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DECOHERENCE AND INFRARED DIVERGENCE 1

Joachim Kupsch, Fachbereich Physik, Universität Kaiserslautern

Published Jan 1, 2002• 3 citations
OpenAlex

Abstract

The dynamics of a particle which is linearly coupled to the environment of a Boson field is investigated. For velocity coupling and for local (position) coupling the reduced dynamics of the particle induces superselection rules for the momentum, if the Boson field is infrared divergent. Thereby the Hamiltonian of the total system remains bounded from below. 1

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The dynamical properties of a quantum system can be profoundly influenced by its environment. Usually, the environment provokes decoherence and its action on the system can often be schematized by adding a noise term in the Hamiltonian. However, other scenarios are possible: we show that by increasing the strength of the noise, the Hilbert space of the system gradually splits into invariant subspaces, among which transitions become increasingly difficult. The phenomenon is equivalent to the formation of the quantum Zeno subspaces. We explore the possibility that noise can prevent, rather than provoke decoherence.

arXiv:quant-ph/0311195•Journal of Modern Optics•Apr 1, 2004•5 citations
The dynamics of a particle which is linearly coupled to the environment of a Boson field is investigated. For velocity coupling and for local (position) coupling the reduced dynamics of the particle induces superselection rules for the momentum, if the Boson field is infrared divergent. Thereby the Hamiltonian of the total system remains bounded from below. 1
Superselection rules induced by the interaction with a mass zero Boson field are investigated for a class of exactly soluble Hamiltonian models. The calculations apply as well to discrete as to continuous superselection rules. The initial state (reference state) of the Boson field is either a normal state or a KMS state. The superselection sectors emerge if and only if the Boson field is infrared divergent, i. e. the bare photon number diverges and the ground state of the Boson field disappears in the continuum. The time scale of the decoherence depends on the strength of the infrared contributions of the interaction and on properties of the initial state of the Boson system. These results are first derived for a Hamiltonian with conservation laws. But in the most general case the Hamiltonian includes an additional scattering potential, and the only conserved quantity is the energy of the total system. The superselection sectors remain stable against the perturbation by the scattering processes.
Superselection rules induced by the interaction with the environment are a basis to understand the emergence of classical observables within quantum theory. The aim of this article is to investigate the decoherence effects, which lead to superselection sectors, with the help of exactly soluble Hamiltonian models. Starting from the examples of Araki and of Zurek more general models with scattering are presented for which the projection operators onto the induced superselection sectors do no longer commute with the Hamiltonian. The example of an environment given by a free quantum field indicates that infrared divergence plays an essential role for the emergence of induced superselection sectors. For all models the induced superselection sectors are uniquely determined by the Hamiltonian, whereas the time scale of the decoherence depends crucially on the initial state of the total system.
The dynamical properties of a quantum system can be profoundly influenced by its environment. Usually, the environment provokes decoherence and its action on the system can often be schematized by adding a noise term in the Hamiltonian. However, other scenarios are possible: we show that by increasing the strength of the noise, the Hilbert space of the system gradually splits into invariant subspaces, among which transitions become increasingly difficult. The phenomenon is equivalent to the formation of the quantum Zeno subspaces. We explore the possibility that noise can prevent, rather than provoke decoherence.