The role of infrared divergence for decoherence
@article{Kupsch1999TheRO,
title={The role of infrared divergence for decoherence},
author={Joachim Kupsch},
journal={Journal of Mathematical Physics},
year={1999},
volume={41},
pages={5945-5953}
}Continuous and discrete superselection rules induced by the interaction with the environment are investigated for a class of exactly soluble Hamiltonian models. The environment is given by a boson field. Stable superselection sectors can only emerge if the low frequences dominate and the ground state of the boson field disappears due to infrared divergence. The models allow uniform estimates of all transition matrix elements between different superselection sectors.
11 Citations
Decoherence and Infrared Divergence 1
- Physics
- 2002
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…
Superselection rules induced by infrared divergence
- Physics
- 2004
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…
Decoherence and infrared divergence
- Physics
- 2002
The dynamics of a particle which is linearly coupled to a boson field is investigated. The boson field induces superselection rules for the momentum of the particle, if the field is infrared…
Applications of canonical transformations
- Physics
- 2005
Canonical transformations are defined and discussed along with the coherent and the ultracoherent vectors. It is shown that the single-mode and the n-mode squeezing operators are elements of the…
Self-adjointness of quadratic Hamiltonians and a representation method for their exponents
- Mathematics
- 2007
Solutions to a series of Cauchy problems for an equation of Schrödinger type with the Hamiltonian obtained by Wiener-Segal-Fock quantization of (finite- and infinite-dimensional) Hamiltonian systems…
Decoherence by Lindblad motion
- Physics
- 2004
The predictive power of Lindblad equations for the dynamics of open systems is discussed. In a model with only one Lindblad operator the asymptotic state (density operator) for t → ∞ determines the…
Frequently Asked Questions About Decoherence
- Physics
- 2000
This work focuses on environment induced decoherence and its degree of usefulness for the interpretation of quantum theory, and discusses the emergence of a classical world.
References
SHOWING 1-10 OF 23 REFERENCES
ASYMPTOTIC PROPERTIES OF A BOSON FIELD WITH GIVEN SOURCE
- Mathematics
- 1961
Some mathematical questions are answered in the theory of quantized boson fields with given linear source distribution. It is proved that the total Hamiltonian in the Fock representation is…
The structure of the quantum mechanical state space and induced superselection rules
- Physics
- 1998
The role of superselection rules for the derivation of classical probability within quantum mechanics is investigated and examples of superselection rules induced by the environment are discussed
Infrateilchen in der Quantenfeldtheorie
- Physics
- 1963
It is shown that in the presence of particles of zero rest mass the spectral assumptions of the quantum field theory have to be modified. Particles coupled to zero-rest-mass particles may not be…
On the Existence and Uniqueness of Ground States of a Generalized Spin-Boson Model
- Mathematics, Physics
- 1997
A generalization of the standard spin-boson model is considered. The HamiltonianH(α) of the model with a coupling parameterα∈Racts in the tensor product H⊕Fbof a Hilbert space H and the boson…
The emergence of classical properties through interaction with the environment
- Physics
- 1985
The dependence of macroscopic systems upon their environment is studied under the assumption that quantum theory is universally valid. In particular scattering of photons and molecules turns out to…
Mathematical Aspects of Decoherence
- Physics
- 2000
The aim of this lecture is to investigate the mathematical frame for environment induced superselection rules. Some exactly soluble models are dicussed in detail and norm estimates on decoherence…
The Method of Second Quantization
- Physics
- 1992
In the usual formalism of quantum mechanics, the first quantization formalism, observables are represented by operators and the wave functions are normal functions. In the method of second…
Asymptotically Disjoint Quantum States
- Physics
- 2000
A clarification of the heuristic concept of decoherence requires a consistent description of the classical behavior of some quantum systems. We adopt algebraic quantum mechanics since it includes not…
Superselection rules; old and new
- Business
- 1995
SummaryThis paper is a historical review of the development of the notion of superselection rule starting from the recognition in 1952 of the charge and univalence superselection rules. Some…
Algebraic methods in statistical mechanics and quantum field theory
- Education
- 1972
Many people are trying to be smarter every day. How's about you? There are many ways to evoke this case you can find knowledge and lesson everywhere you want. However, it will involve you to get what…