Decoherence and the rate of entropy production in chaotic quantum systems

We show that for an open quantum system which is classically chaotic (a quartic double well with harmonic driving coupled to a sea of harmonic oscillators) the rate of entropy production has, as a function of time, two relevant regimes: For short times it is proportional to the diffusion coefficient (fixed by the system--environment coupling strength). For longer times (but before equilibration) there is a regime where the entropy production rate is fixed by the Lyapunov exponent. The nature of the transition time between both regimes is investigated.Comment: Revtex, 4 pages, 3 figures include

Classical and quantum coupled oscillators: symplectic structure

We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum regimes.Comment: 27 pages, 6 figure

Decoherence, Chaos, and the Correspondence Principle

We present evidence that decoherence can produce a smooth quantum-to-classical transition in nonlinear dynamical systems. High-resolution tracking of quantum and classical evolutions reveals differences in expectation values of corresponding observables. Solutions of master equations demonstrate that decoherence destroys quantum interference in Wigner distributions and washes out fine structure in classical distributions bringing the two closer together. Correspondence between quantum and classical expectation values is also re-established.Comment: 4 pages, 2 figures (color figures embedded at low resolution), uses RevTeX plus macro (included). Phys. Rev. Lett. (in press

Coarse graining and decoherence in quantum field theory

We consider a $\lambda \phi^4$ theory in Minkowski spacetime. We compute a "coarse grained effective action" by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients of this equation and analyze the decoherence induced on the long- wavelength modes. We generalize the results to the case of a conformally coupled scalar field in DeSitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius.Comment: 21 pages (RevTeX) and 5 encapsulated postscript figure

Phase-Space Decoherence: a comparison between Consistent Histories and Environment Induced Superselection

We examine the decoherence properties of a quantum open system as modeled by a quantum optical system in the Markov regime. We look for decoherence in both the Environment Induced Superselection (EIS) and Consistent Histories (CH) frameworks. We propose a general measure of the coherence of the reduced density matrix and find that EIS decoherence occurs in a number of bases for this model. The degree of ``diagonality'' achieved increases with bath temperature. We evaluate the Decoherence Functional of Consistent Histories for coarse grained phase space two-time projected histories. Using the measures proposed by Dowker and Halliwell we find that the consistency of the histories improves with increasing bath temperature, time and final grain size and decreases with initial grain size. The peaking increases with increasing grain size and decreases with increasing bath temperature. Adopting the above proposed measure of ``coherence'' to the Decoherence Functional gives similar results. The results agree in general with expectations while the anomalous dependence of the consistency on the initial grain size is discussed.Comment: 27 pages, 5 postscript figs in uuencoded compressed tar format Replaced: definition of special character for the complex number

Noise and Fluctuations in Semiclassical Gravity

We continue our earlier investigation of the backreaction 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 (IF) method, we examine the statistical mechanical meaning and show the interrelation of the many quantum processes involved in the backreaction 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 Bogolubov 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 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 stability and phase transtion phenomena and the non-equilibrium thermodynamics of black holes. It is also essential to an understanding of the transition from any quantum theory of gravity to classical general relativity. \pacs{pacs numbers: 04.60.+n,98.80.Cq,05.40.+j,03.65.Sq}Comment: Latex 37 pages, umdpp 93-216 (submitted to Phys. Rev. D, 24 Nov. 1993

Non-Equilibrium Quantum Fields in the Large N Expansion

An effective action technique for the time evolution of a closed system consisting of one or more mean fields interacting with their quantum fluctuations is presented. By marrying large $N$ expansion methods to the Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective action, causality of the resulting equations of motion is ensured and a systematic, energy conserving and gauge invariant expansion about the quasi-classical mean field(s) in powers of $1/N$ developed. The general method is exposed in two specific examples, $O(N)$ symmetric scalar \l\F^4 theory and Quantum Electrodynamics (QED) with $N$ fermion fields. The \l\F^4 case is well suited to the numerical study of the real time dynamics of phase transitions characterized by a scalar order parameter. In QED the technique may be used to study the quantum non-equilibrium effects of pair creation in strong electric fields and the scattering and transport processes in a relativistic $e^+e^-$ plasma. A simple renormalization scheme that makes practical the numerical solution of the equations of motion of these and other field theories is described.Comment: 43 pages, LA-UR-94-783 (PRD, in press), uuencoded PostScrip

Quantum Brownian Motion in a Bath of Parametric Oscillators: A model for system-field interactions

The quantum Brownian motion paradigm provides a unified framework where one can see the interconnection of some basic quantum statistical processes like decoherence, dissipation, particle creation, noise and fluctuation. We treat the case where the Brownian particle is coupled linearly to a bath of time dependent quadratic oscillators. While the bath mimics a scalar field, the motion of the Brownian particle modeled by a single oscillator could be used to depict the behavior of a particle detector, a quantum field mode or the scale factor of the universe. An important result of this paper is the derivation of the influence functional encompassing the noise and dissipation kernels in terms of the Bogolubov coefficients. This method enables one to trace the source of statistical processes like decoherence and dissipation to vacuum fluctuations and particle creation, and in turn impart a statistical mechanical interpretation of quantum field processes. With this result we discuss the statistical mechanical origin of quantum noise and thermal radiance from black holes and from uniformly- accelerated observers in Minkowski space as well as from the de Sitter universe discovered by Hawking, Unruh and Gibbons-Hawking. We also derive the exact evolution operator and master equation for the reduced density matrix of the system interacting with a parametric oscillator bath in an initial squeezed thermal state. These results are useful for decoherence and backreaction studies for systems and processes of interest in semiclassical cosmology and gravity. Our model and results are also expected to be useful for related problems in quantum optics. %\pacs {05.40.+j,03.65.Sq,98.80.Cq,97.60.Lf}Comment: 42 pages, Latex, umdpp93-210 (submitted to Physical Review D, 3 December 1993

Decoherence, einselection, and the quantum origins of the classical

Decoherence is caused by the interaction with the environment. Environment monitors certain observables of the system, destroying interference 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 non-local "Schr\"odinger cat" states. 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.Comment: Final version of the review, with brutally compressed figures. Apart from the changes introduced in the editorial process the text is identical with that in the Rev. Mod. Phys. July issue. Also available from http://www.vjquantuminfo.or

A New Theory of Stochastic Inflation

The stochastic inflation program is a framework for understanding the dynamics of a quantum scalar field driving an inflationary phase. Though widely used and accepted, there have over recent years been serious criticisms of this theory. In this paper I will present a new theory of stochastic inflation which avoids the problems of the conventional approach. Specifically, the theory can address the quantum-to-classical transition problem, and it will be shown to lead to a dramatic easing of the fine tuning constraints that have plagued inflation theories.Comment: 28 pages in latex (uses revtex), no figures. Changes include 3 pages of extra detail in the derivation of the noise and dissipation kernels, and a more careful description of the approximations made. Results remain unchange