Quasiperiodic Modulated-Spring Model

We study the classical vibration problem of a chain with spring constants which are modulated in a quasiperiodic manner, {\it i. e.}, a model in which the elastic energy is $\sum_j k_j( u_{j-1}-{u_j})^2$, where $k_j=1+\Delta cos[2\pi\sigma(j-1/2)+\theta]$ and $\sigma$ is an irrational number. For $\Delta < 1$, it is shown analytically that the spectrum is absolutely continuous, {\it i.e.}, all the eigen modes are extended. For $\Delta=1$, numerical scaling analysis shows that the spectrum is purely singular continuous, {\it i.e.}, all the modes are critical.Comment: REV TeX fil

Quantum Group, Bethe Ansatz and Bloch Electrons in a Magnetic Field

The wave functions for two dimensional Bloch electrons in a uniform magnetic field at the mid-band points are studied with the help of the algebraic structure of the quantum group $U_q(sl_2)$. A linear combination of its generators gives the Hamiltonian. We obtain analytical and numerical solutions for the wave functions by solving the Bethe Ansatz equations, proposed by Wiegmann and Zabrodin on the basis of above observation. The semi-classical case with the flux per plaquette $\phi=1/Q$ is analyzed in detail, by exploring a structure of the Bethe Ansatz equations. We also reveal the multifractal structure of the Bethe Ansatz solutions and corresponding wave functions when $\phi$ is irrational, such as the golden or silver mean.Comment: 30 pages, 11 GIF figures(use xv, or WWW browser

Disordered Critical Wave functions in Random Bond Models in Two Dimensions -- Random Lattice Fermions at E=0E=0 without Doubling

Random bond Hamiltonians of the $\pi$ flux state on the square lattice are investigated. It has a special symmetry and all states are paired except the ones with zero energy. Because of this, there are always zero-modes. The states near $E=0$ are described by massless Dirac fermions. For the zero-mode, we can construct a random lattice fermion without a doubling and quite large systems ( up to $801 \times 801$) are treated numerically. We clearly demonstrate that the zero-mode is given by a critical wave function. Its multifractal behavior is also compared with the effective field theory.Comment: 4 pages, 2 postscript figure

Conductivity of 2D lattice electrons in an incommensurate magnetic field

We consider conductivities of two-dimensional lattice electrons in a magnetic field. We focus on systems where the flux per plaquette $\phi$ is irrational (incommensurate flux). To realize the system with the incommensurate flux, we consider a series of systems with commensurate fluxes which converge to the irrational value. We have calculated a real part of the longitudinal conductivity $\sigma_{xx}(\omega)$. Using a scaling analysis, we have found $\Re\sigma_{xx}(\omega)$ behaves as $1/\omega ^{\gamma}$ \,$(\gamma =0.55)$ when $\phi =\tau,(\tau =\frac{\sqrt{5}-1}{2})$ and the Fermi energy is near zero. This behavior is closely related to the known scaling behavior of the spectrum.Comment: 16 pages, postscript files are available on reques

Bethe ansatz for the Harper equation: Solution for a small commensurability parameter

The Harper equation describes an electron on a 2D lattice in magnetic field and a particle on a 1D lattice in a periodic potential, in general, incommensurate with the lattice potential. We find the distribution of the roots of Bethe ansatz equations associated with the Harper equation in the limit as alpha=1/Q tends to 0, where alpha is the commensurability parameter (Q is integer). Using the knowledge of this distribution we calculate the higher and lower boundaries of the spectrum of the Harper equation for small alpha. The result is in agreement with the semiclassical argument, which can be used for small alpha.Comment: 17 pages including 5 postscript figures, Latex, minor changes, to appear in Phys.Rev.

A compact proton synchrotron with combined-function lattice dedicated for cancer therapy

A compact proton synchrotron with combined function lattice has been designed as a dedicated machine for cancer therapy because of its merits of easy operation and low construction cost. The lattice has a six-fold symmetry and its radius of curvature and circumference are 1.9 m and 23.9 m, respectively. For the purpose of establishing a good reference design, we have constructed a model magnet based on the three-dimensional magnetic field calculation. A magnetic field measurement has been performed with use of a three-dimensional Hall- probe. In the present paper, the results of these developments is presented together with the outline of the reference design. (3 refs)

Cantor Spectra for Double Exchange Model

We numerically study energy spectra and localization properties of the double exchange model at irrational filling factor. To obtain variational ground state, we use a mumerical technique in momentum space by ``embedded'' boundary condition which has no finite size effect a priori. Although the Hamiltonian has translation invariance, the ground state spontaneously exhibits a self-similarity. Scaling and multi-fractal analysis for the wave functions are performed and the scaling indices $\alpha$'s are obtained. The energy spectrum is found to be a singular continuous, so-called the Cantor set with zero Lebesque measure.Comment: 4 pages, 4 figures, revtex, corrected some typos, accepted for publication in PR