Ripplons interaction

Rayleigh Scattering of the Phonons Due to the Elastic Component of Ripplon-Phonon Interaction... 

Since the contributions of the three constiments of the van der Waals attraction are additive, one can consider each contribution separately. This indeed proves to be convenient not only because all the contributions exhibit distinct scaling with the parameters, but each contribution comes to dominate the expansivity at somewhat distinct temperatures. We consider first the ripplon-ripplon attraction. This contribution appears to dominate the most studied region around 1 K. The off-diagonal (flip-flop) interaction between the ripplons has the form... 

To complete the discussion of the second-order interaction between tunneling centers, we note that the corresponding contribution to the heat capacity in the leading low T term comes from the ripplon-TLS term and scales as 7 +2 where a is the anomalous exponent of the specific law. Within the approximation adopted in this section, a = 0. However, it is easily seen that the magnitude of the interaction-induced specific heat is down from the two-level system value by a factor of 10(a/ ) ([Pg.188]

Erom the qualitative analysis in this section, we tentatively conclude that there are several contributions of comparable magnitude to the thermal expansion at low temperatures. Higher order effects may also be present. In this case, it may be more straightforward to estimate the interaction between ripplons as extended membranes without using a multipole expansion, as indeed is done when computing the regular Casimir force between extended plates. 

APPENDIX A RAYLEIGH SCATTERING OF THE PHONONS DUE TO THE ELASTIC COMPONENT OF RIPPLON-PHONON INTERACTION... 

---