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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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Fermionic Dynamical Systems

Fermionic Dynamical Systems

(p.103) 6 Fermionic Dynamical Systems
Quantum Dynamical Systems

Robert Alicki

Mark Fannes

Oxford University Press

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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