Information geometry and reduced quantum description
type: Item
instance of: scholarly article
title: Information geometry and reduced quantum description
zbMATH Open document ID: 0888.46053
DOI: 10.1016/S0034-4877(97)84892-6
author: Raymond F. Streater
published in: Reports on Mathematical Physics
publication date: 1998-06-11T00:00:00Z
review text: The framework of the so-called statistical dynamics, developed by the present author, is applied to the quantum version of non-equilibrium statistical mechanics, where the ``slow'' variables are represented by selfadjoint operators, not necessarily bounded, on a Hilbert space. The subject of study is the quantum dynamics of a system with two time-scales, having discrete time and unbounded slow variables, under a useful set of axioms, it is argued that the Kubo susceptibility tensor is the appropriate generalizations of the Fisher information metric on the set of density matrices. The geometric picture of reduced quantum dynamics (via suitable projection methods) is extended to some unbounded cases and shown to be related to a contraction in the Bogoliubov norm.
Mathematics Subject Classification ID: 46N50
Mathematics Subject Classification ID: 82C10
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 81P05
zbMATH DE Number: 1090458
zbMATH Keywords: statistical dynamics
zbMATH Keywords: quantum version
zbMATH Keywords: non-equilibrium statistical mechanics
zbMATH Keywords: selfadjoint operators
zbMATH Keywords: system with two time-scales
zbMATH Keywords: unbounded slow variables
zbMATH Keywords: kubo susceptibility tensor
zbMATH Keywords: Fisher information metric
zbMATH Keywords: set of density matrices
zbMATH Keywords: reduced quantum dynamics
zbMATH Keywords: Bogoliubov norm
reviewed by: Piotr Garbaczewski
MaRDI profile type: Publication
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full work available at URL: s0034-4877(97)84892-6
OpenAlex ID: W2050836881
description: scientific article; zbMATH DE number 1090458