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arXiv:quant-ph/9905004 · Lecture notes in physics

The Meaning of Decoherence

H. D. Zeh

Published May 4, 1999• 17 citations
arXivHTMLPDF

Abstract

The conceptual and dynamical aspects of decoherence are analyzed, while their consequences are discussed for several fundamental applications. This mechanism, which is based on a universal Schrödinger equation, is furthermore compared with the phenomenological description of open systems in terms of `quantum dynamical maps'.
DOI
10.48550/arxiv.quant-ph/9905004

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The interaction of a quantum system with a many degree o ff reedom environment entails damping and the loss of quantum coherence. In these two lectures we focus on two aspects of open quantum system dynamics. First, we present decoherence as a dynamical phenomenon and determine the corresponding time scales, discuss an experiment and the nature of robust states, and mention universal properties of short- time decoherence of macroscopic superpositions. Secondly, in analogy to the classical description of open systems in terms of Langevin equations, we present a stochastic approach to open quantum system dynamics in terms of a stochastic Schrodinger equation. We give a microscopic ¨ derivation that allows us to generalize the stochastic approach to non- Markovian situations. We discuss a convolutionless formulation of our theory and finally, we focus on the quantised version of Brownian motion as an often-employed example.
The interaction of a quantum system with a many degree of freedom environment entails damping and the loss of quantum coherence. In these two lectures we focus on two aspects of open quantum system dynamics. First, we present decoherence as a dynamical phenomenon and determine the corresponding time scales, discuss an experiment and the nature of robust states, and mention universal properties of short-time decoherence of macroscopic superpositions. Secondly, in analogy to the classical description of open systems in terms of Langevin equations, we present a stochastic approach to open quantum system dynamics in terms of a stochastic Schrödinger equation. We give a microscopic derivation that allows us to generalize the stochastic approach to non-Markovian situations. We discuss a convolutionless formulation of our theory and finally, we focus on the quantised version of Brownian motion as an often-employed example.
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.
Conceptual Problems in Quantum Cosmology The application of quantum theory to cosmology raises a number of conceptual questions, such as the role of the quantum-mechanical notion of “observer” or the absence of a time variable in the Wheeler–DeWitt equation. I point out that a relational formulation of quantum mechanics, and more in general the observation that evolution is always relational, provides a coherent solution to this tangle of problems. A number of confusing issues appear when we try to apply quantum mechanics to cosmology. Quantum mechanics, for instance, is generally formulated in terms of an observer making measurements on a system. In a laboratory experiment, it is easy to identify the system and the observer: but what is the observer in quantum cosmology? Is it part of the same universe described by the cosmological theory, or should we think of it as external to the universe? Furthermore, the basic quantum dynamical equation describing a system including gravity is not the Schrödinger equation, but rather the Wheeler–DeWitt equation, which has no time parameter: is this related to the absence of an observer external to the universe? How do we describe the quantum dynamics of the universe without a time variable in the dynamical equation and without an observer external to the universe? I suggest that clarity on these issues can be obtained by simply recognizing the relational nature of quantum mechanics and more in general the relational nature of physical evolution. In the context of quantum theory, this nature is emphasized by the so-called relational interpretation of quantum mechanics (Rovelli, 1996). The relational nature of evolution, on the other hand, has been pointed out by the partial-observable formulation of general covariant dynamics (Rovelli, 2002). A central observation is that there is a common confusion between two different meanings of the expression “cosmology”. This is discussed below, in Section 15.1.1. A considerable amount of the difficulties mentioned above stems, I argue, from this confusion. The discussion clarifies on the role of the quantum mechanical observer in cosmology, which is considered in Section 15.1.2. In Section 15.2, I briefly describe the relational interpretation of quantum mechanics and some related aspects of quantum theory.