Introducing Decoherence.- The Basic Formalism and Interpretation of Decoherence.- Decoherence Is Everywhere: Localization Due to Environmental Scattering.- Master-Equation Formulations of Decoherence.- A World of Spins and Oscillators: Canonical Models for Decoherence.- Of Buckey Balls and SQUIDs: Observing Decoherence in Action.- Decoherence and Quantum Computing.- The Role of Decoherence in Interpretations of Quantum Mechanics.- Observations, the Quantum Brain, and Decoherence.
Introducing Decoherence.- The Basic Formalism and Interpretation of Decoherence.- Decoherence Is Everywhere: Localization Due to Environmental Scattering.- Master-Equation Formulations of Decoherence.- A World of Spins and Oscillators: Canonical Models for Decoherence.- Of Buckey Balls and SQUIDs: Observing Decoherence in Action.- Decoherence and Quantum Computing.- The Role of Decoherence in Interpretations of Quantum Mechanics.- Observations, the Quantum Brain, and Decoherence.
The conventional interpretation of quantum mechanics, though it permits a correspondence to classical physics, leaves the exact mechanism of transition unclear. Though this was only of philosophical importance throughout the twentieth century, over the past decade new technological developments, such as quantum computing, require a more thorough understanding of not just the result of quantum emergence, but also its mechanism. Quantum decoherence theory is the model that developed out of necessity to deal with the quantum-classical transition explicitly, and without external observers. In this thesis, we present a self-contained and rigorously argued full derivation of the master equation for quantum Brownian motion, one of the key results in quantum decoherence theory. We accomplish this from a foundational perspective, only assuming a few basic axioms of quantum mechanics and deriving their consequences. We then consider a physical example of the master equation and show that quantum decoherence successfully represents the transition from a quantum to classical system.
In the last decade decoherence has become a very popular topic mainly due to the progress in experimental techniques which allow monitoring of the process of decoherence for single microscopic or mesoscopic systems. The other motivation is the rapid development of quantum information and quantum computation theory where decoherence is the main obstacle in the implementation of bold theoretical ideas. All that makes the second improved and extended edition of this book very timely. Despite the enormous efforts of many authors decoherence with its consequences still remains a rather controversial subject. It touches on, namely, the notoriously confusing issues of quantum measurement theory and interpretation of quantum mechanics. The existence of different points of view is reflected by the structure and content of the book. The first three authors (Joos, Zeh and Kiefer) accept the standard formalism of quantum mechanics but seem to reject orthodox Copenhagen interpretation, Giulini and Kupsch stick to both while Stamatescu discusses models which go beyond the standard quantum theory. Fortunately, most of the presented results are independent of the interpretation and the mathematical formalism is common for the (meta)physically different approaches. After a short introduction by Joos followed by a more detailed review of the basic concepts by Zeh, chapter 3 (the longest chapter) by Joos is devoted to the environmental decoherence. Here the author considers mostly rather `down to earth' and well-motivated mechanisms of decoherence through collisions with atoms or molecules and the processes of emission, absorption and scattering of photons. The issues of decoherence induced superselection rules and localization of objects including the possible explanation of the molecular structure are discussed in details. Many other topics are also reviewed in this chapter, e.g., the so-called Zeno effect, relationships between quantum chaos and decoherence, the role of decoherence in quantum information processing and even decoherence in the brain. The next chapter, written by Kiefer, is devoted to decoherence in quantum field theory and quantum gravity which is a much more speculative and less explored topic. Two complementary aspects are studied in this approach: decoherence of particle states by the quantum fields and decoherence of field states by the particles. Cosmological issues related to decoherence are discussed, not only within the standard Friedmann cosmology, but also using the elements of the theory of black holes, wormholes and strings. The relations between the formalism of consistent histories defined in terms of decoherence functionals and the environmental decoherence are discussed in chapter 5, also written by Kiefer. The Feynman--Vernon influence functional for the quantum open system is presented in detail as the first example of decoherence functional. Then the general theory is outlined together with possible interpretations including cosmological aspects. The next chapter by Giulini presents an overview of the superselection rules arising from physical symmetries and gauge transformations both for nonrelativistic quantum mechanics and quantum field theory. Critical discussion of kinematical superselection rules versus dynamical ones is illustrated by numerous examples like Galilei invariant quantum mechanics, quantum electrodynamics and quantum gravity. The introduction to the theory of quantum open systems and its applications to decoherence models is given in chapter 7 by Kupsch. Generalized master equations, Markovian approximation and a few Hamiltonian models relevant for decoherence are discussed. Some mathematical tools, e.g., complete positivity and entropy inequalities are also presented. The last chapter by Stamatescu is devoted to stochastic collapse models which can be interpreted either as certain representations of the dynamics of open quantum systems or as fundamental modifications of the Schr\"odinger equation. The final part of the book consists of remarks by Zeh on related concepts and methods and seven appendices. The broad spectrum, mathematically-friendly presentation, inclusion of the very recent developments and the extensive bibliography (about 550 references) make this book a valuable reference for all researchers, graduate and PhD students interested in the foundations of quantum mechanics, quantum open systems and quantum information. The relative independence of the chapters and numerous redundancies allow for selective reading, which is very helpful for newcomers to this field.
This chapter explains the basic concept of decoherence and how it damps out quantum interference of a superposition state. Quantum decoherence plays an important role in the interpretation of quantum mechanics. The quantum information processing fields like quantum computers, quantum communication and quantum cryptography depend very much on how to minimize and control the quantum decoherence. Quantum decoherence helps to know the fundamental reasons of understanding the very nature of quantum mechanics, the measurement process and the boundary between quantum and classical behaviour. A double-slit experiment can be used to explain the basic concept of decoherence. The chapter discusses the master equations which give the dynamical evolution of the quantum system and the environment entangled state. It also discusses some of the decoherence models. In the collisional decoherence model, a massive free quantum particle scatters environmental particles. In the spin-boson models, the quantum system is represented by qubits and the environment by collision of harmonic oscillators.
Quantum decoherence is a dynamical process whereby a system's phase relations become delocalized due to interaction and subsequent entanglement with its environment. This delocalization, or decoherence, forces the quantum system into a state that is apparently classical (or apparently an eigenstate) by prodigiously suppressing features that typically give rise to so-called quantum behavior. Thus it has been frequently proposed by physicists and philosophers alike that decoherence explains the dynamical transition from quantum behavior to classical behavior. Statements like this assume the existence of distinct realms, however, and the present thesis is an exploration of the metaphysical consequences of quantum decoherence motivated by the question of the quantum-to-classical transition and interlevel relations: if there are in-principle ``classical' and ``quantum' levels, what are the relations between them? And if there are no such levels, what follows? Importantly, the following philosophical investigations are carried out by intentionally leaving aside the measurement problem and concerns about particular interpretations of quantum mechanics. Good philosophical work, it is argued, can be done without adopting a specific interpretational framework and without recourse to the measurement problem. After introducing the physics of decoherence and exploring the four canonical models applied to system-environment interactions, it is argued that, ontologically speaking, there exist no levels. This claim--called the ``nontological thesis'--exposes as ill-posed questions regarding the transition from the quantum regime to the classical regime and reveals the inappropriateness of interlevel relations (like reduction, supervenience and emergence) operating within metaphysical frameworks. The nontological thesis has further important consequences regarding intralevel relations: not only are there no meaningful ways to carve the world into levels, but there are no meaningful ways to carve the world into parts and wholes either. These conclusions, supported by quantum decoherence and the empirical success of its models, drastically alter the philosophical terrain--not just in physics or in the philosophy of physics, but in traditional metaphysics as well.