1. 6. LOW-TEMPERATURE PROPERTIES OF NON-CRYSTALLINE SOLIDS T > 1 K: other low-frequency excitations, “soft modes”, and the Soft-Potential Model

2. T > 1 K ? U. Buchenau et al., Phys.Rev. B34, 5665 (1986)

4. Basic assumptions of the SOFT-POTENTIAL MODEL: The SOFT-POTENTIAL MODEL V(x) = W (D 1 x + D 2 x 2 + x 4 ) (i) The soft modes can on average be characterized by a single energy W (ii) D 1 and D 2 are randomly distributed around the origin of the D 1 - D 2 plane: P(D 1, D 2 ) = P(0, 0)  P s (iii) The interaction between the soft modes and the sound waves is bilinear in the displacement of the soft mode and in the strain field of the sound wave:  V l,t =  l,t x  l,t

5. D 2 < 0 V(x) = W x 4 D 2 > 0 D 2 =D 1 =0 V(x) = W (D 1 x + D 2 x 2 + x 4 )

6. TUNNELING MODEL  SOFT POTENTIAL MODEL  SPM universal constants:

7. SOFT-POTENTIAL MODEL: Specific heat

8. SPM fit: {,

9. M.A.R., Philos. Mag. (2004)

10. CALCULATION OF THE THERMAL CONDUCTIVITY ( ( ) () ()

11. TcTc SPM M.A.R. and U. Buchenau, Phys. Rev. B 55, 5749 (1997)

12. L. Gil et al., Phys. Rev. Lett. 70, 182 (1993)

14. Ioffe-Regel limit: SPM phonon localization when its mean free path decreases down to half the wavelength: for Brillouin scattering: