Intrinsic Localized Modes in the Bulk and at the Surface of Anharmonic Chains

  • V. Bortolani
  • A. Franchini
  • R. F. Wallis


In this paper we will review recents results relative to localized modes induced by anharmonicity in one-dimensional lattices. We will show that localized modes exists in monoatomic chains with and without a local inhomogeneity in the anharmonic force field. We will compare the discrete and the quasi-continuum intrinsic even and odd localized solutions. This analysis is carried out by taking into account harmonic and quartic anharmonic interactions. We will also present results for the diatomic chains showing the presence of surface modes and gap modes related to the maximum of the acoustic band. In this analysis will be also studied the effect of the cubic anharmonicity. One of the major effects of the cubic anharmonicity is to produce gap modes that split off from the bottom of the optical branch.


Localize Mode Surface Mode Atomic Displacement Rotate Wave Approximation Displacement Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. J. Sievers and S. Taken, Phys. Rev. B 39, 3037 (1989).CrossRefGoogle Scholar
  2. 2.
    J. B. Page, Phys. Rev. B 41, 7835 (1990).CrossRefGoogle Scholar
  3. 3.
    Y. S. Kivshar, Phys. Lett. A 161, 80 (1991).CrossRefGoogle Scholar
  4. 4.
    S. A. Kiselev, S. R. Bickham, and A. J. Sievers, Plays. Rev. B 50, 9135 (1.993).Google Scholar
  5. 5.
    R,. F. Wallis, A. Franchini, and V. Bortolani, Phys. Rev. B 50, 9851 (1994).CrossRefGoogle Scholar
  6. 6.
    A. Franchini, V. Bortolani, F. Corsini, and R. F. Wallis, Nuovo Cimento,to be published.Google Scholar
  7. 7.
    S. R. Bickham, S. A. Kiselev, and A. J. Sievers, Phys. Rev. B 47, 14206 (1993).Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • V. Bortolani
    • 1
  • A. Franchini
    • 1
  • R. F. Wallis
    • 2
  1. 1.INFM and Dipartimento di FisicaUniversitá di ModenaModenaItaly
  2. 2.Department of PhysicsUniversity of CaliforniaIrvineUSA

Personalised recommendations