Anomalous thermal conductivity and local temperature distribution on harmonic Fibonacci chains

The harmonic Fibonacci chain, which is one of a quasiperiodic chain constructed with a recursion relation, has a singular continuous frequency-spectrum and critical eigenstates. The validity of the Fourier law is examined for the harmonic Fibonacci chain with stochastic heat baths at both ends by investigating the system size N dependence of the heat current J and the local temperature distribution. It is shown that J asymptotically behaves as (ln N)^{-1} and the local temperature strongly oscillates along the chain. These results indicate that the Fourier law does not hold on the harmonic Fibonacci chain. Furthermore the local temperature exhibits two different distribution according to the generation of the Fibonacci chain, i.e., the local temperature distribution does not have a definite form in the thermodynamic limit. The relations between N-dependence of J and the frequency-spectrum, and between the local temperature and critical eigenstates are discussed.Comment: 10 pages, 4 figures, submitted to J. Phys.: Cond. Ma

Influence of Homeotropic Anchoring Walls upon Nematic and Smectic Phases

McMillan liquid crystal model sandwiched between strong homeotropic anchoring walls is studied. Phase transitions between isotropic, nematic, and smectic A phases are investigated for wide ranges of an interaction parameter and of the system thickness. It is confirmed that the anchoring walls induce an increase in transition temperatures, dissappearance of phase transitions, and an appearance of non-spontaneous nematic phase. The similarity between influence of anchoring walls and that of external fields is discussed.Comment: 5 pages, 6 figure

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