Short-time critical dynamics of the three-dimensional systems with long-range correlated disorder

Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional Ising and XY models with long-range correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are determined for systems starting separately from ordered and disordered initial states. The obtained values of the exponents are in a good agreement with results of the field-theoretic description of the critical behavior of these models in the two-loop approximation and with our results of Monte Carlo simulations of three-dimensional Ising model in equilibrium state.Comment: 24 RevTeX pages, 12 figure

Pulsar Kicks With Modified URCA and Electrons in Landau Levels

We derive the energy asymmetry given the proto-neutron star during the time when the neutrino sphere is near the surface of the proto-neutron star, using the modified URCA process. The electrons produced with the anti-neutrinos are in Landau levels due to the strong magnetic field, and this leads to asymmetry in the neutrino momentum, and a pulsar kick. The magnetic field must be strong enough for a large fraction of the eletrons to be in the lowest Landau level, however, there is no direct dependence of our pulsar velocity on the strength of the magnetic field. Our main prediction is that the large pulsar kicks start at about 10 s and last for about 10 s, with the corresponding neutrinos correlated in the direction of the magnetic field. We predict a pulsar velocity of 1.03 $\times 10^{-4} (T/10^{10}K)^7$ km/s, which reaches 1000 km/s if T $\simeq 9.96 \times 10^{10}$ K.Comment: 11 pages, 6 figure

On the problem of boundedness of a signed measure on projections of a von Neumann algebra

Let M be a von Neumann algebra and Mn be the set of all orthogonal projections in M. We call a mapping ηMn → C a signed measure on M if η is totally orthoadditive, that is, η(∑i ε{lunate} IPi) = ε{lunate}i ε{lunate} I η(Pi) for Pi ε{lunate} Mn, Pi⊥ Pj (i ≠ j). Here the condition of boundedness is usually required for the effective study and application of signed measures. So a natural problem of the existence of unbounded signed measures arises. In the present paper it is proved that any signed measure on the set of projections of a continuous von Neumann algebra is bounded. This fact is generalized also for vector-valued measures. © 1992

Spontaneous symmetry breaking for long-wave gravitons in the early Universe

It is shown that nonlinear terms in equations of gravitons on the background of curved space-time of the expanding Universe can solve the problem of the negative square of the effective mass formally arising in linear approximation for gravitons. Similar to well known spontaneous breaking of symmetry in Goldstone model one must take another vacuum so that nonzero vacuum expectation value of the quantized graviton field leads to change of spectrum for gravitons. There appears two graviton fields, one with the positive mass, another with the zero mass. Energy density and the density of particles created by gravitation of the expanding Universe are calculated for some special cases of the scale factor. Numerical results are obtained for the dust universe case.Comment: 13 page

On the Possible Enhancement of the Magnetic Field by Neutrino Reemission Processes in the Mantle of a Supernova

URCA neutrino reemission processes under the conditions in the mantle of a supernova with a strong toroidal magnetic field are investigated. It is shown that parity violation in these processes can be manifested macroscopically as a torque that rapidly spins up the region of the mantle occupied by such a field. Neutrino spin-up of the mantle can strongly affect the mechanism of further generation of the toroidal field, specifically, it can enhance the field in a small neighborhood of the rigid-body-rotating core of the supernova remnant.Comment: 8 pages, late

Parity Violation in Neutrino Transport and the Origin of Pulsar Kicks

In proto-neutron stars with strong magnetic fields, the neutrino-nucleon scattering/absorption cross sections depend on the direction of neutrino momentum with respect to the magnetic field axis, a manifestation of parity violation in weak interactions. We study the deleptonization and thermal cooling (via neutrino emission) of proto-neutron stars in the presence of such asymmetric neutrino opacities. Significant asymmetry in neutrino emission is obtained due to multiple neutrino-nucleon scatterings. For an ordered magnetic field threading the neutron star interior, the fractional asymmetry in neutrino emission is about $0.006 (B/10^{14}G)$, corresponding to a pulsar kick velocity of about $200 (B/10^{14}G)$ km/s for a total radiated neutrino energy of $3\times 10^{53}$ erg.Comment: AASTeX, 10 pages including 2 ps figures; ApJ Letter in press (March 10, 1998). Shortened to agree with the published versio

Pulsar kicks and dark matter from a sterile neutrino

The observed velocities of radio pulsars, which range in the hundreds kilometers per second, and many of which exceed 1000 km/s, are not explained by the standard physics of the supernova explosion. However, if a sterile neutrino with mass in the 1-20 keV range exists, it would be emitted asymmetrically from a cooling neutron star, which could give it a sufficient recoil to explain the pulsar motions. The same particle can be the cosmological dark mater. Future observations of X-ray telescopes and gravitational wave detectors can confirm or rule out this explanation.Comment: 7 pages, 1 figure; invited talk at the Coral Gables Conference (CG2003), Ft. Lauderdale, Florida, December 17-21, 200

Functorial methods in the theory of group representations I

We introduce a candidate for the group algebra of a Hausdorff group which plays the same role as the group algebra of a finite group. It allows to define a natural bijection between k-continuous representations of the group in a Hilbert space and continuous representations of the group algebra. Such bijections are known, but to our knowledge only for locally compact groups. We can establish such a bijection for more general groups, namely Hausdorff groups, because we replace integration techniques by functorial methods, i.e., by using a duality functor which lives in certain categories of topological Banach balls (resp., unit balls of Saks spaces). © 1995 Kluwer Academic Publishers

Pulsar Kicks With Sterile Neutrinos and Landau Levels

We use a model with two sterile neutrinos obtained by fits to the MiniBoone and LSND experiments. Using formulations with neutrinos created by URCA Processes in a strong magnetic field, so the lowest Landau level has a sizable probability, we find that with known paramenters the assymetric sterile neutrino emissivity might account for large pulsar kicks.Comment: 3 pages, 1 figur