11,002 research outputs found
Collisionless Hydrodynamics of Doped Graphene in a Magnetic Field
The electrodynamics of a two-dimensional gas of massless fermions in graphene
is studied by a collisionless hydrodynamic approach. A low-energy dispersion
relation for the collective modes (plasmons) is derived both in the absence and
in the presence of a perpendicular magnetic field. The results for graphene are
compared to those for a standard two-dimensional gas of massive electrons. We
further compare the results within the classical hydrodynamic approach to the
full quantum mechanical calculation in the random phase approximation. The
low-energy dispersion relation is shown to be a good approximation at small
wave vectors. The limitations of this approach at higher order is also
discussed.Comment: 7 pages, 1 figur
Dynamical friction force exerted on spherical bodies
We present a rigorous calculation of the dynamical friction force exerted on
a spherical massive perturber moving through an infinite homogenous system of
field stars. By calculating the shape and mass of the polarization cloud
induced by the perturber in the background system, which decelerates the motion
of the perturber, we recover Chandrasekhar's drag force law with a modified
Coulomb logarithm. As concrete examples we calculate the drag force exerted on
a Plummer sphere or a sphere with the density distribution of a Hernquist
profile. It is shown that the shape of the perturber affects only the exact
form of the Coulomb logarithm. The latter converges on small scales, because
encounters of the test and field stars with impact parameters less than the
size of the massive perturber become inefficient. We confirm this way earlier
results based on the impulse approximation of small angle scatterings.Comment: 5 pages, 2 figures, accepted in MNRA
Mathematical theory of the Goddard trajectory determination system
Basic mathematical formulations depict coordinate and time systems, perturbation models, orbital estimation techniques, observation models, and numerical integration methods
- …