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Quantum Physics in One Dimension$
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Thierry Giamarchi

Print publication date: 2003

Print ISBN-13: 9780198525004

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198525004.001.0001

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Quantum Physics in One Dimension

Thierry Giamarchi

Oxford University Press

This chapter looks at less usual realizations of Luttinger liquids than the ones coming from fermionic systems. The first realization is provided by interacting bosons. Indeed, in one dimension it is impossible to decouple completely the statistics from the interactions, and one- and quasi-one-dimensional bosons are also described by Luttinger liquids. The discussion shows how the techniques used to tackle one dimension can be used in higher dimensions as well. An important class of problems examined in this chapter is the case of impurities coupled with a three-dimensional electron gas. Josephson junction arrays and Bose condensates are also considered, along with X-ray, Kondo, and multi-channel Kondo problems. Applications of bosonization to the study of quantum impurities in three-dimensional Fermi liquids are analyzed.

Keywords:   Luttinger liquids, one-dimensional systems, bosonization, bosons, Josephson junctions, Fermi liquids, quantum impurities, Bose glass

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