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

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

MUBs inequivalence and affine planes

There are fairly large families of unitarily inequivalent complete sets of N+1 mutually unbiased bases (MUBs) in C^N for various prime powers N. The number of such sets is not bounded above by any polynomial as a function of N. While it is standard that there is a superficial similarity between complete sets of MUBs and finite affine planes, there is an intimate relationship between these large families and affine planes. This note briefly summarizes "old" results that do not appear to be well-known concerning known families of complete sets of MUBs and their associated planes.Comment: This is the version of this paper appearing in J. Mathematical Physics 53, 032204 (2012) except for format changes due to the journal's style policie

Theta-point universality of polyampholytes with screened interactions

By an efficient algorithm we evaluate exactly the disorder-averaged statistics of globally neutral self-avoiding chains with quenched random charge $q_i=\pm 1$ in monomer i and nearest neighbor interactions $\propto q_i q_j$ on square (22 monomers) and cubic (16 monomers) lattices. At the theta transition in 2D, radius of gyration, entropic and crossover exponents are well compatible with the universality class of the corresponding transition of homopolymers. Further strong indication of such class comes from direct comparison with the corresponding annealed problem. In 3D classical exponents are recovered. The percentage of charge sequences leading to folding in a unique ground state approaches zero exponentially with the chain length.Comment: 15 REVTEX pages. 4 eps-figures . 1 tabl

Pseudo-boundaries in discontinuous 2-dimensional maps

It is known that Kolmogorov-Arnold-Moser boundaries appear in sufficiently smooth 2-dimensional area-preserving maps. When such boundaries are destroyed, they become pseudo-boundaries. We show that pseudo-boundaries can also be found in discontinuous maps. The origin of these pseudo-boundaries are groups of chains of islands which separate parts of the phase space and need to be crossed in order to move between the different sub-spaces. Trajectories, however, do not easily cross these chains, but tend to propagate along them. This type of behavior is demonstrated using a ``generalized'' Fermi map.Comment: 4 pages, 4 figures, Revtex, epsf, submitted to Physical Review E (as a brief report

Damping of sound waves in superfluid nucleon-hyperon matter of neutron stars

We consider sound waves in superfluid nucleon-hyperon matter of massive neutron-star cores. We calculate and analyze the speeds of sound modes and their damping times due to the shear viscosity and non-equilibrium weak processes of particle transformations. For that, we employ the dissipative relativistic hydrodynamics of a superfluid nucleon-hyperon mixture, formulated recently [M.E. Gusakov and E.M. Kantor, Phys. Rev. D78, 083006 (2008)]. We demonstrate that the damping times of sound modes calculated using this hydrodynamics and the ordinary (nonsuperfluid) one, can differ from each other by several orders of magnitude.Comment: 15 pages, 5 figures, Phys. Rev. D accepte

Orbits of Exceptional Groups, Duality and BPS States in String Theory

We give an invariant classification of orbits of the fundamental representations of exceptional groups $E_{7(7)}$ and $E_{6(6)}$ which classify BPS states in string and M theories toroidally compactified to d=4 and d=5. The exceptional Jordan algebra and the exceptional Freudenthal triple system and their cubic and quartic invariants play a major role in this classification. The cubic and quartic invariants correspond to the black hole entropy in d=5 and d=4, respectively. The classification of BPS states preserving different numbers of supersymmetries is in close parallel to the classification of the little groups and the orbits of timelike, lightlike and space-like vectors in Minkowski space. The orbits of BPS black holes in N=2 Maxwell-Einstein supergravity theories in d=4 and d=5 with symmetric space geometries are also classified including the exceptional N=2 theory that has $E_{7(-25)}$ and $E_{6(-26)}$ as its symmety in the respective dimensions.Comment: New references and two tables added, a new section on the orbits of N=2 Maxwell-Einstein supergravity theories in d=4 and d=5 included and some minor changes were made in other sections. 17 pages. Latex fil

Triple Products and Yang-Baxter Equation (II): Orthogonal and Symplectic Ternary Systems

We generalize the result of the preceeding paper and solve the Yang-Baxter equation in terms of triple systems called orthogonal and symplectic ternary systems. In this way, we found several other new solutions.Comment: 38 page

On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory

Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper we develop a hyperbolic analogue of pseudoanalytic function theory using the algebra of hyperbolic numbers. We consider the Klein-Gordon equation with a potential. With the aid of one particular solution we factorize the Klein-Gordon operator in terms of two Vekua-type operators. We show that real parts of the solutions of one of these Vekua-type operators are solutions of the considered Klein-Gordon equation. Using hyperbolic pseudoanalytic function theory, we then obtain explicit construction of infinite systems of solutions of the Klein-Gordon equation with potential. Finally, we give some examples of application of the proposed procedure