Tunneling Systems in Solids

  • Igor S. Osad’ko
Part of the Springer Series in Chemical Physics book series (CHEMICAL, volume 69)


A system consisting of N nuclei has six degrees of freedom which describe three translations and three rotations of the whole system, and 3N-6 internal degrees of freedom which relate to displacements of all nuclei. By choosing a potential that was quadratic in nuclear displacements, we assumed that the nuclei carried out small vibrations near their equilibrium positions. However, we have not yet discussed how many equilibrium positions can exist in a solid. One typically assumes that the number of equilibrium positions equals the number of vibrational degrees of freedom. However, a simple example demonstrates that such an assumption may be unjustified.


Matrix Element Quantum State Equilibrium Position Energy Relaxation Amorphous Solid 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Igor S. Osad’ko
    • 1
  1. 1.Department of LuminescenceLebedev Physical Institute of RASMoscowRussia

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