2,111 research outputs found
A realization of the Lie algebra associated to a Kantor triple system
We present a nonlinear realization of the 5-graded Lie algebra associated to
a Kantor triple system. Any simple Lie algebra can be realized in this way,
starting from an arbitrary 5-grading. In particular, we get a unified
realization of the exceptional Lie algebras f_4, e_6, e_7, e_8, in which they
are respectively related to the division algebras R, C, H, O.Comment: 11 page
Berezinians, Exterior Powers and Recurrent Sequences
We study power expansions of the characteristic function of a linear operator
in a -dimensional superspace . We show that traces of exterior
powers of satisfy universal recurrence relations of period .
`Underlying' recurrence relations hold in the Grothendieck ring of
representations of \GL(V). They are expressed by vanishing of certain Hankel
determinants of order in this ring, which generalizes the vanishing of
sufficiently high exterior powers of an ordinary vector space. In particular,
this allows to explicitly express the Berezinian of an operator as a rational
function of traces. We analyze the Cayley--Hamilton identity in a superspace.
Using the geometric meaning of the Berezinian we also give a simple formulation
of the analog of Cramer's rule.Comment: 35 pages. LaTeX 2e. New version: paper substantially reworked and
expanded, new results include
Dissipation in relativistic superfluid neutron stars
We analyze damping of oscillations of general relativistic superfluid neutron
stars. To this aim we extend the method of decoupling of superfluid and normal
oscillation modes first suggested in [Gusakov & Kantor PRD 83, 081304(R)
(2011)]. All calculations are made self-consistently within the finite
temperature superfluid hydrodynamics. The general analytic formulas are derived
for damping times due to the shear and bulk viscosities. These formulas
describe both normal and superfluid neutron stars and are valid for oscillation
modes of arbitrary multipolarity. We show that: (i) use of the ordinary
one-fluid hydrodynamics is a good approximation, for most of the stellar
temperatures, if one is interested in calculation of the damping times of
normal f-modes; (ii) for radial and p-modes such an approximation is poor;
(iii) the temperature dependence of damping times undergoes a set of rapid
changes associated with resonance coupling of neighboring oscillation modes.
The latter effect can substantially accelerate viscous damping of normal modes
in certain stages of neutron-star thermal evolution.Comment: 25 pages, 9 figures, 1 table, accepted for publication in MNRA
Quasi-normal modes of superfluid neutron stars
We study non-radial oscillations of neutron stars with superfluid baryons, in
a general relativistic framework, including finite temperature effects. Using a
perturbative approach, we derive the equations describing stellar oscillations,
which we solve by numerical integration, employing different models of nucleon
superfluidity, and determining frequencies and gravitational damping times of
the quasi-normal modes. As expected by previous results, we find two classes of
modes, associated to superfluid and non-superfluid degrees of freedom,
respectively. We study the temperature dependence of the modes, finding that at
specific values of the temperature, the frequencies of the two classes of
quasi-normal modes show avoided crossings, and their damping times become
comparable. We also show that, when the temperature is not close to the avoided
crossings, the frequencies of the modes can be accurately computed by
neglecting the coupling between normal and superfluid degrees of freedom. Our
results have potential implications on the gravitational wave emission from
neutron stars.Comment: 16 pages, 7 figures, 2 table
Collapse of Randomly Self-Interacting Polymers
We use complete enumeration and Monte Carlo techniques to study
self--avoiding walks with random nearest--neighbor interactions described by
, where is a quenched sequence of ``charges'' on the
chain. For equal numbers of positive and negative charges (), the
polymer with undergoes a transition from self--avoiding behavior to a
compact state at a temperature . The collapse temperature
decreases with the asymmetry Comment: 8 pages, TeX, 4 uuencoded postscript figures, MIT-CMT-
- …