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Ultracold Atoms in Optical LatticesSimulating quantum many-body systems$
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Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger

Print publication date: 2012

Print ISBN-13: 9780199573127

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199573127.001.0001

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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: 03 December 2021

Statistical physics of condensed matter: basic concepts

Statistical physics of condensed matter: basic concepts

Chapter:
(p.13) 2 Statistical physics of condensed matter: basic concepts
Source:
Ultracold Atoms in Optical Lattices
Author(s):

Maciej Lewenstein

Anna Sanpera

Verònica Ahufinger

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199573127.003.0002

This chapter explains the basic ideas and concepts of the modern quantum theory of condensed matter. It starts by discussing phase transition in classical systems, scaling, and renormalisation theory, both in real and in momentum space. The chapter then moves on to quantum systems and discusses Bose–Einstein condensation (BEC) in non-interacting gases. It presents the concept of quantum phase transitions, illustrating it with spin systems and BEC in weakly interacting gases. Finally, the chapter discusses specific properties of low dimensional Bose systems: the role of phase fluctuations in 1D and 2D gases, Tonks-Girardeau gas in 1D, and Berezinskii-Kosterlitz-Thouless transition in 2D.

Keywords:   phase transitions, scaling theory, renormalization, quantum phase transitions, Bose–Einstein condensation, Tonks-Girardeau gas, Berezinskii-Kosterlitz-Thouless, phase fluctuations

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