Non-Equilibrium Quantum Electrodynamics

We employ the influence functional technique to trace out the photonic contribution from full quantum electrodynamics. The reduced density matrix propagator for the spinor field is then constructed. We discuss the role of time-dependent renormalization in the propagator and focus on the possibility of obtaining dynamically induced superselection rules. Finally, we derive the master equation for the case of the field being in an one-particle state in a non-relativistic regime and discuss whether EM vacuumm fluctuations are sufficient to produce decoherence in the position basis.Comment: 28 pages, 2 figures. Substantially revised, one important mistake corrected; discussion on decoherence upgraded, section 4 essentially rewritte

Moving Atom-Field Interactions: Quantum Motional Decoherence and Relaxation

The reduced dynamics of an atomic qubit coupled both to its own quantized center of mass motion through the spatial mode functions of the electromagnetic field, as well as the vacuum modes, is calculated in the influence functional formalism. The formalism chosen can describe the entangled non-Markovian evolution of the system with a full account of the coherent back-action of the environment on the qubit. We find a slight increase in the decoherence due to the quantized center of mass motion and give a condition on the mass and qubit resonant frequency for which the effect is important. In optically resonant alkali-metal atom systems, we find the effect to be negligibly small. The framework presented here can nevertheless be used for general considerations of the coherent evolution of qubits in moving atoms in an electromagnetic field.Comment: 9 pages, 1 figure, minor change

Classical Vs Quantum Probability in Sequential Measurements

We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are contextual, namely they depend strongly on the specific measurement scheme through which they are determined. We construct Positive-Operator-Valued measures (POVM) that provide such probabilities. For observables with continuous spectrum, the constructed POVMs depend strongly on the resolution of the measurement device, a conclusion that persists even if we consider a quantum mechanical measurement device or the presence of an environment. We then examine the same issues in alternative interpretations of quantum theory. We first show that multi-time probabilities cannot be naturally defined in terms of a frequency operator. We next prove that local hidden variable theories cannot reproduce the predictions of quantum theory for sequential measurements, even when the degrees of freedom of the measuring apparatus are taken into account. Bohmian mechanics, however, does not fall in this category. We finally examine an alternative proposal that sequential measurements can be modelled by a process that does not satisfy the Kolmogorov axioms of probability. This removes contextuality without introducing non-locality, but implies that the empirical probabilities cannot be always defined (the event frequencies do not converge). We argue that the predictions of this hypothesis are not ruled out by existing experimental results (examining in particular the "which way" experiments); they are, however, distinguishable in principle.Comment: 56 pages, latex; revised and restructured. Version to appear in Found. Phy

Bayesian Probabilities and the Histories Algebra

We attempt a justification of a generalisation of the consistent histories programme using a notion of probability that is valid for all complete sets of history propositions. This consists of introducing Cox's axioms of probability theory and showing that our candidate notion of probability obeys them. We also give a generalisation of Bayes' theorem and comment upon how Bayesianism should be useful for the quantum gravity/cosmology programmes.Comment: 10 pages, accepted by Int. J. Theo. Phys. Feb 200

Decoherence and classical predictability of phase space histories

We consider the decoherence of phase space histories in a class of quantum Brownian motion models, consisting of a particle moving in a potential $V(x)$ in interaction with a heat bath at temperature $T$ and dissipation gamma, in the Markovian regime. The evolution of the density operator for this open system is thus described by a non-unitary master equation. The phase space histories of the system are described by a class of quasiprojectors. Generalizing earlier results of Hagedorn and Omn\`es, we show that a phase space projector onto a phase space cell $\Gamma$ is approximately evolved under the master equation into another phase space projector onto the classical dissipative evolution of $\Gamma$, and with a certain amount of degradation due to the noise produced by the environment. We thus show that histories of phase space samplings approximately decohere, and that the probabilities for these histories are peaked about classical dissipative evolution, with a width of peaking depending on the size of the noise.Comment: 34 pages, LATEX, revised version to avoid LATEX error

