Renormalization Group Study of the Electron-phonon Interaction in the High Tc Cuprates

We generalize the numerical renormalization group scheme to study the phonon-mediated retarded interactions in the high Tc cuprates. We find that three sets of phonon-mediated retarded quasiparticle scatterings grow under RG flow. These scatterings share the following common features: 1) the initial and final quasiparticle momenta are in the antinodal regions, and 2) the scattering amplitudes have a $x^2-y^2$ symmetry. All three sets of retarded interaction are driven to strong coupling by the magnetic fluctuations around $(\pi,\pi)$. After growing strong, these retarded interaction will trigger density wave orders with d-wave symmetry. However, due to the d-wave form factor they will leave the nodal quasiparticle unaffected. We conclude that the main effect of electron-phonon coupling in the cuprates is to promote these density wave orders.Comment: 4 pages, 3 figures, references added, added more details about others' previous studie

On Inhomogeneity of a String Bit Model for Quantum Gravity

We study quantum gravitational effect on a two-dimensional open universe with one particle by means of a string bit model. We find that matter is necessarily homogeneously distributed if the influence of the particle on the size of the universe is optimized.Comment: 16 pages, LaTeX2

Unitary Irreducible Representations of a Lie Algebra for Matrix Chain Models

There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way. Moreover, they are the only states with a finite number of non-zero quantum numbers with respect to a certain set of maximally commuting linearly independent quantum observables. Any other state is a tensor product of a multiple meson state and a state coming from a representation of a quotient algebra that extends and generalizes the Virasoro algebra. We expect the representation theory of this quotient algebra to describe physical systems at the thermodynamic limit.Comment: 46 pages, no figure; LaTeX2e, amssymb, latexsym; typos correcte

Survey of aircraft electrical power systems

Areas investigated include: (1) load analysis; (2) power distribution, conversion techniques and generation; (3) design criteria and performance capabilities of hydraulic and pneumatic systems; (4) system control and protection methods; (5) component and heat transfer systems cooling; and (6) electrical system reliability

Direct relation between the low-energy spin excitations and superconductivity of overdoped high-TcT_c superconductors

The dynamic spin susceptibility, $\chi''(\omega)$, has been measured over the energy range of $2 \leq \omega \leq 10$ meV for overdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$. Incommensurate (IC) spin excitations are observed at 8 K for all superconducting samples for $0.25 \leq x \leq 0.28$ with $\chi''$ peaking at $\sim 6$ meV. The IC peaks at 6 meV become smaller in intensity with increasing $x$ and, finally, become unobservable for a sample with $x=0.30$ which has no bulk superconductivity. The maximum $\chi''$ decreases linearly with $T_c$(onset) in the overdoped region, implying a direct cooperative relation between the spin fluctuations and the superconductivity.Comment: 4 pages, 4 figure