Weak-Coupling Limit. I A Contraction Semigroup for Infinite Subsystems

TL;DR

This paper introduces a method to ensure the uniqueness of contraction semigroups generated by quantum master equations on Banach spaces, using a dynamical time averaging map, applicable regardless of subspace dimensions or spectral properties.

Contribution

It presents a novel approach to establish a unique contraction semigroup for quantum master equations via a dynamical time averaging map, generalizing previous methods.

Findings

The semigroup approximation is not unique without additional structure.

Introducing the dynamical time averaging map guarantees a well-defined generator.

The approach applies to systems of arbitrary dimension and spectral characteristics.

Abstract

We consider the class of quantum mechanical master equations defined on a generic Banach space, arising by projecting weakly perturbed one-parameter groups of isometries. We show that the possible semigroup approximations are far from unique. However, uniqueness can be reestablished through the introduction of a dynamical time averaging map. The generator of the resulting Contraction Semigroup is always well defined, irrespective of the dimensions of the projected subspace, and of the spectral properties of its free dynamics. We show how our approach includes and generalizes the preexisting literature.