The Density of States and the Spectral Shift Density of Random Schroedinger Operators

In this article we continue our analysis of Schroedinger operators with a random potential using scattering theory. In particular the theory of Krein's spectral shift function leads to an alternative construction of the density of states in arbitrary dimensions. For arbitrary dimension we show existence of the spectral shift density, which is defined as the bulk limit of the spectral shift function per unit interaction volume. This density equals the difference of the density of states for the free and the interaction theory. This extends the results previously obtained by the authors in one dimension. Also we consider the case where the interaction is concentrated near a hyperplane.Comment: 1 figur

Cug2 is essential for normal mitotic control and CNS development in zebrafish.

Background: We recently identified a novel oncogene, Cancer-upregulated gene 2 (CUG2), which is essential for kinetochore formation and promotes tumorigenesis in mammalian cells. However, the in vivo function of CUG2 has not been studied in animal models. Results: To study the function of CUG2 in vivo, we isolated a zebrafish homologue that is expressed specifically in the proliferating cells of the central nervous system (CNS). Morpholino-mediated knockdown of cug2 resulted in apoptosis throughout the CNS and the development of neurodegenerative phenotypes. In addition, cug2-deficient embryos contained mitotically arrested cells displaying abnormal spindle formation and chromosome misalignment in the neural plate. Conclusions: Therefore, our findings suggest that Cug2 is required for normal mitosis during early neurogenesis and has functions in neuronal cell maintenance, thus demonstrating that the cug2 deficient embryos may provide a model system for human neurodegenerative disorders

Boltzmann Suppression of Interacting Heavy Particles

Matsumoto and Yoshimura have recently argued that the number density of heavy particles in a thermal bath is not necessarily Boltzmann-suppressed for T << M, as power law corrections may emerge at higher orders in perturbation theory. This fact might have important implications on the determination of WIMP relic densities. On the other hand, the definition of number densities in a interacting theory is not a straightforward procedure. It usually requires renormalization of composite operators and operator mixing, which obscure the physical interpretation of the computed thermal average. We propose a new definition for the thermal average of a composite operator, which does not require any new renormalization counterterm and is thus free from such ambiguities. Applying this definition to the model of Matsumoto and Yoshimura we find that it gives number densities which are Boltzmann-suppressed at any order in perturbation theory. We discuss also heavy particles which are unstable already at T=0, showing that power law corrections do in general emerge in this case.Comment: 7 pages, 5 figures. New section added, with the discussion of the case of an unstable heavy particle. Version to appear on Phys. Rev.

Localization in a Disordered Multi-Mode Waveguide with Absorption or Amplification

An analytical and numerical study is presented of transmission of radiation through a multi-mode waveguide containing a random medium with a complex dielectric constant $\epsilon= \epsilon'+i\epsilon''$. Depending on the sign of $\epsilon''$, the medium is absorbing or amplifying. The transmitted intensity decays exponentially $\propto\exp(-L/\xi)$ as the waveguide length $L\to\infty$, regardless of the sign of $\epsilon''$. The localization length $\xi$ is computed as a function of the mean free path $l$, the absorption or amplification length $|\sigma|^{-1}$, and the number of modes in the waveguide $N$. The method used is an extension of the Fokker-Planck approach of Dorokhov, Mello, Pereyra, and Kumar to non-unitary scattering matrices. Asymptotically exact results are obtained for $N\gg1$ and $|\sigma|\gg1/N^2l$. An approximate interpolation formula for all $\sigma$ agrees reasonably well with numerical simulations.Comment: 13 pages, RevTeX, 1 postscript figur

New Kinetic Equation for Pair-annihilating Particles: Generalization of the Boltzmann Equation

A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most straightforward way, including the off-shell effect. A detailed balance equation for the equilibrium abundance is further analyzed. Perturbative analysis of this equation supports a previous result for the equilibrium abundance using the thermal field theory, and gives the temperature power dependence of equilibrium value at low temperatures. Estimate of the relic abundance is possible using this new equilibrium abundance in the sudden freeze-out approximation.Comment: 19 pages, LATEX file with 2 PS figure

Temperature Power Law of Equilibrium Heavy Particle Density

A standard calculation of the energy density of heavy stable particles that may pair-annihilate into light particles making up thermal medium is performed to second order of coupling, using the technique of thermal field theory. At very low temperatures a power law of temperature is derived for the energy density of the heavy particle. This is in sharp contrast to the exponentially suppressed contribution estimated from the ideal gas distribution function. The result supports a previous dynamical calculation based on the Hartree approximation, and implies that the relic abundance of dark matter particles is enhanced compared to that based on the Boltzmann equation.Comment: 12 pages, LATEX file with 6 PS figure