Coulomb drag

Coulomb Drag between Quantum Wires Effect of Small Momentum Transfer... 

Summary. We demonstrate that in a wide range of temperatures Coulomb drag between two weakly coupled quantum wires is dominated by processes with a small interwire momentum transfer. Such processes, not accounted for in the conventional Luttinger liquid theory, cause drag only because the electron dispersion relation is not linear. The corresponding contribution to the drag resistance scales with temperature as T2 if the wires are identical, and as T5 if the wires are different. 

Fig. 1. Coulomb drag between quantum wires. A dc current H flows through the active wire (1). A voltage bias It is applied to the passive wire (2) in such a way that I2 = 0.

To conclude, the small momentum transfer contribution dominates Coulomb drag at almost all temperatures if the distance between the wires exceeds the Fermi wavelength, see Fig. 2. Drag by small momentum transfer is possible because electron dispersion relation is not linear, and therefore can not be accounted for in the conventional Tomonaga-Luttinger model. 

Bodmer P, Bochsler P (1998b) The helium isotopic ratio in the solar wind and ion fractionation in the corona by inefficient Coulomb drag. Astron Astrophys 337 921-927 Bogard DD (1988) On the origin of Venus atmosphere possible contributions from simple component mixtures and fractionated solar wind. Icarus 74 3-20... 

To estimate the particle migration velocity, it is assumed that (1) particles are spherical and have the same size (2) all particles are charged to the same extent (3) the particle motion is governed by the Coulomb force and the Stokes drag only and (4) the direction of the applied electric field is perpendicular to the direction of the suspension flow. 

Various models will be used for the interface between the fiber and the matrix. For bonded interfaces, complete continuity of all components of the velocity will be invoked. The simplest model for a weak interface is that a shear drag equal to r opposes the relative shear velocity jump across the interface. The direction of the shear drag is determined by the direction of the relative velocity. However, the magnitude of r is independent of the velocities. This model is assumed to represent friction occurring mainly because of roughness of the surfaces or due to a superposed large normal pressure on the interface. Creep can, of course, relax the superposed normal stress over time, but on a short time scale the parameter r can be assumed to be relatively invariant. No attempt will be made to account for Coulomb friction associated with local normal pressures on the interface. 

When a solute ion, i, with Zj elementary charges of an electron (valence), e (1.602 X 10 coulombs) is placed in an electric field of intensity E (Vm ), it will be accelerated until the force is balanced by the drag force F exerted on the ion by the hydrodynamic medium in which it is placed [73]. 

For proteins with comparable surface hydrophobicity, the adsorption uptake correlates strongly with the extent of protein under-wrapping [19]. As an adequate control, only proteins with the same extent of surface hydrophobicity or solvent-exposed nonpolar area were included in the comparative analysis. Hence, the attractive drag exerted by dehydrons on test hydrophobes became accessible. The net gain in Coulomb energy associated with wrapping a dehydron has been experimentally determined to be 4 kJ/mol [19]. The adhesive force exerted by a dehydron on a hydrophobe at 6 A distance is 7.8 pN, a magnitude comparable to the hydrophobic attraction between two nonpolar moieties that frame unfavorable interfaces with water. 

Coulomb contributed what is often called the third law of friction, i.e. that is relatively independent of sliding velocity. The experiments discussed in Section I.D show that the actual dependence is logarithmic in many experimental systems and that often increases with decreasing velocity. Thus there is a fundamental difference between kinetic friction and viscous or drag forces that decrease to zero linearly with v. A nearly constant kinetic friction implies that motion does not become adiabatic even as the center-of-mass velocity decreases to zero, and the system is never in the linear response regime described by the fluctuation dissipation theorem. Why and how this behavior occurs is closely related to the second issue raised above. 

Pressure gradient measurements for setthng slurries show that the total frictional drag at the pipe wall can be expressed as the sum of kinetic and Coulombic components. In term of shear stresses,... 

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