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A quantum field theory of localized and resonant modes in 3D nonlinear lattices at finite temperatures II

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  • Kitamura, Toyoyuki
  • Takeno, Shozo

Abstract

We solve the eigenvalue equation derived in paper I under the assumption that a localized or resonant mode is well-localized at a lattice site. Localized modes appear above the top of the phonon band for an appropriate positive quartic potential at any temperatures. Resonant modes appear in the middle of the phonon band for an appropriate negative quartic potential at low temperatures due to the frequency dependent coupling of the mode. This fact is essentially different from that in the force constant defect, where resonant modes appear in the lower frequency regions due to the frequency independent couplings. Both modes are investigated numerically using the tables of the Green's functions for monoatomic simple cubic lattices in terms of the Bessel functions. Resonant modes are also investigated in the Debye approximation.

Suggested Citation

  • Kitamura, Toyoyuki & Takeno, Shozo, 1995. "A quantum field theory of localized and resonant modes in 3D nonlinear lattices at finite temperatures II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 213(4), pages 539-550.
    • Handle: RePEc:eee:phsmap:v:213:y:1995:i:4:p:539-550
    DOI: 10.1016/0378-4371(94)00238-O
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    References listed on IDEAS

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    1. Inoki, Takenori, 1994. "Job Tenure and Occupational Tenure―A Comparison between Japan and U. S. A.―," Economic Review, Hitotsubashi University, vol. 45(4), pages 289-300, October.
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    Cited by:

    1. Kitamura, Toyoyuki, 1996. "A quantum field theory of the structure of phonons in amorphous solids and liquids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 223(1), pages 227-243.

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    2. Kitamura, Toyoyuki, 1996. "A quantum field theory of the structure of phonons in amorphous solids and liquids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 223(1), pages 227-243.

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