Thermal Properties of an Inflationary Universe

An energetic justification of a thermal component during inflation is given. The thermal component can act as a heat reservoir which induces thermal fluctuations on the inflaton field system. We showed previously that such thermal fluctuations could dominate quantum fluctuations in producing the initial seeds of density perturbations. A Langevin-like rate equation is derived from quantum field theory which describes the production of fluctuations in the inflaton field when acted upon by a simple modeled heat reservoir. In a certain limit this equation is shown to reduce to the standard Langevin equation, which we used to construct "Warm Inflation" scenarios in previous work. A particle physics interpretation of our system-reservoir model is offered.Comment: 28 pages, 0 figures, In Press Physical Review D 199

The Zero-Point Field and Inertia

A brief overview is presented of the basis of the electromagnetic zero-point field in quantum physics and its representation in stochastic electrodynamics. Two approaches have led to the proposal that the inertia of matter may be explained as an electromagnetic reaction force. The first is based on the modeling of quarks and electrons as Planck oscillators and the method of Einstein and Hopf to treat the interaction of the zero-point field with such oscillators. The second approach is based on analysis of the Poynting vector of the zero-point field in accelerated reference frames. It is possible to derive both Newton's equation of motion, F=ma, and its relativistic co-variant form from Maxwell's equations as applied to the zero-point field of the quantum vacuum. This appears to account, at least in part, for the inertia of matter.Comment: 8 pages, no fig

Quantum noise in current biased Josephson junction

Quantum fluctuations in a current biased Josephson junction, described in terms of the RCSJ-model, are considered. The fluctuations of the voltage and phase across the junction are assumed to be initiated by equilibrium current fluctuations in the shunting resistor. This corresponds to low enough temperatures, when fluctuations of the normal current in the junction itself can be neglected. We used the quantum Langevin equation in terms of random variables related to the limit cycle of the nonlinear Josephson oscillator. This allows to go beyond the perturbation theory and calculate the widths of the Josephson radiation lines

Path Integrals and Their Application to Dissipative Quantum Systems

Introduction Path Integrals - Introduction - Propagator - Free Particle - Path Integral Representation of Quantum Mechanics - Particle on a Ring - Particle in a Box - Driven Harmonic Oscillator - Semiclassical Approximation - Imaginary Time Path Integral Dissipative Systems - Introduction - Environment as Collection of Harmonic Oscillators - Effective Action Damped Harmonic Oscillator - Partition Function - Ground State Energy and Density of States - Position Autocorrelation FunctionComment: 55 pages, 13 figures. To be published in "Coherent Evolution in Noisy Environments", Lecture Notes in Physics (http://link.springer.de/series/lnpp/) (Springer Verlag, Berlin-Heidelberg-New York

Spontaneous excitation of an accelerated atom: The contributions of vacuum fluctuations and radiation reaction

We consider an atom in interaction with a massless scalar quantum field. We discuss the structure of the rate of variation of the atomic energy for an arbitrary stationary motion of the atom through the quantum vacuum. Our main intention is to identify and to analyze quantitatively the distinct contributions of vacuum fluctuations and radiation reaction to the spontaneous excitation of a uniformly accelerated atom in its ground state. This gives an understanding of the role of the different physical processes underlying the Unruh effect. The atom's evolution into equilibrium and the Einstein coefficients for spontaneous excitation and spontaneous emission are calculated.Comment: 13 pages, KONS-RGKU-94-09, to appear in Phys. Rev.

Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions

Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {\it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their co-ordinates and momenta we derive a generalized quantum Langevin equation in $c$-numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski equations are the {\it exact} quantum analogues of their classical counterparts. The present work is {\it independent} of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (Smoluchowski equation being considered in the overdamped limit).Comment: RevTex, 16 pages, 7 figures, To appear in Physical Review E (minor revision

Approximate Decoherence of Histories and 't Hooft's Deterministic Quantum Theory

This paper explores the possibility that an exactly decoherent set of histories may be constructed from an approximately decoherent set by small distortions of the operators characterizing the histories. In particular, for the case of histories of positions and momenta, this is achieved by doubling the set of operators and then finding, amongst this enlarged set, new position and momentum operators which commute, so decohere exactly, and which are ``close'' to the original operators. The enlarged, exactly decoherent, theory has the same classical dynamics as the original one, and coincides with the so-called deterministic quantum theories of the type recently studied by 't Hooft. These results suggest that the comparison of standard and deterministic quantum theories may provide an alternative method of characterizing emergent classicality. A side-product is the surprising result that histories of momenta in the quantum Brownian motion model (for the free particle in the high-temperature limit) are exactly decoherent.Comment: 41 pages, plain Te

Effective Theories of Coupled Classical and Quantum Variables from Decoherent Histories: A New Approach to the Backreaction Problem

We use the decoherent histories approach to quantum theory to derive the form of an effective theory describing the coupling of classical and quantum variables. The derivation is carried out for a system consisting of a large particle coupled to a small particle with the important additional feature that the large particle is also coupled to a thermal environment producing the decoherence necessary for classicality. The effective theory is obtained by tracing out both the environment and the small particle variables. It consists of a formula for the probabilities of a set of histories of the large particle, and depends on the dynamics and initial quantum state of the small particle. It has the form of an almost classical particle coupled to a stochastic variable whose probabilities are determined by a formula very similar to that given by quantum measurement theory for continuous measurements of the small particle's position. The effective theory gives intuitively sensible answers when the small particle is in a superposition of localized states.Comment: 27 pages, plain Te

Effective Theories of Coupled Classical and Quantum Variables

We address the issue of coupling variables which are essentially classical to variables that are quantum. Two approaches are discussed. In the first (based on collaborative work with L.Di\'osi), continuous quantum measurement theory is used to construct a phenomenological description of the interaction of a quasiclassical variable $X$ with a quantum variable $x$, where the quasiclassical nature of $X$ is assumed to have come about as a result of decoherence. The state of the quantum subsystem evolves according to the stochastic non-linear Schr\"odinger equation of a continuously measured system, and the classical system couples to a stochastic c-number \x (t) representing the imprecisely measured value of $x$. The theory gives intuitively sensible results even when the quantum system starts out in a superposition of well-separated localized states. The second approach involves a derivation of an effective theory from the underlying quantum theory of the combined quasiclassical--quantum system, and uses the decoherent histories approach to quantum theory.Comment: 25 pages, plain Tex. To appear in proceedings of the conference Open Systems and Measurement in Relativistic Quantum Theory, Naples, April 3-4, 1998, edited by H.P.Breuer and F.Petruccion

Coupling Classical and Quantum Variables using Continuous Quantum Measurement Theory

We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously and imprecisely measured by the classical system. The effective equations of motion for the classical system therefore consist of treating the quantum variable $x$ as a stochastic c-number \x (t) the probability distibution for which is given by the theory of continuous quantum measurements. The resulting theory is similar to the usual mean field equations (in which $x$ is replaced by its quantum expectation value) but with two differences: a noise term, and more importantly, the state of the quantum subsystem evolves according to the stochastic non-linear Schrodinger equation of a continuously measured system. In the case in which the quantum system starts out in a superposition of well-separated localized states, the classical system goes into a statistical mixture of trajectories, one trajectory for each individual localized state.Comment: 11 pages, plain Tex (with revised settings for \vsize and \voffset to accommodate US paper sizes