Miniatures on Open Quantum Systems

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Derezinski, Jan, Jaksic, Vojkan, Pillet, Claude-Alain
Format: Preprint
Published: 2026
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866913025678639104
author Derezinski, Jan
Jaksic, Vojkan
Pillet, Claude-Alain
author_facet Derezinski, Jan
Jaksic, Vojkan
Pillet, Claude-Alain
contents We presents a unified and concise exposition of key topics in the mathematical theory of open quantum systems, developed within the framework of operator algebras. The manuscript consolidates and extends a series of invited articles originally prepared for the Modern Encyclopedia of Mathematical Physics, combining foundational material with modern perspectives on non-equilibrium quantum statistical mechanics. After introducing the C*- and W*-algebraic formulation of quantum mechanics, the paper reviews quantum dynamical systems, KMS states, and Tomita-Takesaki modular theory, as well as CCR and CAR algebras for bosonic and fermionic systems. Particular emphasis is placed on infinite systems, non-equilibrium steady states, entropy production, and linear response theory. The later sections develop a systematic treatment of small systems coupled to reservoirs, open lattice quantum spin systems, culminating in a detailed discussion of competing notions of quantum entropy production. The presentation highlights structural insights, conceptual clarity, and connections between equilibrium and non-equilibrium phenomena, providing a self-contained reference for researchers and graduate students in mathematical physics.
format Preprint
id arxiv_https___arxiv_org_abs_2601_20373
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Miniatures on Open Quantum Systems
Derezinski, Jan
Jaksic, Vojkan
Pillet, Claude-Alain
Mathematical Physics
Operator Algebras
Quantum Physics
We presents a unified and concise exposition of key topics in the mathematical theory of open quantum systems, developed within the framework of operator algebras. The manuscript consolidates and extends a series of invited articles originally prepared for the Modern Encyclopedia of Mathematical Physics, combining foundational material with modern perspectives on non-equilibrium quantum statistical mechanics. After introducing the C*- and W*-algebraic formulation of quantum mechanics, the paper reviews quantum dynamical systems, KMS states, and Tomita-Takesaki modular theory, as well as CCR and CAR algebras for bosonic and fermionic systems. Particular emphasis is placed on infinite systems, non-equilibrium steady states, entropy production, and linear response theory. The later sections develop a systematic treatment of small systems coupled to reservoirs, open lattice quantum spin systems, culminating in a detailed discussion of competing notions of quantum entropy production. The presentation highlights structural insights, conceptual clarity, and connections between equilibrium and non-equilibrium phenomena, providing a self-contained reference for researchers and graduate students in mathematical physics.
title Miniatures on Open Quantum Systems
topic Mathematical Physics
Operator Algebras
Quantum Physics
url https://arxiv.org/abs/2601.20373