Gravitational backreaction in cosmological spacetimes

We develop a new formalism for the treatment of gravitational backreaction in the cosmological setting. The approach is inspired by projective techniques in non-equilibrium statistical mechanics. We employ group-averaging with respect to the action of the isotropy group of homogeneous and isotropic spacetimes (rather than spatial averaging), in order to define effective FRW variables for a generic spacetime. Using the Hamiltonian formalism for gravitating perfect fluids, we obtain a set of equations for the evolution of the effective variables; these equations incorporate the effects of backreaction by the inhomogeneities. Specializing to dust-filled spacetimes, we find regimes that lead to a closed set of backreaction equations, which we solve for small inhomogeneities. We then study the case of large inhomogeneities in relation to the proposal that backreaction can lead to accelerated expansion. In particular, we identify regions of the gravitational state space that correspond to effective cosmic acceleration. Necessary conditions are (i) a strong expansion of the congruences corresponding to comoving observers, and (ii) a large negative value of a dissipation variable that appears in the effective equations (i.e, an effective "anti-dissipation").Comment: 36 pages, latex. Extended discussion on results and on relation to Lemaitre-Tolman-Bondi models. Version to appear in PR

Quantum recoil effects in finite-time disentanglement of two distinguishable atoms

Starting from the requirement of distinguishability of two atoms by their positions, it is shown that photon recoil has a strong influence on finite-time disentanglement and in some cases prevents its appearance. At near-field inter atomic distances well localized atoms, with maximally one atom being initially excited, may suffer disentanglement at a single finite time or even at a series of equidistant finite times, depending on their mean inter atomic distance and their initial electronic preparation.Comment: 13 pages, 1 figure, submitted to Physical Review on august 2

Quantum optical versus quantum Brownian motion master-equation in terms of covariance and equilibrium properties

Structures of quantum Fokker-Planck equations are characterized with respect to the properties of complete positivity, covariance under symmetry transformations and satisfaction of equipartition, referring to recent mathematical work on structures of unbounded generators of covariant quantum dynamical semigroups. In particular the quantum optical master-equation and the quantum Brownian motion master-equation are shown to be associated to $\mathrm{U(1)}$ and $\mathrm{R}$ symmetry respectively. Considering the motion of a Brownian particle, where the expression of the quantum Fokker-Planck equation is not completely fixed by the aforementioned requirements, a recently introduced microphysical kinetic model is briefly recalled, where a quantum generalization of the linear Boltzmann equation in the small energy and momentum transfer limit straightforwardly leads to quantum Brownian motion.Comment: 11 pages, latex, no figures, slight changes and a few references added, to appear in J. Math. Phy

Moving Atom-Field Interaction: Correction to Casimir-Polder Effect from Coherent Back-action

The Casimir-Polder force is an attractive force between a polarizable atom and a conducting or dielectric boundary. Its original computation was in terms of the Lamb shift of the atomic ground state in an electromagnetic field (EMF) modified by boundary conditions along the wall and assuming a stationary atom. We calculate the corrections to this force due to a moving atom, demanding maximal preservation of entanglement generated by the moving atom-conducting wall system. We do this by using non-perturbative path integral techniques which allow for coherent back-action and thus can treat non-Markovian processes. We recompute the atom-wall force for a conducting boundary by allowing the bare atom-EMF ground state to evolve (or self-dress) into the interacting ground state. We find a clear distinction between the cases of stationary and adiabatic motions. Our result for the retardation correction for adiabatic motion is up to twice as much as that computed for stationary atoms. We give physical interpretations of both the stationary and adiabatic atom-wall forces in terms of alteration of the virtual photon cloud surrounding the atom by the wall and the Doppler effect.Comment: 16 pages, 2 figures, clarified discussions; to appear in Phys. Rev.