Decoherence: Concepts and Examples

We give a pedagogical introduction to the process of decoherence - the irreversible emergence of classical properties through interaction with the environment. After discussing the general concepts, we present the following examples: Localisation of objects, quantum Zeno effect, classicality of fields and charges in QED, and decoherence in gravity theory. We finally emphasise the important interpretational features of decoherence.Comment: 24 pages, LATEX, 9 figures, needs macro lamuphys.sty, to appear in the Proceedings of the 10th Born Symposiu

Toy models for gravitational and scalar QED decoherence

We investigate the dynamics of two quantum mechanical oscillator system-bath toy models obtained by dimensionally truncating linearized gravity coupled to a massive scalar field and scalar QED. The scalar-gravity toy model maps onto the phase damped oscillator, while the scalar QED toy model approximately maps onto an oscillator system subject to two-photon damping. The toy models provide potentially useful insights into solving for open system quantum dynamics relevant to the full scalar QED and weak gravitational field systems, in particular the decoherence of initial scalar field system superposition states

Symmetries, superselection rules, and decoherence

We discuss the applicability of the programme of decoherence -- emergence of approximate classical behaviour through interaction with the environment -- to cases where it was suggested that the presence of symmetries would lead to exact superselection rules. For this discussion it is useful to make a distinction between pure symmetries and redundancies, which results from an investigation into the constraint equations of the corresponding theories. We discuss, in particular, superpositions of states with different charges, as well as with different masses, and suggest how the corresponding interference terms, although they exist in principle, become inaccessible through decoherence.Comment: 12 pages, LATEX, Report Freiburg THEP-94/3

Problems with the Newton-Schr\"odinger Equations

We examine the origin of the Newton-Schr\"odinger equations (NSEs) that play an important role in alternative quantum theories (AQT), macroscopic quantum mechanics and gravity-induced decoherence. We show that NSEs for individual particles do not follow from general relativity (GR) plus quantum field theory (QFT). Contrary to what is commonly assumed, the NSEs are not the weak-field (WF), non-relativistic (NR) limit of the semi-classical Einstein equation (SCE) (this nomenclature is preferred over the `M\/oller-Rosenfeld equation') based on GR+QFT. The wave-function in the NSEs makes sense only as that for a mean field describing a system of $N$ particles as $N \rightarrow \infty$, not that of a single or finite many particles. From GR+QFT the gravitational self-interaction leads to mass renormalization, not to a non-linear term in the evolution equations of some AQTs. The WF-NR limit of the gravitational interaction in GR+QFT involves no dynamics. To see the contrast, we give a derivation of the equation (i) governing the many-body wave function from GR+QFT and (ii) for the non-relativistic limit of quantum electrodynamics (QED). They have the same structure, being linear, and very different from NSEs. Adding to this our earlier consideration that for gravitational decoherence the master equations based on GR+QFT lead to decoherence in the energy basis and not in the position basis, despite some AQTs desiring it for the `collapse of the wave function', we conclude that the origins and consequences of NSEs are very different, and should be clearly demarcated from those of the SCE equation, the only legitimate representative of semiclassical gravity, based on GR+QFT.Comment: 18 pages. Invited paper for the Focus Issue on 'Gravitational quantum physics' in New Journal of Physic

Decoherence of Schrodinger cat states in a Luttinger liquid

Schrodinger cat states built from quantum superpositions of left or right Luttinger fermions located at different positions in a spinless Luttinger liquid are considered. Their decoherence rates are computed within the bosonization approach using as environments the quantum electromagnetic field or two or three dimensionnal acoustic phonon baths. Emphasis is put on the differences between the electromagnetic and acoustic environments.Comment: 22 pages revtex4, 7 figures in a separate PS fil