On The Generators Of Quantum Stochastic Operator Cocycles

TL;DR

This paper investigates the generators of quantum stochastic operator cocycles, focusing on various classes such as positive, projection, and partially isometric cocycles, and introduces a polar decomposition for positive contraction cocycles.

Contribution

It provides a detailed analysis of stochastic generators for different types of quantum cocycles and presents a new polar decomposition result for positive contraction cocycles.

Findings

Characterization of generators for positive cocycles

Analysis of projection and partially isometric cocycles

Introduction of a polar decomposition for positive contraction cocycles

Abstract

The stochastic generators of Markov-regular operator cocycles on symmetric Fock space are studied in a variety of cases: positive cocycles, projection cocycles, and partially isometric cocycles. Moreover a class of transformations of positive contraction cocycles is exhibited which leads to a polar decomposition result.