689 research outputs found
Dynamics of spin 1/2 quantum plasmas
The fully nonlinear governing equations for spin 1/2 quantum plasmas are
presented. Starting from the Pauli equation, the relevant plasma equations are
derived, and it is shown that nontrivial quantum spin couplings arise, enabling
studies of the combined collective and spin dynamics. The linear response of
the quantum plasma in an electron--ion system is obtained and analyzed.
Applications of the theory to solid state and astrophysical systems as well as
dusty plasmas are pointed out.Comment: 4 pages, 2 figures, to appear in Physical Review Letter
Fractional analytic index
For a finite rank projective bundle over a compact manifold, so associated to
a torsion, Dixmier-Douady, 3-class, w, on the manifold, we define the ring of
differential operators `acting on sections of the projective bundle' in a
formal sense. In particular, any oriented even-dimensional manifold carries a
projective spin Dirac operator in this sense. More generally the corresponding
space of pseudodifferential operators is defined, with supports sufficiently
close to the diagonal, i.e. the identity relation. For such elliptic operators
we define the numerical index in an essentially analytic way, as the trace of
the commutator of the operator and a parametrix and show that this is homotopy
invariant. Using the heat kernel method for the twisted, projective spin Dirac
operator, we show that this index is given by the usual formula, now in terms
of the twisted Chern character of the symbol, which in this case defines an
element of K-theory twisted by w; hence the index is a rational number but in
general it is not an integer.Comment: 23 pages, Latex2e, final version, to appear in JD
Relativistic quantum plasma dispersion functions
Relativistic quantum plasma dispersion functions are defined and the
longitudinal and transverse response functions for an electron (plus positron)
gas are written in terms of them. The dispersion is separated into
Landau-damping, pair-creation and dissipationless regimes. Explicit forms are
given for the RQPDFs in the cases of a completely degenerate distribution and a
nondegenerate thermal (J\"uttner) distribution. Particular emphasis is placed
on the relation between dissipation and dispersion, with the dissipation
treated in terms of the imaginary parts of RQPDFs. Comparing the dissipation
calculated in this way with the existing treatments leads to the identification
of errors in the literature, which we correct. We also comment on a controversy
as to whether the dispersion curves in a superdense plasma pass through the
region where pair creation is allowed.Comment: 16 pages, 1 figur
Elliptic operators on manifolds with singularities and K-homology
It is well known that elliptic operators on a smooth compact manifold are
classified by K-homology. We prove that a similar classification is also valid
for manifolds with simplest singularities: isolated conical points and fibered
boundary. The main ingredients of the proof of these results are: an analog of
the Atiyah-Singer difference construction in the noncommutative case and an
analog of Poincare isomorphism in K-theory for our singular manifolds.
As applications we give a formula in topological terms for the obstruction to
Fredholm problems on manifolds with singularities and a formula for K-groups of
algebras of pseudodifferential operators.Comment: revised version; 25 pages; section with applications expande
Changes in Polarization Position Angle across the Eclipse in the Double Pulsar System
We investigate the changes in polarization position angle in radiation from
pulsar A around the eclipse in the Double Pulsar system PSR J0737-3039A/B at
the 20 cm and 50 cm wavelengths using the Parkes 64-m telescope. The changes
are ~2\sigma\ during and shortly after the eclipse at 20 cm but less
significant at 50 cm. We show that the changes in position angle during the
eclipse can be modelled by differential synchrotron absorption in the eclipse
regions. Position angle changes after the eclipse are interpreted as Faraday
rotation in the magnetotail of pulsar B. Implied charge densities are
consistent with the Goldreich-Julian density, suggesting that the particle
energies in the magnetotail are mildly relativistic.Comment: Accepted for publication in The Astrophysical Journal Letter
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