as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ''Schrodinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ''collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ''classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ''found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ''fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.

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Decoherence, einselection, and the quantum origins of the classical

From the Publisher:
Orthogonal frequency-division multiplexing (OFDM) is a method of digital modulation in which a signal is split into several narrowband channels at different frequencies.
CDMA is a form of multiplexing, which allows numerous signals to occupy a single transmission channel, optimising the use of available bandwidth. Multiplexing is sending multiple signals or streams of information on a carrier at the same time in the form of a single, complex signal and then recovering the separate signals at the receiving end.
Multi-Carrier (MC) CDMA is a combined technique of Direct Sequence (DS) CDMA (Code Division Multiple Access) and OFDM techniques. It applies spreading sequences in the frequency domain.
Wireless communications has witnessed a tremendous growth during the past decade and further spectacular enabling technology advances are expected in an effort to render ubiquitous wireless connectivity a reality.
This technical in-depth book is unique in its detailed exposure of OFDM, MIMO-OFDM and MC-CDMA. A further attraction of the joint treatment of these topics is that it allows the reader to view their design trade-offs in a comparative context.
Divided into three main parts:
Part I provides a detailed exposure of OFDM designed for employment in various applications
Part II is another design alternative applicable in the context of OFDM systems where the channel quality fluctuations observed are averaged out with the aid of frequency-domain spreading codes, which leads to the concept of MC-CDMA
Part III discusses how to employ multiple antennas at the base station for the sake of supporting multiple users in the uplink
Portrays theentire body of knowledge currently available on OFDMProvides the first complete treatment of OFDM, MIMO(Multiple Input Multiple Output)-OFDM and MC-CDMAConsiders the benefits of channel coding and space time coding in the context of various application examples and features numerous complete system design examplesConverts the lessons of Shannon's information theory into design principles applicable to practical wireless systemsCombines the benefits of a textbook with a research monograph where the depth of discussions progressively increase throughout the book

This all-encompassing self-contained treatment will appeal to researchers, postgraduate students and academics, practising research and development engineers working for wireless communications and computer networking companies and senior undergraduate students and technical managers.

OFDM and MC-CDMA for Broadband Multi-User Communications, WLANs and Broadcasting

Based on a calculation of neural decoherence rates, we argue that the degrees of freedom of the human brain that relate to cognitive processes should be thought of as a classical rather than quantum system, i.e., that there is nothing fundamentally wrong with the current classical approach to neural network simulations. We find that the decoherence time scales ( approximately 10(-13)-10(-20) s) are typically much shorter than the relevant dynamical time scales ( approximately 10(-3)-10(-1) s), both for regular neuron firing and for kinklike polarization excitations in microtubules. This conclusion disagrees with suggestions by Penrose and others that the brain acts as a quantum computer, and that quantum coherence is related to consciousness in a fundamental way.

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Importance of quantum decoherence in brain processes.

Uniform domains and the quasi-hyperbolic metric

The space of all Bloch functions will be denoted by «^. There are several distinct characterisations of Bloch functions: (i) f € @l if and only if the f amily of functions f,(*) = ΐ(φ(*ϊ) f(?(0)); φ(ζ) = -ff^·, | a |< l, is finitely normal in D [28]. (ii) Let df(z) denote the largest schlicht disc around the point f(z) on the Riemann image surf ace by /. Then f € SS if and only if b = sup df(z) < oo. z€D This is equivalent to a well-known theorem of Bloch. In quantitative terms

On Bloch functions and normal functions.

The Schwarz Principle of Reflection. The Logarithmic Potential, Balayage, and Quadrature Domains. Examples of ''Quadrature Identities''. Quadrature Domains: Basic Properties, 1. Quadrature Domains: Basic Properties, 2. Schwarzian Reflection, Revisited. Projectors from L2 ( OMEGA) to H2 ( OMEGA). The Friedrichs Operator. Concluding Remarks. Bibliography. Index.

The Schwarz Function and Its Generalization to Higher Dimensions

Extremal problems for polynomials and power series

Domains on which analytic functions satisfy quadrature identities

One of the earliest attempts to rigorously prove the solvability of Dirichlet’s boundary value problem was based on seeking the solution in the form of a “potential of double layer”, and this leads to an integral equation whose kernel is (in general) both singular and non-symmetric. C. Neumann succeeded with this approach for smoothly bounded convex domains, and H. Poincare, by a tremendous tour de force, showed how to push through the analysis for domains with sufficiently smooth boundaries but no hypothesis of convexity. In this work he was (according to his own account) guided by consideration of a variational problem involving the partition of energy of an electrostatic field induced by charges placed on the boundary of a domain, more precisely the charge distributions which render stationary the energy of the field inside the domain divided by the energy of the field outside the domain. Unfortunately, a rigorous treatment of this problem was not possible with the tools available at that time (as Poincare was well aware). So far as we know, the only one to propose a rigorous treatment of Poincare’s problem was T. Carleman (in the two-dimensional case) in his doctoral dissertation. Thanks to later developments (especially concerning Sobolev spaces, and spectral theory of operators on Hilbert space) we can now give a complete, general and rigorous account of Poincare’s variational problem, and that is the main object of the present paper. As a by-product, we refine some technical aspects in the theory of symmetrizable operators and prove in any number of dimensions the basic properties of the analogue of the planar Bergman–Schiffer singular integral equation. We interpret Poincare’s variational principle as a non-selfadjoint eigenvalue problem for the angle operator between two distinct pairs of subspaces of potentials. We also prove a series of novel spectral analysis facts (some of them conjectured by Poincare) related to the Poincare–Neumann integral operator.

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Harold S. Shapiro

Papers

The Schwarz Function and Its Generalization to Higher Dimensions

Extremal problems for polynomials and power series

Domains on which analytic functions satisfy quadrature identities

Poincare's variational problem in potential theory

Some theorems on Čebyšev approximation