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.

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 λ${\phi }^4$ 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.

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 λ${\phi }^4$ 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.

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 to produce new continuous‐wave lasers in SO₂ and HCN are described.

We examine from first principles one of the basic assumptions of modern quantum theories of structure formation in the early Universe, i.e., the conditions upon which fluctuations of a quantum field may transmute into classical stochastic perturbations, which grew into galaxies. Our earlier works have discussed the quantum origin of noise in stochastic inflation and quantum fluctuations as measured by particle creation in semiclassical gravity. Here we focus on decoherence and the relation of quantum and classical fluctuations. Instead of using the rather ad hoc splitting of a quantum field into long and short wavelength parts, the latter providing the noise which decoheres the former, we treat a nonlinear theory and examine the decoherence of a quantum mean field by its own quantum fluctuations, or that of other fields it interacts with. This is an example of how a quantum system can be viewed as effectively open and decoheres through its own dynamics. The model we use to discuss fluctuation generation has the inflaton field coupled to the graviton field. We show that when the quantum to classical transition is propertly treated, with due consideration of the relation of decoherence, noise, fluctuation, and dissipation, the amplitude of density contrast predicted falls in the acceptable range without requiring a fine-tuning of the coupling constant of the inflaton field. The conventional treatment which requires an unnaturally small λ≊${10}^{\mathrm{-}12}$ in a λ${\mathrm{\Phi }}^4$ inflaton field stems from a basic flaw in naively identifying classical perturbations with quantum fluctuations. © 1995 The American Physical Society.

We continue our earlier investigation of the back reaction problem in semiclassical gravity with the Schwinger-Keldysh or closed-time-path (CTP) functional formalism using the language of the decoherent history formulation of quantum mechanics. Making use of its intimate relation with the Feynman-Vernon influence functional method, we examine the statistical mechanical meaning and show the interrelation of the many quantum processes involved in the back reaction problem, such as particle creation, decoherence, and dissipation. We show how noise and fluctuation arise naturally from the CTP formalism. We derive an expression for the CTP effective action in terms of the Bogoliubov coefficients and show how noise is related to the fluctuations in the number of particles created. In so doing we have extended the old framework of semiclassical gravity, based on the mean field theory of Einstein equation with a source given by the expectation value of the energy-momentum tensor, to that based on a Langevin-type equation, where the dynamics of the fluctuations of spacetime is driven by the quantum fluctuations of the matter field. This generalized framework is useful for the investigation of quantum processes in the early Universe involving fluctuations, vacuum instability, and phase transition phenomena as well as the nonequilibrium thermodynamics of black holes. It is also essential to an understanding of the transition from any quantum theory of gravity to classical general relativity.