Apparatus for making curved reflectors Patent

Forming mold for polishing and machining curved solar magnesium reflector with reinforcing rib

Chern-Simons Invariants of Closed Hyperbolic 3-Manifolds

The Chern-Simons invariants of irreducible U(n)- flat connections on compact hyperbolic 3-manifolds of the form {\Gamma}\H^3 are derived. The explicit formula for the Chern-Simons functional is given in terms of Selberg type zeta functions related to the twisted eta invariants of Atiyah-Patodi-Singer.Comment: 10 pages, 2 diagram

Distribution of Eigenvalues of Ensembles of Asymmetrically Diluted Hopfield Matrices

Using Grassmann variables and an analogy with two dimensional electrostatics, we obtain the average eigenvalue distribution $\rho(\omega)$ of ensembles of $N \times N$ asymmetrically diluted Hopfield matrices in the limit $N \rightarrow \infty$. We found that in the limit of strong dilution the distribution is uniform in a circle in the complex plane.Comment: 9 pages, latex, 4 figure

Charged branes interactions via Kalb-Ramond field

Because of its versatility, the 2-form field has been employed to describe a multitude of scenarios that range from high energy to condensed matter physics. Pushing forward in this endeavor we study the interaction energy, intermediated by this kind of field, between branes in a variety of configurations. Also, the so-called Cremmer-Scherk-Kalb-Ramond model, which consists of the electromagnetic field coupled to the Kalb-Ramond gauge potential, is considered. It turns out that these models exhibit a much richer class of sources than usually thought, able to intermediate novel forms of interactions in different scenarios.Comment: 12 latex pages, more general result

Method and apparatus for making curved reflectors Patent

Fabrication of curved reflector segments for solar mirro

A minimum hypothesis explanation for an IMF with a lognormal body and power law tail

We present a minimum hypothesis model for an IMF that resembles a lognormal distribution at low masses but has a distinct power-law tail. Even if the central limit theorem ensures a lognormal distribution of condensation masses at birth, a power-law tail in the distribution arises due to accretion from the ambient cloud, coupled with a non-uniform (exponential) distribution of accretion times.Comment: 2 pages, 1 figure, to appear in IMF@50, eds. E. Corbelli, F. Palla, and H. Zinnecker, Kluwer, Astrophysics and Space Science Librar

The Wess-Zumino-Witten term in non-commutative two-dimensional fermion models

We study the effective action associated to the Dirac operator in two dimensional non-commutative Field Theory. Starting from the axial anomaly, we compute the determinant of the Dirac operator and we find that even in the U(1) theory, a Wess-Zumino-Witten like term arises.Comment: 11 pages, no figures, LaTex fil

Vacuum Energy: Myths and Reality

We discuss the main myths related to the vacuum energy and cosmological constant, such as: ``unbearable lightness of space-time''; the dominating contribution of zero point energy of quantum fields to the vacuum energy; non-zero vacuum energy of the false vacuum; dependence of the vacuum energy on the overall shift of energy; the absolute value of energy only has significance for gravity; the vacuum energy depends on the vacuum content; cosmological constant changes after the phase transition; zero-point energy of the vacuum between the plates in Casimir effect must gravitate, that is why the zero-point energy in the vacuum outside the plates must also gravitate; etc. All these and some other conjectures appear to be wrong when one considers the thermodynamics of the ground state of the quantum many-body system, which mimics macroscopic thermodynamics of quantum vacuum. In particular, in spite of the ultraviolet divergence of the zero-point energy, the natural value of the vacuum energy is comparable with the observed dark energy. That is why the vacuum energy is the plausible candidate for the dark energy.Comment: 24 pages, 2 figures, submitted to the special issue of Int. J. Mod. Phys. devoted to dark energy and dark matter, IJMP styl

Matrix Hamiltonians: SUSY approach to hidden symmetries

A new supersymmetric approach to the analysis of dynamical symmetries for matrix quantum systems is presented. Contrary to standard one dimensional quantum mechanics where there is no role for an additional symmetry due to nondegeneracy, matrix hamiltonians allow for non-trivial residual symmetries. This approach is based on a generalization of the intertwining relations familiar in SUSY Quantum Mechanics. The corresponding matrix supercharges, of first or of second order in derivatives, lead to an algebra which incorporates an additional block diagonal differential matrix operator (referred to as a "hidden" symmetry operator) found to commute with the superhamiltonian. We discuss some physical interpretations of such dynamical systems in terms of spin 1/2 particle in a magnetic field or in terms of coupled channel problem. Particular attention is paid to the case of transparent matrix potentials.Comment: 20 pages, LaTe

Asymptotics of the deuteron form factors in the nucleon model and JLab experiments

Using the instant form dynamics of Poincar\'e invariant quantum mechanics and the modified relativistic impulse approximation proposed previously we calculate asymptotics of electromagnetic form factors for the deuteron considered as two--nucleon system. We show that today experiment on the elastic $ed$-scattering has reached asymptotic regime. The possible range of momentum transfer when the quark degrees of freedom could be seen in future JLab experiments is estimated. The explicit relation between the behavior of deuteron wave function at $r=0$ and the form factors asymptotics is obtained. The conditions on wave functions to give the asymptotics predicted by QCD and quark counting rules are formulated.Comment: 9 pages, 1 figur