6,357 research outputs found
Spin Drag and Spin-Charge Separation in Cold Fermi Gases
Low-energy spin and charge excitations of one-dimensional interacting
fermions are completely decoupled and propagate with different velocities.
These modes however can decay due to several possible mechanisms. In this paper
we expose a new facet of spin-charge separation: not only the speeds but also
the damping rates of spin and charge excitations are different. While the
propagation of long-wavelength charge excitations is essentially ballistic,
spin propagation is intrinsically damped and diffusive. We suggest that cold
Fermi gases trapped inside a tight atomic waveguide offer the opportunity to
measure the spin-drag relaxation rate that controls the broadening of a spin
packet.Comment: 4 pages, 4 figures, submitte
Dielectric function and plasmons of doped three-dimensional Luttinger semimetals
Luttinger semimetals are three-dimensional electron systems with a parabolic
band touching and an effective total spin . In this paper, we present an
analytical theory of dielectric screening of inversion-symmetric Luttinger
semimetals with an arbitrary carrier density and conduction-valence effective
mass asymmetry. Assuming a spherical approximation for the single-particle
Luttinger Hamiltonian, we determine analytically the dielectric screening
function in the random phase approximation for arbitrary values of the wave
vector and frequency, the latter in the complex plane. We use this analytical
expression to calculate the dispersion relation and Landau damping of the
collective modes in the charge sector (i.e., plasmons).Comment: 17 pages, 5 figures, published versio
Generalized Hilbert Functions
Let be a finite module and let be an arbitrary ideal over a
Noetherian local ring. We define the generalized Hilbert function of on
using the 0th local cohomology functor. We show that our definition
re-conciliates with that of Ciuperc. By generalizing Singh's
formula (which holds in the case of ), we prove that the
generalized Hilbert coefficients are preserved under a
general hyperplane section, where . We also keep track of the
behavior of . Then we apply these results to study the generalized
Hilbert function for ideals that have minimal -multiplicity or almost
minimal -multiplicity. We provide counterexamples to show that the
generalized Hilbert series of ideals having minimal or almost minimal
-multiplicity does not have the `expected' shape described in the case where
. Finally we give a sufficient condition such that the
generalized Hilbert series has the desired shape.Comment: arXiv admin note: text overlap with arXiv:1101.228
Divisors class groups of singular surfaces
We compute divisors class groups of singular surfaces. Most notably we
produce an exact sequence that relates the Cartier divisors and almost Cartier
divisors of a surface to the those of its normalization. This generalizes
Hartshorne's theorem for the cubic ruled surface in P^3. We apply these results
to limit the possible curves that can be set-theoretic complete intersection in
P^3 in characteristic zero
Simple D-module components of local cohomology modules
For a projective variety V in P^n over a field of characteristic zero, with
homogeneous ideal I in A = k[x0,x1,...,xn], we consider the local cohomology
modules H^i_I(A). These have a structure of holonomic D-module over A, and we
investigate their filtration by simple D-modules. In case V is nonsingular, we
can describe completely these simple components in terms of the Betti numbers
of V.Comment: 22 page
- …