In the earlier chapters we presented basic features of certain advanced topics including supersymmetric quantum mechanics, coherent and squeezed states, quantum computers and quantum cryptography. There are several other topics which also received considerable interest and have a wide range of applications. In the present chapter we consider some of them. Particularly, we give a very brief introduction to the following fascinating topics: 1. Quantum gravity 2. Quantum Zeno effect 3. Quantum teleportation 4. Quantum games 5. Quantum cloning 6. Quantum diffusion 7. Quantum chaos.
In the earlier chapters we presented basic features of certain advanced topics including supersymmetric quantum mechanics, coherent and squeezed states, quantum computers and quantum cryptography. There are several other topics which also received considerable interest and have a wide range of applications. In the present chapter we consider some of them. Particularly, we give a very brief introduction to the following fascinating topics: 1. Quantum gravity 2. Quantum Zeno effect 3. Quantum teleportation 4. Quantum games 5. Quantum cloning 6. Quantum diffusion 7. Quantum chaos.
Quantum Mechanics II: Advanced Topics offers a comprehensive exploration of the state-of-the-art in various advanced topics of current research interest. A follow-up to the authors’ introductory book Quantum Mechanics I: The Fundamentals, this book expounds basic principles, theoretical treatment, case studies, worked-out examples and applications of advanced topics including quantum technologies. A thoroughly revised and updated this unique volume presents an in-depth and up-to-date progress on the growing topics including latest achievements on quantum technology. In the second edition six new chapters are included and the other ten chapters are extensively revised. Features Covers classical and quantum field theories, path integral formalism and supersymmetric quantum mechanics. Highlights coherent and squeezed states, Berry’s phase, Aharonov—Bohm effect and Wigner function. Explores salient features of quantum entanglement and quantum cryptography. Presents basic concepts of quantum computers and the features of no-cloning theorem and quantum cloning machines. Describes the theory and techniques of quantum tomography, quantum simulation and quantum error correction. Introduces other novel topics including quantum versions of theory of gravity, cosmology, Zeno effect, teleportation, games, chaos and steering. Outlines the quantum technologies of ghost imaging, detection of weak amplitudes and displacements, lithography, metrology, teleportation of optical images, sensors, batteries and internet. Contains several worked-out problems and exercises in each chapter. Quantum Mechanics II: Advanced Topics addresses various currently emerging exciting topics of quantum mechanics. It emphasizes the fundamentals behind the latest cutting-edge developments to help explain the motivation for deeper exploration. The book is a valuable resource for graduate students in physics and engineering wishing to pursue research in quantum mechanics.
This chapter presents some basic ideas and the features of quantum gravity. It gives a compact summary of fundamental ideas of the approaches of semiclassical gravity, loop quantum gravity and string theory. Reconstructing the quantum state of a system on another system of the same type at a distant place is termed as quantum teleportation. Quantum Zeno effect is important in understanding quantum theory of measurement and is in fact a vital tool in quantum computing. Quantum cosmology is considered an application of quantum mechanics to the universe as a whole. The classical cosmology theory is mainly based on the cosmological principle and the expansion of the universe. George Antonovich Gamow and his collaborators Ralph Asher Alpher and Robert Herman proposed the Big-Bang model of the universe to account for the abundances of the elements. Cosmic inflation is based on the hypothesis that the early universe underwent an extremely rapid expansion.
Quantum Mechanics II: Advanced Topics uses more than a decade of research and the authors’ own teaching experience to expound on some of the more advanced topics and current research in quantum mechanics. A follow-up to the authors introductory book Quantum Mechanics I: The Fundamentals, this book begins with a chapter on quantum field theory, and goes on to present basic principles, key features, and applications. It outlines recent quantum technologies and phenomena, and introduces growing topics of interest in quantum mechanics. The authors describe promising applications that include ghost imaging, detection of weak amplitude objects, entangled two-photon microscopy, detection of small displacements, lithography, metrology, and teleportation of optical images. They also present worked-out examples and provide numerous problems at the end of each chapter.
In this book so far we are concerned with the various fundamentals of quantum mechanics. In the latter part of the century the subject has started growing on multi direction. Newer quantum phenomena were identified. Quantum version of certain classical phenomena and concepts have been formulated. New topics in quantum physics have born. Application of quantum physics to other branches of science and technology has started. For example, a great deal of research has been focused on the topics such as supersymmetry, Berry’s phase, Aharonov-Bohm effect, Wigner distribution function, coherent and squeezed states, quantum computing, quantum cryptography, quantum imaging and quantum lithography to name a few. Theoretical and experimental progress have been made in these topics. The fundamentals and the progresses made in these advanced topics are covered in the volume-II of this book. Before we move on to these advanced topics we wish to mention that in classical physics several fascinating newer phenomena were first realized in numerical simulation and then necessary theory and mathematical tools were developed. Thus, it is important to develop numerical schemes to study quantum systems.
Quantum entanglement does not only provide a field of fundamental studies, but can also be harnessed as a tool for applications. In this chapter, after introducing two general theorems that are useful in the context of this discussion (§7.1), we propose a few examples: quantum cryptography (§7.2), teleportation (§7.3), and quantum computing (§7.4). For the moment, only quantum cryptography has given rise to real applications, and has been used in practical (and even commercial) applications; its purpose is the sharing of cryptographic keys between several partners by using a protocol where privacy is guaranteed by fundamental laws of physics. As for quantum computation, it is based on the general manipulation of quantum information, and is probably a more futuristic field of research in terms of applications, but it is certainly a domain of intense activity throughout the world. Strictly speaking, none of these subjects in itself brings a really new view on the interpretation of quantum mechanics. Nevertheless, in addition to their strong intrinsic interests, they provide very direct and particularly interesting applications of its basic principles. This is the reason we study them in this chapter. We will only summarize the main ideas; the interested reader is invited to read the proposed references. Two theorems The two theorems that follow are similar; one deals with the creation and duplication of quantum states, the other with their determination. No-cloning The duplication of a quantum state, often called “quantum cloning”, is an operation where one starts from one particle in an arbitrary quantum state and reaches a situation where two particles are in the same state ∣φ〈.