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Tomonaga—Luttinger Liquid in Quantum Wires

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Mesoscopic Physics and Electronics

Part of the book series: NanoScience and Technology ((NANO))

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Abstract

Landauer’s formula discussed in Sect. 1.3.3 gives the quantized conductance in an ideal quantum wire without impurities,

$$ G = \frac{{2{e^2}}}{h}N $$
(2.1.1)

where N is the number of subbands which cross the Fermi energy EF. This formula was derived in noninteracting case. In one-dimensional systems, it has long been known that the mutual interaction has strong effects. In fact, each order of perturbation calculations has a divergence and thus the ground state is a non-perturbative one. Such a state is described as a Tomonaga—Luttinger liquid [1], which differs from the conventional Fermi liquid. It exhibits several anomalous behaviors such as a power-law decay of physical quantities and a spin-charge separation [2–5]. It is thus very interesting and important to study quantum wires and to find out such anomalous phenomena characteristic of the Tomonaga—Luttinger liquid.

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Authors
  1. M. Ogata
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  2. H. Fukuyama
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Editor information

Editors and Affiliations

  1. Institute for Solid State Physics, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106, Japan

    T. Ando

  2. Institute of Industrial Science, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106, Japan

    Y. Arakawa

  3. Department of Electrical and Electronic Engineering, Tokyo Institute of Technology, 2-1-12 O-okayama, Meguro-ku, Tokyo 152, Japan

    K. Furuya

  4. Department of Basic Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153, Japan

    S. Komiyama

  5. Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567, Japan

    H. Nakashima

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© 1998 Springer-Verlag Berlin Heidelberg

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Ogata, M., Fukuyama, H. (1998). Tomonaga—Luttinger Liquid in Quantum Wires. In: Ando, T., Arakawa, Y., Furuya, K., Komiyama, S., Nakashima, H. (eds) Mesoscopic Physics and Electronics. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71976-9_7

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  • DOI: https://doi.org/10.1007/978-3-642-71976-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-71978-3

  • Online ISBN: 978-3-642-71976-9

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