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Quantum Dynamical Systems$
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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

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 12 April 2021

Fermionic Dynamical Systems

Fermionic Dynamical Systems

Chapter:
(p.103) 6 Fermionic Dynamical Systems
Source:
Quantum Dynamical Systems
Author(s):

Robert Alicki

Mark Fannes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198504009.003.0006

This chapter focuses on the mathematical description of Fermionic systems. It first describes the usual formalism of second quantization in terms of operators on anti-symmetric Fock space. It then studies quadratic Hamiltonians and their corresponding equilibrium states. It presents a more abstract algebraic approach, suitable for the description of infinite systems: the CAR-formalism. It discusses the main properties of quasi-free states and automorphisms; they are the Fermionic counterparts of classical Gaussian measures and are widely applicable in approximate or effective treatments.

Keywords:   Fock space, CAR-algebra, quasi-free state, Fermionic systems, Gaussian measures, quadratic Hamiltonian, automorphism

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