Ambient betatron motion and its excitation by ghost lines in Tevatron

Transverse betatron motion of the Tevatron proton beam is measured and analyzed. It is shown that the motion is coherent and excited by external sources of unknown origins. Observations of the time varying ghost lines in the betatron spectra are reported.Comment: 9 p

New distal marker closely linked to the fragile X locus

We have isolated II-10, a new X-chromosomal probe that identifies a highly informative two-allele TaqI restriction fragment length polymorphism at locus DXS466. Using somatic cell hybrids containing distinct portions of the long arm of the X chromosome, we could localize DXS466 between DXS296 and DXS304, both of which are closely linked distal markers for fragile X. This regional localization was supported by the analysis, in fragile X families, of recombination events between these three loci, the fragile X locus and locus DXS52, the latter being located at a more distal position. DXS466 is closely linked to the fragile X locus with a peak lod score of 7.79 at a recombination fraction of 0.02. Heterozygosity of DXS466 is approximately 50%. Its close proximity and relatively high informativity make DXS466 a valuable new diagnostic DNA marker for fragile X

On Darboux-Treibich-Verdier potentials

It is shown that the four-parameter family of elliptic functions $$u_D(z)=m_0(m_0+1)\wp(z)+\sum_{i=1}^3 m_i(m_i+1)\wp(z-\omega_i)$$ introduced by Darboux and rediscovered a hundred years later by Treibich and Verdier, is the most general meromorphic family containing infinitely many finite-gap potentials.Comment: 8 page

Distribution of local density of states in disordered metallic samples: logarithmically normal asymptotics

Asymptotical behavior of the distribution function of local density of states (LDOS) in disordered metallic samples is studied with making use of the supersymmetric $\sigma$--model approach, in combination with the saddle--point method. The LDOS distribution is found to have the logarithmically normal asymptotics for quasi--1D and 2D sample geometry. In the case of a quasi--1D sample, the result is confirmed by the exact solution. In 2D case a perfect agreement with an earlier renormalization group calculation is found. In 3D the found asymptotics is of somewhat different type: P(\rho)\sim \exp(-\mbox{const}\,|\ln^3\rho|).Comment: REVTEX, 14 pages, no figure

Stabilization of Extra Dimensions and The Dimensionality of the Observed Space

We present a simple model for the late time stabilization of extra dimensions. The basic idea is that brane solutions wrapped around extra dimensions, which is allowed by string theory, will resist expansion due to their winding mode. The momentum modes in principle work in the opposite way. It is this interplay that leads to dynamical stabilization. We use the idea of democratic wrapping \cite{art5}-\cite{art6}, where in a given decimation of extra dimensions, all possible winding cases are considered. To simplify the study further we assumed a symmetric decimation in which the total number of extra dimensions is taken to be $Np$ where N can be called the order of the decimation. We also assumed that extra dimensions all have the topology of tori. We show that with these rather conservative assumptions, there exists solutions to the field equations in which the extra dimensions are stabilized and that the conditions do not depend on $p$. This fact means that there exists at least one solution to the asymmetric decimation case. If we denote the number of observed space dimensions (excluding time) by $m$, the condition for stabilization is $m\geq 3$ for pure Einstein gravity and $m\leq 3$ for dilaton gravity massaged by string theory parameters.Comment: Final versio

The Dynamics of Small Instanton Phase Transitions

The small instanton transition of a five-brane colliding with one end of the S1/Z2 interval in heterotic M-theory is discussed, with emphasis on the transition moduli, their potential function and the associated non-perturbative superpotential. Using numerical methods, the equations of motion of these moduli coupled to an expanding Friedmann-Robertson-Walker spacetime are solved including non-perturbative interactions. It is shown that the five-brane collides with the end of the interval at a small instanton. However, the moduli then continue to evolve to an isolated minimum of the potential, where they are trapped by gravitational damping. The torsion free sheaf at the small instanton is ``smoothed out'' into a vector bundle at the isolated minimum, thus dynamically completing the small instanton phase transition. Radiative damping at the origin of moduli space is discussed and shown to be insufficient to trap the moduli at the small instanton point.Comment: LaTeX, 23 pages, 7 figures; minor corrections, references adde

