collective phenomena: the escaping particles fragment and lose their coherence with the source and among each other, whilst correlations build up within the system. The detailed understanding of the many-body process is used to devise and test a scheme to control the final state, momentum distributions and even the correlation dynamics of the tunneling process.
The central theme of this lecture collection is quantum dynamics, regarded mostly as the dynamics of entanglement and that of decoherence phenomena. Both these concepts appear to refer to the behavior of surprisingly fragile features of quantum systems supposed to model quantum memories and to implement quantum date processing routines. This collection may serve as an essential resource for those interested in both theoretical description and practical applications of fundamentals of quantum mechanics.
A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.
Changes and additions to the new edition of this classic textbook include a new chapter on symmetries, new problems and examples, improved explanations, more numerical problems to be worked on a computer, new applications to solid state physics, and consolidated treatment of time-dependent potentials.
The issue which the new ideas of these new books really raise with our culture, is not about whether they are true, since these new ideas identify a valid context for physical description, and whereas the current context for math and physics (2014) cannot do that, ie they cannot describe the stable properties of a general many-(but-few)-body system. Whereas the new ideas about math and physics can be used to solve the most fundamental problems about the physical world, in regard to understanding physical stability, a problem which the current descriptive context of math and physics (2014) cannot solve. That is, "what now, in 2014, passes for math and physics knowledge are delusions."* Yet these delusions are the ideas expressed in our propaganda-education system about math and physics. Rather The real issue, which these new ideas present to our culture, is about our cultural relation to "what is beyond the material world." That is, it is about our cultural representation of religion, or the spirit. In particular, in relation to the "previous knowledge humans needed to possess" in order to make Gobekli-tepe, Puma Punku, Stonehenge, etc, ie simply to be able to lift and position such large stones, as well as the understanding which is needed to go beyond the context of the material world, and into the context of all the ancient mythologies in regard to the ancient religious stories, etc etc *The current paradigm (in 2014) describes a general state of indefi nable randomness in which there is always "a chaotic transitioning process" which exists as random elementary-particle collisions, and which, supposedly, is perpetually occurring. Thus, their description of the wide range of the generally stable states of the many-(but-few)-body systems..., into which this "forever chaotically transitioning" process supposedly settles but explicit descriptions of this process do not exist. Instead their answer is that "such stable, many-(but-few)-body systems are too complicated to describe."
The first edition of this work appeared in 1930, and its originality won it immediate recognition as a classic of modern physical theory. The fourth edition has been bought out to meet a continued demand. Some improvements have been made, the main one being the complete rewriting of the chapter on quantum electrodymanics, to bring in electron-pair creation. This makes it suitable as an introduction to recent works on quantum field theories.