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A quantum field theory of crystals near melting temperature

Author

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  • Kitamura, T.
  • Umezawa, H.

Abstract

A quantum field theory of one-dimensional crystals composed of bosons or fermions is developed near the melting temperature. It will be shown that the mixing of two momentum states, differing only by a reciprocal lattice vector and having almost the same energies, plays a significant role in the course of the construction of crystals. This mixing leads to the energy gap and molecular density wave. The Bethe-Salpeter equations are solved within the formalism of thermo field dynamics. The gap equation, melting temperature, gapless phonon spectrum and the dynamical map of the density operator are obtained. The phonon spectrum corresponds to the acoustic phonon. The dynamical map of the density operator satisfies the Ward-Takahashi relations.

Suggested Citation

  • Kitamura, T. & Umezawa, H., 1983. "A quantum field theory of crystals near melting temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(1), pages 38-58.
    • Handle: RePEc:eee:phsmap:v:121:y:1983:i:1:p:38-58
    DOI: 10.1016/0378-4371(83)90241-8
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    Cited by:

    1. Kitamura, Toyoyuki, 1988. "A quantum field theory of phonons and boiling in liquids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 151(2), pages 303-317.
    2. Kitamura, Toyoyuki, 1992. "A quantum field theory of phonons in crystals extended to the multi-band model II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 183(1), pages 201-208.
    3. Kitamura, Toyoyuki, 1995. "The Heisenberg equation for phonon operators and soliton solutions in nonlinear lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 214(2), pages 295-308.
    4. Lebedev, V.V. & Smilga, A.V., 1992. "Anomalous damping in plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 181(1), pages 187-220.

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