Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top

2019 | Book

Introduction to Classical and Quantum Markov Semigroups Read chapter Read first chapter

Open Quantum Systems

A Mathematical Perspective

Editors: Dorothea Bahns, Prof. Dr. Anke Pohl, Prof. Dr. Ingo Witt

Publisher: Springer International Publishing

Book Series : Tutorials, Schools, and Workshops in the Mathematical Sciences

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Login to get access
insite
SEARCH

About this book

This book presents four survey articles on various aspects of open quantum systems, specifically addressing quantum Markovian processes, Feller semigroups and nonequilibrium dynamics. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen, Germany. Starting from basic notions, the authors of these lecture notes accompany the reader on a journey up to the latest research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. Though the book is primarily addressed to graduate students, it will also be of interest to researchers.

Table of Contents

Frontmatter
Introduction to Classical and Quantum Markov Semigroups
Abstract
We provide a self-contained and fast-paced introduction to the theories of operator semigroups, Markov semigroups and quantum dynamical semigroups. The level is appropriate for well-motivated graduate students who have a background in analysis or probability theory, with the focus on the characterisation of infinitesimal generators for various classes of semigroups. The theorems of Hille–Yosida, Hille–Yosida–Ray, Lumer–Phillips and Gorini–Kossakowski–Sudarshan–Lindblad are all proved, with the necessary technical prerequisites explained in full. Exercises are provided throughout.
Alexander C. R. Belton
Introduction to Non-Markovian Evolution of n-Level Quantum Systems
Abstract
We analyze quantum dynamical maps and the corresponding master equations beyond the celebrated quantum Markovian master equation derived by Gorini, Kossakowski, Sudarshan, and Lindblad. In the Heisenberg picture such maps are represented by completely positive and unital maps, whereas in the Schrödinger picture by completely positive and trace-preserving maps. Both time-local equations governed by time dependent generators and time non-local equations of the Nakajima-Zwanzig form governed by the corresponding memory kernels are considered. We use the Schrödinger picture to discuss time-local case and Heisenberg picture for the non-local one. These equations describe quantum non-Markovian evolution that takes into account memory effects. Our analysis is illustrated by several simple examples.
Dariusz Chruściński
Aspects of Micro-Local Analysis and Geometry in the Study of Lévy-Type Generators
Abstract
Generators of Feller processes are pseudo-differential operators with negative definite symbols, thus they are objects of micro-local analysis. Continuous negative definite functions (and symbols) give often raise to metrics and these metrics are important to understand, for example, transition functions of certain Feller processes. In this survey we outline some of the more recent results and ideas while at the same time we long to introduce into the field.
Niels Jacob, Elian O. T. Rhind
Lectures on Entropy. I: Information-Theoretic Notions

These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested in research careers. Besides basic notions of analysis related to convergence that are typically taught in the first or second year of undergraduate studies, no other background is needed to read the notes. The notes might be also of interest to any mathematically inclined reader who wishes to learn basic facts about notions of entropy in an elementary setting.

Vojkan Jakšić
Metadata
Title
Open Quantum Systems
Editors
Dorothea Bahns
Prof. Dr. Anke Pohl
Prof. Dr. Ingo Witt
Copyright Year
2019
Electronic ISBN
978-3-030-13046-6
Print ISBN
978-3-030-13045-9
DOI
https://doi.org/10.1007/978-3-030-13046-6