There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory} But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding However, it appeared that this new resource is
very complex and difficult to detect Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon A basic role of entanglement
witnesses in detection of entanglement is emphasized

Quantum entanglement

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

In the past few years one of the most exciting areas of research in physics has been the interdisciplinary field of cosmology and particle physics. The NSF's Institute for Theoretical Physics in Santa Barbara devoted a 6-month program and an intensive 1-week workshop to the subject. A brief review is given of both the workshop and this field which is attracting attention, in part, because the early Universe seems to be the only laboratory in which to study grand unification.

The early Universe

We use the influence functional path-integral method to derive an exact master equation for the quantum Brownian motion of a particle linearly coupled to a general environment (ohmic, subohmic, or supraohmic) at arbitrary temperature and apply it to study certain aspects of the loss of quantum coherence.

Quantum Brownian motion in a general environment: Exact master equation with nonlocal dissipation and colored noise.

This is the first of a series of papers which describe the functional-integral approach to the study of the statistical and kinetic properties of nonequilibrium quantum fields in flat and curved spacetimes. In this paper we treat a system of self-interacting bosons described by \ensuremath{\lambda}${\ensuremath{\varphi}}^{4}$ scalar fields in flat space. We adopt the closed-time-path (CTP or ``in-in'') functional formalism and use a two-particle irreducible (2PI) representation for the effective action. These formalisms allow for a full account of the dynamics of quantum fields, and put the correlation functions on an equal footing with the mean fields. By assuming a thermal distribution we recover the real-time finite-temperature theory as a special case. By requiring the CTP effective action to be stationary with respect to variations of the correlation functions we obtain an infinite set of coupled equations which is the quantum-field-theoretical generalization of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Truncation of this series leads to dissipative characteristics in the subsystem. In this context we discuss the nature of dissipation in interacting quantum fields.To one-loop order in a perturbative expansion of the CTP effective action, the 2PI formalism yields results equivalent to the leading 1/N expansion for an O(N)-symmetric scalar field. To higher-loop order we introduce a two-time approximation to separate the quantum-field effects of radiative correction and renormalization from the statistical-kinetic effects of collisions and relaxation. In the weak-coupling quasiuniform limit, the system of nonequilibrium quantum fields can subscribe to a kinetic theory description wherein the propagators are represented in terms of relativistic Wigner distribution functions. From a two-loop calculation we derive the Boltzmann equation for the distribution function and the gap equation for the effective mass of the quasiparticles. One can define an entropy function for the quantum gas of quasiparticles which satisfies the H theorem. We also calculate the limits to the validity of the binary collision approximation from a three-loop analysis. The theoretical framework established here can be generalized to nonconstant background fields and for curved spacetimes.

Nonequilibrium quantum fields: Closed-time-path effective action, Wigner function, and Boltzmann equation

We discuss the generalization to curved spacetime of a path-integral formalism of quantum field theory based on the sum over paths first going forward in time in the presence of one external source from an in vacuum to a state defined on a hypersurface of constant time in the future, and then backwards in time in the presence of a different source to the same in vacuum. This closed-time-path formalism which generalizes the conventional method based on in-out vacuum persistence amplitudes yields real and causal effective actions, field equations, and expectation values. We apply this method to two problems in semiclassical cosmology. First we study the back reaction of particle production in a radiation-filled Bianchi type-I universe with a conformal scalar field. Unlike the in-out formalism which yields complex geometries the real and causal effective action here yields equations for real effective geometries, with more readily interpretable results. It also provides a clear identification of particle production as a dissipative process in semiclassical theories. In the second problem we calculate the vacuum expectation value of the stress-energy tensor for a nonconformal massive \ensuremath{\lambda}${\ensuremath{\varphi}}^{4}$ theory in a Robertson-Walker universe. This study serves to illustrate the use of Feynman diagrams and higher-loop calculations in this formalism. It also demonstrates the economy of this method in the calculation of expectation values over the mode-sum Bogolubov transformation methods ordinarily applied to matrix elements calculated in the conventional in-out approach. The capability of the closed-time-path formalism of dealing with Feynman, causal, and correlation functions on the same footing makes it a potentially powerful and versatile technique for treating nonequilibrium statistical properties of dynamical systems as in early-Universe quantum processes.

Closed-time-path functional formalism in curved spacetime: Application to cosmological back-reaction problems.

Laser‐excited vibrational fluorescence measurements have been made on the asymmetric‐stretching vibrational level (00°1) of CO2. Vibration→vibration energy‐transfer rates from this level due to collisions with CO2 and with a number of other collision partners are presented. The rate of near‐resonant exchange of vibrational energy between CO2 and N2 (ΔE=18 cm−1) has been measured. The kinetics of the CO2 laser system are analyzed in terms of a three‐level scheme. Observed laser performance is compared with that calculated by use of collisional and radiative coupling rates observed in nonionized gases and of electron activation and deactivation rates estimated from CO2 discharge systems. In accordance with the scheme presented, the relative effectiveness of small amounts of added H2, D2, and He on laser output parallels their effectiveness in deactivating the lower laser level. The criteria for selecting molecules with vibrational‐energy‐level patterns likely to produce laser systems are outlined. Attempts ...

Vibrational Energy Transfer in CO2 Lasers

In preparation for an investigation of whether field-theoretic effects helped to make the early universe become isotropic, we seek to determine the physical (divergence-free) energy-momentum tensor through which the geometry of spacetime is influenced by a quantized scalar field with conformal ("new improved") coupling to the metric. The cosmological models studied are the Kasner-like (type I) metrics (homogeneous, spatially flat, nonrotating, but anisotropic), and also the isotropic Robertson-Walker metrics. The methods employed have previously been expounded in the context of a minimally coupled scalar field and a Robertson-Walker metric. Three divergent leading terms are extracted from an adiabatic expansion of the formal expressions for the expectation values of the energy density and pressures. In the Kasner case a slight reshuffling of the leading terms in the energy density displays all divergences to be proportional to either the metric tensor or a second-order curvature tensor which vanishes when the spacetime is isotropic; hence a finite energy-momentum tensor remains after renormalization of the cosmological constant and one other coupling constant in a generalized Einstein equation. In the Robertson-Walker cases, because of conformal flatness, there is no divergence beyond the usual quartically divergent constant vacuum energy; when the mass is not zero, however, a finite renormalization of the gravitational constant is suggested. The correctness of the methods is tested by considering a coordinate system in which flat spacetime assumes the form of a Kasner universe: The adiabatic definition of particle number and vacuum, which is basic to our expansion and renormalization methods, is seen to be consistent with the usual flat-space concepts.

Bei-Lok Hu

Papers

Quantum Brownian motion in a general environment: Exact master equation with nonlocal dissipation and colored noise.

Nonequilibrium quantum fields: Closed-time-path effective action, Wigner function, and Boltzmann equation

Closed-time-path functional formalism in curved spacetime: Application to cosmological back-reaction problems.

Vibrational Energy Transfer in CO2 Lasers

Conformal energy-momentum tensor in curved spacetime: Adiabatic regularization and renormalization