104 research outputs found
Electronic band gaps and transport in aperiodic graphene superlattices of Thue-Morse sequence
We have studied the electronic properties in aperiodic graphene superlattices
of Thue-Morse sequence. Although the structure is aperiodic, an unusual Dirac
point (DP) does exist and its location is exactly at the position of the
zero-averaged wave number (zero-. Furthermore, the zero- gap
associated with the DP is robust against the lattice constants and the incident
angles, and multi-DPs can appear under the suitable conditions. A resultant
controllability of electron transport in Thue-Morse sequence is predicted,
which may facilitate the development of many graphene-based electronics.Comment: Accepted for publication in Applied Physics Letters; 4 pagese, 5
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The singular continuous diffraction measure of the Thue-Morse chain
The paradigm for singular continuous spectra in symbolic dynamics and in
mathematical diffraction is provided by the Thue-Morse chain, in its
realisation as a binary sequence with values in . We revisit this
example and derive a functional equation together with an explicit form of the
corresponding singular continuous diffraction measure, which is related to the
known representation as a Riesz product.Comment: 6 pages, 1 figure; revised and improved versio
Aperiodic Ising model on the Bethe lattice: Exact results
We consider the Ising model on the Bethe lattice with aperiodic modulation of
the couplings, which has been studied numerically in Phys. Rev. E 77, 041113
(2008). Here we present a relevance-irrelevance criterion and solve the
critical behavior exactly for marginal aperiodic sequences. We present
analytical formulae for the continuously varying critical exponents and discuss
a relationship with the (surface) critical behavior of the aperiodic quantum
Ising chain.Comment: 7 pages, 3 figures, minor correction
Critical properties of an aperiodic model for interacting polymers
We investigate the effects of aperiodic interactions on the critical behavior
of an interacting two-polymer model on hierarchical lattices (equivalent to the
Migadal-Kadanoff approximation for the model on Bravais lattices), via
renormalization-group and tranfer-matrix calculations. The exact
renormalization-group recursion relations always present a symmetric fixed
point, associated with the critical behavior of the underlying uniform model.
If the aperiodic interactions, defined by s ubstitution rules, lead to relevant
geometric fluctuations, this fixed point becomes fully unstable, giving rise to
novel attractors of different nature. We present an explicit example in which
this new attractor is a two-cycle, with critical indices different from the
uniform model. In case of the four-letter Rudin-Shapiro substitution rule, we
find a surprising closed curve whose points are attractors of period two,
associated with a marginal operator. Nevertheless, a scaling analysis indicates
that this attractor may lead to a new critical universality class. In order to
provide an independent confirmation of the scaling results, we turn to a direct
thermodynamic calculation of the specific-heat exponent. The thermodynamic free
energy is obtained from a transfer matrix formalism, which had been previously
introduced for spin systems, and is now extended to the two-polymer model with
aperiodic interactions.Comment: 19 pages, 6 eps figures, to appear in J. Phys A: Math. Ge
Log-periodic corrections to scaling: exact results for aperiodic Ising quantum chains
Log-periodic amplitudes of the surface magnetization are calculated
analytically for two Ising quantum chains with aperiodic modulations of the
couplings. The oscillating behaviour is linked to the discrete scale invariance
of the perturbations. For the Fredholm sequence, the aperiodic modulation is
marginal and the amplitudes are obtained as functions of the deviation from the
critical point. For the other sequence, the perturbation is relevant and the
critical surface magnetization is studied.Comment: 12 pages, TeX file, epsf, iopppt.tex, xref.tex which are joined. 4
postcript figure
Repetitions in beta-integers
Classical crystals are solid materials containing arbitrarily long periodic
repetitions of a single motif. In this paper, we study the maximal possible
repetition of the same motif occurring in beta-integers -- one dimensional
models of quasicrystals. We are interested in beta-integers realizing only a
finite number of distinct distances between neighboring elements. In such a
case, the problem may be reformulated in terms of combinatorics on words as a
study of the index of infinite words coding beta-integers. We will solve a
particular case for beta being a quadratic non-simple Parry number.Comment: 11 page
Symbolic approach and induction in the Heisenberg group
We associate a homomorphism in the Heisenberg group to each hyperbolic
unimodular automorphism of the free group on two generators. We show that the
first return-time of some flows in "good" sections, are conjugate to
niltranslations, which have the property of being self-induced.Comment: 18 page
Pure point diffraction and cut and project schemes for measures: The smooth case
We present cut and project formalism based on measures and continuous weight
functions of sufficiently fast decay. The emerging measures are strongly almost
periodic. The corresponding dynamical systems are compact groups and
homomorphic images of the underlying torus. In particular, they are strictly
ergodic with pure point spectrum and continuous eigenfunctions. Their
diffraction can be calculated explicitly. Our results cover and extend
corresponding earlier results on dense Dirac combs and continuous weight
functions with compact support. They also mark a clear difference in terms of
factor maps between the case of continuous and non-continuous weight functions.Comment: 30 page
Anisotropic Scaling in Layered Aperiodic Ising Systems
The influence of a layered aperiodic modulation of the couplings on the
critical behaviour of the two-dimensional Ising model is studied in the case of
marginal perturbations. The aperiodicity is found to induce anisotropic
scaling. The anisotropy exponent z, given by the sum of the surface
magnetization scaling dimensions, depends continuously on the modulation
amplitude. Thus these systems are scale invariant but not conformally invariant
at the critical point.Comment: 7 pages, 2 eps-figures, Plain TeX and epsf, minor correction
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