Ground-state clusters of two-, three- and four-dimensional +-J Ising spin glasses

A huge number of independent true ground-state configurations is calculated for two-, three- and four-dimensional +- J spin-glass models. Using the genetic cluster-exact approximation method, system sizes up to N=20^2,8^3,6^4 spins are treated. A ``ballistic-search'' algorithm is applied which allows even for large system sizes to identify clusters of ground states which are connected by chains of zero-energy flips of spins. The number of clusters n_C diverges with N going to infinity. For all dimensions considered here, an exponential increase of n_C appears to be more likely than a growth with a power of N. The number of different ground states is found to grow clearly exponentially with N. A zero-temperature entropy per spin of s_0=0.078(5)k_B (2d), s_0=0.051(3)k_B (3d) respectively s_0=0.027(5)k_B (4d) is obtained.Comment: large extensions, now 12 pages, 9 figures, 27 reference

Quantumgroups in the Higgs Phase

In the Higgs phase we may be left with a residual finite symmetry group H of the condensate. The topological interactions between the magnetic- and electric excitations in these so-called discrete H gauge theories are completely described by the Hopf algebra or quantumgroup D(H). In 2+1 dimensional space time we may add a Chern-Simons term to such a model. This deforms the underlying Hopf algebra D(H) into a quasi-Hopf algebra by means of a 3-cocycle H. Consequently, the finite number of physically inequivalent discrete H gauge theories obtained in this way are labelled by the elements of the cohomology group H^3(H,U(1)). We briefly review the above results in these notes. Special attention is given to the Coulomb screening mechanism operational in the Higgs phase. This mechanism screens the Coulomb interactions, but not the Aharonov-Bohm interactions. (Invited talk given by Mark de Wild Propitius at `The III International Conference on Mathematical Physics, String Theory and Quantum Gravity', Alushta, Ukraine, June 13-24, 1993. To be published in Theor. Math. Phys.)Comment: 19 pages in Latex, ITFA-93-3

Dynamical System Approach to Cosmological Models with a Varying Speed of Light

Methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods of reduction of dynamics to the form of planar Hamiltonian dynamical systems for models with a time dependent equation of state. The solutions are analyzed on two-dimensional phase space in the variables $(x, \dot{x})$ where $x$ is a function of a scale factor $a$. Then we show how the horizon problem may be solved on some evolutional paths. It is shown that the models with negative curvature overcome the horizon and flatness problems. The presented method of reduction can be adopted to the analysis of dynamics of the universe with the general form of the equation of state $p=\gamma(a)\epsilon$. This is demonstrated using as an example the dynamics of VSL models filled with a non-interacting fluid. We demonstrate a new type of evolution near the initial singularity caused by a varying speed of light. The singularity-free oscillating universes are also admitted for positive cosmological constant. We consider a quantum VSL FRW closed model with radiation and show that the highest tunnelling rate occurs for a constant velocity of light if $c(a) \propto a^n$ and $-1 < n \le 0$. It is also proved that the considered class of models is structurally unstable for the case of $n < 0$.Comment: 18 pages, 5 figures, RevTeX4; final version to appear in PR

Knots, Braids and BPS States in M-Theory

In previous work we considered M-theory five branes wrapped on elliptic Calabi-Yau threefold near the smooth part of the discriminant curve. In this paper, we extend that work to compute the light states on the worldvolume of five-branes wrapped on fibers near certain singular loci of the discriminant. We regulate the singular behavior near these loci by deforming the discriminant curve and expressing the singularity in terms of knots and their associated braids. There braids allow us to compute the appropriate string junction lattice for the singularity and,hence to determine the spectrum of light BPS states. We find that these techniques are valid near singular points with N=2 supersymmetry.Comment: 38 page