The weak coupling limit as a quantum functional central limit

Unifying decoherence and the Heisenberg Principle

“…where the evolution of the unitary cocycle t →Û t is described (see [1]) by a quantum stochastic differential equation or QSDE. Explicitly calculating the maximal added variances Σ 2 by solving the QSDE is in general rather nontrivial, if possible at all.…”

“…A normal state ρ ∈ S (A ) on A induces a probability measure on the spectrum Spec(A) of an observable A, and it is the B Bas Janssens janssens@mpim-bonn.mpg.de 1 Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany objective of a quantum measurement to portray this probability measure as faithfully as possible.…”

Adiabatic Elimination in Quantum Stochastic Models

“…We study adiabatic elimination in the context of quantum stochastic models [15] which arise by taking a weak coupling limit of QED (quantum electrodynamics) models [1,13,5], and are widely applicable to systems studied in quantum optics. Specifically, quantum stochastic models are the starting point for deriving master equations, filtering equations, and input-output relations.…”

The interacting-free quantum stochastic limit of quantum field theory

“…vacuum or thermal) is prescribed for the reservoir and one makes a separation of time scales (van Hove limit): time t being rescaled as t/λ 2 followed by the limit λ → 0. In an approach pioneered by Accardi, Frigerio and Lu [2], one constructs suitable collective reservoir fields in which to examine the limiting behaviour of observables and these collective fields have the property of themselves converging to basic quantum stochastic processes (typically quantum Brownian motion). This fact was exploited by Accardi, Lu and Volovich [3] to establish a (quantum) stochastic sector in quantum field theory.…”

“…The original scope of [2] was very limited due to the fact that almost all the standard simplifying assumptions (vacuum state, rotating wave approximation, dipole approximation, etc.) were made in order to make an already complicated problem accessible.…”