Related papers: Miniatures on Open Quantum Systems
These notes are a short introduction to the mathematical theory of open quantum systems. They are meant to serve as an entry point into a broad research area which has applications across the quantum sciences dealing with systems subjected…
Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…
We provide a systematic approach to quantum mechanics from an information-theoretic perspective using the language of tensor networks. Our formulation needs only a single kind of object, so-called positive *-tensors. Physical models…
The laws of thermodynamics are a cornerstone for describing nanoscale and open quantum systems. However, formulating these laws for systems under continuous feedback control and under experimentally relevant conditions is challenging. In…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
This survey article is concerned with the modeling of the kinematical structure of quantum systems in an algebraic framework which eliminates certain conceptual and computational difficulties of the conventional approaches. Relying on the…
This text is a detailed overview of the theories of W*-algebras and noncommutative integration, up to the Falcone-Takesaki theory of noncommutative Lp spaces over arbitrary W*-algebras, and its extension to noncommutative Orlicz spaces. The…
The dynamical entropy on von Neumann algebras defined by Accardi, Ohya and Watanabe (AOW entropy) is a natural noncommutative extension of the classical dynamical entropy. On the other hand, quantum spin lattice systems currently used in…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications…
We give a pedagogical introduction to a selection of recently discussed topics in nonequilibrium statistical mechanics, concentrating mostly on formal structures and on general principles. Part I contains an overview of the formalism of…
The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum…
We develop an algebraic frame for the simultaneous treatment of actual and possible properties of quantum systems. We show that, in spite of the fact that the language is enriched with the addition of a modal operator to the orthomodular…
The central physical concepts and mathematical techniques used in the theory of open quantum systems are reviewed. Particular emphasis is laid on the interrelations of apparently different approaches. Starting from the appropriate…
We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and…
This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations,…
A pedagogical derivation of statistical mechanics from quantum mechanics is provided, by means of open quantum systems. Besides, a new definition of Boltzmann entropy for a quantum closed system is also given to count microstates in a way…
Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras and von Neumann algebras, which is increasingly of interest in…
Lecture notes prepared for the EMS--IAMP Spring School ``Symmetries and Measurement in Quantum Field Theory''. This set of lecture notes covers four lectures: 1. Operator Algebras and Quantum Field Theory, 2. Tomita-Takesaki Modular Theory…
In this paper we address the problem to give a concrete support to the idea, originally stemming from Niels Bohr, that quantum mechanics must be rooted inside the physics of macroscopic systems. It is shown that, starting from the formalism…