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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 examines how one-dimensional physics is changed when one goes from a purely one-dimensional system to a two- or three-dimensional situation. Such an effect can be realized by considering a system of one-dimensional chains where the electrons can hop from one chain to the other. As for the spin chains, there are two interesting limiting cases for which one can study this problem: the coupling of a small number of chains that corresponds to a fermion ladder, and an infinite number of coupled chains. The more complicated case of fermions with spins is also discussed, along with the physical realizations of ladders and the single electron hopping term between the chains. The application of coupled fermionic chains to organic conductors is also considered.

Keywords:   fermions, fermionic chains, one-dimensional systems, ladders, two-body hopping, organic conductors

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