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Cambridge University Press eBooks

Miscellany and Addenda to Part III

Giancarlo Calvanese Strinati

Published Feb 6, 2026• 0 citations
Publisher

Abstract

Similar to Chapter 20 of Part I and Chapter 31 of Part II, this chapter considers the treatment of a few topics, which are relevant to the general purposes of the book, but whose inclusion in previous chapters would have diverted the discussion of the main topics of interest therein. Specifically, it addresses a schematic derivation of the Lindblad Master equation (aimed at helping the reader in retracing and better identifying the essential steps made and approximations adopted in the more general derivation presented in Chapter 35), as well as the physical assumptions underlying the original Kadanoff–Baym ansatz.

DOI
10.1017/9781009411509.040

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Similar to Chapter 20 of Part I and Chapter 31 of Part II, this chapter considers the treatment of a few topics, which are relevant to the general purposes of the book, but whose inclusion in previous chapters would have diverted the discussion of the main topics of interest therein. Specifically, it addresses a schematic derivation of the Lindblad Master equation (aimed at helping the reader in retracing and better identifying the essential steps made and approximations adopted in the more general derivation presented in Chapter 35), as well as the physical assumptions underlying the original Kadanoff–Baym ansatz.
Similar to Chapter 20 of Part I, this chapter considers the treatment of a few topics, which are relevant to the general purposes of the book but whose inclusion in previous chapters would have diverted the discussion of the main topics of interest therein. Specifically, it considers the Dyson equations for the contour single-particle Green’s function in the Nambu representation, the relative strength of different frequency terms in the derivation of the time-dependent Gross–Pitaevskii equation, the detailed calculation of an integral occurring in the derivation of the time-dependent Ginzburg–Landau equation, the irrelevance of the reference time t ₀ for the convolutions entering the Kadanoff–Baym equations at equilibrium, and the average energy of the system expressed in terms of the lesser Green’s function even in nonequilibrium situations.
In the last two decades there has been an enormous progress in the experimental investigation of single quantum systems. This progress covers fields such as quantum optics, quantum computation, quantum cryptography, and quantum metrology, which are sometimes summarized as `quantum technologies'. A key issue there is entanglement, which can be considered as the characteristic feature of quantum theory. As disparate as these various fields maybe, they all have to deal with a quantum mechanical treatment of the measurement process and, in particular, the control process. Quantum control is, according to the authors, `control for which the design requires knowledge of quantum mechanics'. Quantum control situations in which measurements occur at important steps are called feedback (or feedforward) control of quantum systems and play a central role here. This book presents a comprehensive and accessible treatment of the theoretical tools that are needed to cope with these situations. It also provides the reader with the necessary background information about the experimental developments. The authors are both experts in this field to which they have made significant contributions. After an introduction to quantum measurement theory and a chapter on quantum parameter estimation, the central topic of open quantum systems is treated at some length. This chapter includes a derivation of master equations, the discussion of the Lindblad form, and decoherence – the irreversible emergence of classical properties through interaction with the environment. A separate chapter is devoted to the description of open systems by the method of quantum trajectories. Two chapters then deal with the central topic of quantum feedback control, while the last chapter gives a concise introduction to one of the central applications – quantum information. All sections contain a bunch of exercises which serve as a useful tool in learning the material. Especially helpful are also various separate boxes presenting important background material on topics such as the block representation or the feedback gain-bandwidth relation. The two appendices on quantum mechanics and phase-space and on stochastic differential equations serve the same purpose. As the authors emphasize, the book is aimed at physicists as well as control engineers who are already familiar with quantum mechanics. It takes an operational approach and presents all the material that is needed to follow research on quantum technologies. On the other hand, conceptual issues such as the relevance of the measurement process for the interpretation of quantum theory are neglected. Readers interested in them may wish to consult instead a textbook such as Decoherence and the Quantum-to-Classical Transition by Maximilian Schlosshauer. Although the present book does not contain applications to gravity, part of its content might become relevant for the physics of gravitational-wave detection and quantum gravity phenomenology. In this respect it should be of interest also for the readers of this journal.