Classification of one-dimensional quasilattices into mutual local-derivability classes

One-dimensional quasilattices are classified into mutual local-derivability (MLD) classes on the basis of geometrical and number-theoretical considerations. Most quasilattices are ternary, and there exist an infinite number of MLD classes. Every MLD class has a finite number of quasilattices with inflation symmetries. We can choose one of them as the representative of the MLD class, and other members are given as decorations of the representative. Several MLD classes of particular importance are listed. The symmetry-preserving decorations rules are investigated extensively.Comment: 42 pages, latex, 5 eps figures, Published in JPS

Universalities in One-electron Properties of Limit Quasi-periodic Lattices

We investigate one-electron properties of one-dimensional self-similar structures called limit quasi-periodic lattices. The trace map of such a lattice is nonconservative in contrast to the quasi-periodic case, and we can determine the structure of its attractor. It allows us to obtain the three new features of the present system: 1) The multi-fractal characters of the energy spectra are {\it universal}. 2) The supports of the $f(\alpha)$-spectra extend over the whole unit interval, $[0, 1]$. 3) There exist marginal critical states.Comment: 4 pages, 2figure

Sound modes broadening for Fibonacci one dimensional quasicrystals

We investigate vibrational excitation broadening in one dimensional Fibonacci model of quasicrystals (QCs). The chain is constructed from particles with two masses following the Fibonacci inflation rule. The eigenmode spectrum depends crucially on the mass ratio. We calculate the eigenstates and eigenfunctions. All calculations performed self-consistently within the regular expansion over the three wave coupling constant. The approach can be extended to three dimensional systems. We find that in the intermediate range of mode coupling constants, three-wave broadening for the both types of systems (1D Fibonacci and 3D QCs) depends universally on frequency. Our general qualitative conclusion is that for a system with a non-simple elementary cell phonon spectrum broadening is always larger than for a system with a primitive cell (provided all other characteristics are the same).Comment: 2o pages, 15 figure

Binary self-similar one-dimensional quasilattices: Mutual local-derivability classification and substitution rules

Self-similar binary one-dimensional (1D) quasilattices (QLs) are classified into mutual local-derivability (MLD) classes. It is shown that the MLD classification is closely related to the number-theoretical classification of parameters which specify the self-similar binary 1D QLs. An algorithm to derive an explicit substitution rule, which prescribes the transformation of a QL into another QL in the same MLD class, is presented. An explicit inflation rule, which prescribes the transformation of the self-similar 1D QL into itself, is obtained as a composition of the explicit substitution rules. Symmetric substitution rules and symmetric inflation rules are extensively discussed.Comment: 24 pages, 4 figures, submitted to PR

Measurement of Single and Double Spin-Flip Probabilities in Inelastic Deuteron Scattering on 12C at 270 MeV

The deuteron single and double spin-flip probabilities, S1 and S2, have been measured for the 12C(pol{d},pol{d}') reaction at Ed = 270 MeV for an excitation energy range between 4 and 24 MeV and a scattering angular range between Theta_lab = 2.5 and 7.5 deg. The extracted S1 exhibits characteristic values depending on the structure of the excited state. The S2 is close to zero over the measured excitation energy range. The SFP angular distribution data for the 2+ (4.44 MeV) and 1+ (12.71 MeV) states are well described by the microscopic DWIA calculations

Equipments for Neutron Induced Experiments by Using a Monoenergetic Neutron Beam

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Continuum elastic sphere vibrations as a model for low-lying optical modes in icosahedral quasicrystals

The nearly dispersionless, so-called "optical" vibrational modes observed by inelastic neutron scattering from icosahedral Al-Pd-Mn and Zn-Mg-Y quasicrystals are found to correspond well to modes of a continuum elastic sphere that has the same diameter as the corresponding icosahedral basic units of the quasicrystal. When the sphere is considered as free, most of the experimentally found modes can be accounted for, in both systems. Taking into account the mechanical connection between the clusters and the remainder of the quasicrystal allows a complete assignment of all optical modes in the case of Al-Pd-Mn. This approach provides support to the relevance of clusters in the vibrational properties of quasicrystals.Comment: 9 pages without figure

Observation of Quenching in Gamow-Teller Strength in the (p,n) Reaction on sd-Shell Nuclei

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Two-dimensional XY spin/gauge glasses on periodic and quasiperiodic lattices

Via Monte Carlo studies of the frustrated XY or classical planar model we demonstrate the possibility of a finite (nonzero) temperature spin/gauge glass phase in two dimensions. Examples of both periodic and quasiperiodic two dimensional lattices, where a high temperature paramagnetic phase changes to a spin/gauge glass phase with the lowering of temperature, are presented. The existence of the spin/gauge glass phase is substantiated by our study of the temperature dependence of the Edwards-Anderson order parameter, spin glass susceptibility, linear susceptibility and the specific heat. Finite size scaling analysis of spin glass susceptibility and order parameter yields a nonzero critical temperature and exponents that are in close agreement with those obtained by Bhatt and Young in their random ${\pm J}$ Ising model study on a square lattice. These results suggest that certain periodic and quasiperiodic two-dimensional arrays of superconducting grains in suitably chosen transverse magnetic fields should behave as superconducting glasses at low temperatures.Comment: RevTex, 25 pages. 11 epsf figures available upon request ([email protected] or [email protected]). Submitted to Phys. Rev.