Jump to ContentJump to Main Navigation
Quantum Dynamical Systems$
Users without a subscription are not able to see the full content.

Robert Alicki and Mark Fannes

Print publication date: 2001

Print ISBN-13: 9780198504009

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780198504009.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 05 June 2020

Deterministic Dynamics

Deterministic Dynamics

Chapter:
(p.54) 3 Deterministic Dynamics
Source:
Quantum Dynamical Systems
Author(s):

Robert Alicki

Mark Fannes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198504009.003.0003

This chapter presents the basic mathematical facts concerning Schrödinger's equation with constant and time-dependent Hamiltonians: Stone's theorem on strongly continuous one-parameter groups of unitaries, the Kato–Rellich criterion for self-adjointness, and the Dyson expansion. In particular, Floquet's theory for periodic perturbations is outlined and illustrated by examples of kicked systems: the kicked top and the baker map. Then classical mechanics is introduced as a limit of quantum theory using coherent states and mean-field limits. The formalism of classical differentiable dynamics is briefly described and the classical and quantum aspects of the motion of a free particle on a compact Riemannian manifold are discussed including Weyl's theorem characterizing spectra of generalized Laplacians such as Beltrami–Laplace operators.

Keywords:   Stone's theorem, Kato–Rellich criterion, Dyson expansion, Floquet operator, kicked top, baker map, coherent state, mean-field limit, Beltrami–Laplace operator

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .