Viscous corrections to the resistance of nano-junctions: a dispersion relation approach

http://arxiv.org/PS_cache/arxiv/pdf/1010/1010.2959v2.pdfIt is well known that the viscosity of a homogeneous electron liquid diverges in the limits of zero frequency and zero temperature. A nanojunction breaks translational invariance and necessarily cuts off this divergence. However, the estimate of the ensuing viscosity is far from trivial. Here, we propose an approach based on a Kramers-Kr\"onig dispersion relation, which connects the zero- frequency viscosity, $\eta(0)$, to the high-frequency shear modulus, $\mu_{\infty}$, of the electron liquid via $\eta(0) =\mu_{\infty} \tau$, with $\tau$ the junction-specific momentum relaxation time. By making use of a simple formula derived from time-dependent current-density functional theory we then estimate the many-body contributions to the resistance for an integrable junction potential and find that these viscous effects may be much larger than previously suggested for junctions of low conductance.DR and MD acknowledge support from the DOE grant DE-FG02-05ER46204 and UC Laboratories, GV from DOE under Grant No. DE-FG02-05ER46203