13 research outputs found
Electronic properties of ternary quasicrystals in one dimension
The one-electron properties of a certain class of one-dimensional ternary
quasicrystals are investigated. In particular, we show in detail the presence
of a special kind of critical states called marginal critical states in these
QCs. By the use of a real-space renormalization-group method, it is shown that
the scaling properties of marginal critical states are characterized by
stretched exponentials. These states are virtually localized, so that their
presence may make a QC less conductive.Comment: 19 pages, 9 figures, 2 tables, uses REVTeX. (V3) Title, abstract, and
introduction have been modified. To appear in Phys. Rev.
Coherent State Path Integral for Bloch Particle
We construct a coherent state path integral formalism for the one-dimensional
Bloch particle within the single band model. The transition amplitude between
two coherent states is a sum of transition amplitudes with different winding
numbers on the two-dimensional phase space which has the same topology as that
of the cylinder. Appearance of the winding number is due to the periodicity of
the quasi-momentum of the Bloch particle. Our formalism is successfully applied
to a semiclassical motion of the Bloch particle under a uniform electric field.
The wave packet exhibits not only the Bloch oscillation but also a similar
breathing to the one for the squeezed state of a harmonic oscillator.Comment: 10 pages, Revtev
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 -spectra extend
over the whole unit interval, . 3) There exist marginal critical
states.Comment: 4 pages, 2figure