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Statistical Physics and ThermodynamicsAn Introduction to Key Concepts$
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Jochen Rau

Print publication date: 2017

Print ISBN-13: 9780199595068

Published to Oxford Scholarship Online: November 2017

DOI: 10.1093/oso/9780199595068.001.0001

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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: 17 October 2021

Quantum Theory

Quantum Theory

(p.10) 2 Quantum Theory
Statistical Physics and Thermodynamics

Jochen Rau

Oxford University Press

From the outset statistical mechanics will be framed in the language of quantum theory. The typical macroscopic system is composed of multiple constituents, and hence described in some many-particle Hilbert space. In general, not much is known about such a system, certainly not the precise preparation of all its microscopic details. Thus, its description requires a more general notion of a quantum state, a so-called mixed state. This chapter begins with a brief review of the basic axioms of quantum theory regarding observables, pure states, measurements, and time evolution. Particular attention is paid to the use of projection operators and to the most elementary quantum system, a two-level system. The chapter then motivates the introduction of mixed states and examines in detail their mathematical representation and properties. It also dwells on the description of composite systems, introducing, in particular, the notions of statistical independence and correlations.

Keywords:   quantum theory, projection operator, two-level system, mixed state, composite system, statistical indepence, correlations

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