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 $A$ in a $p|q$-dimensional superspace $V$. We show that traces of exterior powers of $A$ satisfy universal recurrence relations of period $q$. `Underlying' recurrence relations hold in the Grothendieck ring of representations of \GL(V). They are expressed by vanishing of certain Hankel determinants of order $q+1$ 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 $v_0q_iq_j$, where $q_i=\pm1$ is a quenched sequence of ``charges'' on the chain. For equal numbers of positive and negative charges ($N_+=N_-$), the polymer with $v_0>0$ undergoes a transition from self--avoiding behavior to a compact state at a temperature $\theta\approx1.2v_0$. The collapse temperature $\theta(x)$ decreases with the asymmetry $x=|N_+-N_-|/(N_++N_-)$Comment: 8 pages, TeX, 4 uuencoded postscript figures, MIT-CMT-