Effect of phonon scattering by surface roughness on the universal thermal conductance

The effect of phonon scattering by surface roughness on the thermal conductance in mesoscopic systems at low temperatures is calculated using full elasticity theory. The low frequency behavior of the scattering shows novel power law dependences arising from the unusual properties of the elastic modes. This leads to new predictions for the low temperature depression of the thermal conductance below the ideal universal value. Comparison with the data of Schwab et al. [Nature 404, 974 (2000)] suggests that surface roughness on a scale of the width of the thermal pathway is important in the experiment.Comment: 6 pages, 3 figure

Construction of coherent states for physical algebraic systems

We construct a general state which is an eigenvector of the annihilation operator of the Generalized Heisenberg Algebra. We show for several systems, which are characterized by different energy spectra, that this general state satisfies the minimal set of conditions required to obtain Klauder's minimal coherent states.Comment: 15 pages, 3 figure

The Effect of Surface Roughness on the Universal Thermal Conductance

We explain the reduction of the thermal conductance below the predicted universal value observed by Schwab et al. in terms of the scattering of thermal phonons off surface roughness using a scalar model for the elastic waves. Our analysis shows that the thermal conductance depends on two roughness parameters: the roughness amplitude $\delta$ and the correlation length $a$. At sufficiently low temperatures the conductance decrease from the universal value quadratically with temperature at a rate proportional to $\delta ^{2}a$. Values of $\delta$ equal to 0.22 and $a$ equal to about 0.75 of the width of the conduction pathway give a good fit to the data.Comment: 10 pages, 5 figures. Ref. added, typo correcte