274 research outputs found
Interacting two helical edge modes in quantum spin Hall systems
We study theoretically the two interacting one-dimensional helical modes at
the edges of the quantum spin Hall systems. A new type of inter-edge correlated
liquid (IECL) without the spin gap is found. This liquid shows the diverging
density wave (DW) and superconductivity (SC) correlations much stronger than
those of the spinfull electrons. Possible experimental observations are also
discussed
Gate-controlled one-dimensional channel on the topological surface
We investigate the formation of the one-dimensional channels on the
topological surface under the gate electrode. The energy dispersion of these
channels is almost linear in the momentum with the velocity sensitively
depending on the strength of the gate voltage. The energy is also restricted to
be positive or negative depending on the strength of the gate voltage.
Consequently, the local density of states near the gated region has an
asymmetric structure with respect to zero energy. In the presence of the
electron-electron interaction, the correlation effect can be tuned by the gate
voltage. We also suggest a tunneling experiment to verify the presence of these
bound states.Comment: 5 pages, 4 figure
The Symplectic Penrose Kite
The purpose of this article is to view the Penrose kite from the perspective
of symplectic geometry.Comment: 24 pages, 7 figures, minor changes in last version, to appear in
Comm. Math. Phys
Chiral Quasicrystalline Order and Dodecahedral Geometry in Exceptional Families of Viruses
On the example of exceptional families of viruses we i) show the existence of
a completely new type of matter organization in nanoparticles, in which the
regions with a chiral pentagonal quasicrystalline order of protein positions
are arranged in a structure commensurate with the spherical topology and
dodecahedral geometry, ii) generalize the classical theory of quasicrystals
(QCs) to explain this organization, and iii) establish the relation between
local chiral QC order and nonzero curvature of the dodecahedral capsid faces.Comment: 8 pages, 3 figure
Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons
We present a unified approach for qualitative and quantitative analysis of
stability and instability dynamics of positive bright solitons in
multi-dimensional focusing nonlinear media with a potential (lattice), which
can be periodic, periodic with defects, quasiperiodic, single waveguide, etc.
We show that when the soliton is unstable, the type of instability dynamic that
develops depends on which of two stability conditions is violated.
Specifically, violation of the slope condition leads to an amplitude
instability, whereas violation of the spectral condition leads to a drift
instability. We also present a quantitative approach that allows to predict the
stability and instability strength
Weak local rules for planar octagonal tilings
We provide an effective characterization of the planar octagonal tilings
which admit weak local rules. As a corollary, we show that they are all based
on quadratic irrationalities, as conjectured by Thang Le in the 90s.Comment: 23 pages, 6 figure
Diffusive limits on the Penrose tiling
In this paper random walks on the Penrose lattice are investigated. Heat
kernel estimates and the invariance principle are shown
Symmetry of Magnetically Ordered Quasicrystals
The notion of magnetic symmetry is reexamined in light of the recent
observation of long range magnetic order in icosahedral quasicrystals [Charrier
et al., Phys. Rev. Lett. 78, 4637 (1997)]. The relation between the symmetry of
a magnetically-ordered (periodic or quasiperiodic) crystal, given in terms of a
``spin space group,'' and its neutron diffraction diagram is established. In
doing so, an outline of a symmetry classification scheme for magnetically
ordered quasiperiodic crystals is provided. Predictions are given for the
expected diffraction patterns of magnetically ordered icosahedral crystals,
provided their symmetry is well described by icosahedral spin space groups.Comment: 5 pages. Accepted for publication in Phys. Rev. Letter
Going beyond defining: Preschool educators\u27 use of knowledge in their pedagogical reasoning about vocabulary instruction
Previous research investigating both the knowledge of early childhood educators and the support for vocabulary development present in early childhood settings has indicated that both educator knowledge and enacted practice are less than optimal, which has grave implications for children\u27s early vocabulary learning and later reading achievement. Further, the nature of the relationship between educators\u27 knowledge and practice is unclear, making it difficult to discern the best path towards improved knowledge, practice, and children\u27s vocabulary outcomes. The purpose of the present study was to add to the existing literature by using stimulated recall interviews and a grounded approach to examine how 10 preschool educators used their knowledge to made decisions about their moment-to-moment instruction in support of children\u27s vocabulary development. Results indicate that educators were thinking in highly context-specific ways about their goals and strategies for supporting vocabulary learning, taking into account important knowledge of their instructional history with children and of the children themselves to inform their decision making in the moment. In addition, they reported thinking about research-based goals and strategies for supporting vocabulary learning that went beyond simply defining words for children. Implications for research and professional development are discussed
Tiling groupoids and Bratteli diagrams
Let T be an aperiodic and repetitive tiling of R^d with finite local
complexity. Let O be its tiling space with canonical transversal X. The tiling
equivalence relation R_X is the set of pairs of tilings in X which are
translates of each others, with a certain (etale) topology. In this paper R_X
is reconstructed as a generalized "tail equivalence" on a Bratteli diagram,
with its standard AF-relation as a subequivalence relation.
Using a generalization of the Anderson-Putnam complex, O is identified with
the inverse limit of a sequence of finite CW-complexes. A Bratteli diagram B is
built from this sequence, and its set of infinite paths dB is homeomorphic to
X. The diagram B is endowed with a horizontal structure: additional edges that
encode the adjacencies of patches in T. This allows to define an etale
equivalence relation R_B on dB which is homeomorphic to R_X, and contains the
AF-relation of "tail equivalence".Comment: 34 pages, 4 figure
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