4,173 research outputs found
Electronic structure near an impurity and terrace on the surface of a 3-dimensional topological insulator
Motivated by recent scanning tunneling microscopy experiments on surfaces of
BiSb\cite{yazdanistm,gomesstm} and
BiTe,\cite{kaptunikstm,xuestm} we theoretically study the electronic
structure of a 3-dimensional (3D) topological insulator in the presence of a
local impurity or a domain wall on its surface using a 3D lattice model. While
the local density of states (LDOS) oscillates significantly in space at
energies above the bulk gap, the oscillation due to the in-gap surface Dirac
fermions are very weak. The extracted modulation wave number as a function of
energy satisfies the Dirac dispersion for in-gap energies and follows the
border of the bulk continuum above the bulk gap. We have also examined
analytically the effects of the defects by using a pure Dirac fermion model for
the surface states and found that the LDOS decays asymptotically faster at
least by a factor of 1/r than that in normal metals, consistent with the
results obtained from our lattice model.Comment: 7 pages, 5 figure
On the Derivative Imbalance and Ambiguity of Functions
In 2007, Carlet and Ding introduced two parameters, denoted by and
, quantifying respectively the balancedness of general functions
between finite Abelian groups and the (global) balancedness of their
derivatives , (providing an
indicator of the nonlinearity of the functions). These authors studied the
properties and cryptographic significance of these two measures. They provided
for S-boxes inequalities relating the nonlinearity to ,
and obtained in particular an upper bound on the nonlinearity which unifies
Sidelnikov-Chabaud-Vaudenay's bound and the covering radius bound. At the
Workshop WCC 2009 and in its postproceedings in 2011, a further study of these
parameters was made; in particular, the first parameter was applied to the
functions where is affine, providing more nonlinearity parameters.
In 2010, motivated by the study of Costas arrays, two parameters called
ambiguity and deficiency were introduced by Panario \emph{et al.} for
permutations over finite Abelian groups to measure the injectivity and
surjectivity of the derivatives respectively. These authors also studied some
fundamental properties and cryptographic significance of these two measures.
Further studies followed without that the second pair of parameters be compared
to the first one.
In the present paper, we observe that ambiguity is the same parameter as
, up to additive and multiplicative constants (i.e. up to rescaling). We
make the necessary work of comparison and unification of the results on ,
respectively on ambiguity, which have been obtained in the five papers devoted
to these parameters. We generalize some known results to any Abelian groups and
we more importantly derive many new results on these parameters
Dynamics of Order Parameter in Photoexcited Peierls Chain
The photoexcited dynamics of order parameter in Peierls chain is investigated
by using a microscopic quantum theory in the limit where the hot electrons may
establish themselves into a quasi-equilibrium state described by an effective
temperature. The optical phonon mode responsible for the Peierls instability is
coupled to the electron subsystem, and its dynamic equation is derived in terms
of the density matrix technique. Recovery dynamics of the order parameter is
obtained, which reveals a number of interesting features including the change
of oscillation frequency and amplitude at phase transition temperature and the
photo-induced switching of order parameter.Comment: 5 pages, 3 figure
A Recursive Construction of Permutation Polynomials over with Odd Characteristic from R\'{e}dei Functions
In this paper, we construct two classes of permutation polynomials over
with odd characteristic from rational R\'{e}dei functions. A
complete characterization of their compositional inverses is also given. These
permutation polynomials can be generated recursively. As a consequence, we can
generate recursively permutation polynomials with arbitrary number of terms.
More importantly, the conditions of these polynomials being permutations are
very easy to characterize. For wide applications in practice, several classes
of permutation binomials and trinomials are given. With the help of a computer,
we find that the number of permutation polynomials of these types is very
large
Lifshitz spacetimes, solitons, and generalized BTZ black holes in quantum gravity at a Lifshitz point
In this paper, we study static vacuum solutions of quantum gravity at a fixed
Lifshitz point in (2+1) dimensions, and present all the diagonal solutions in
closed forms in the infrared limit. The exact solutions represent spacetimes
with very rich structures: they can represent generalized BTZ black holes,
Lifshitz space-times or Lifshitz solitons, in which the spacetimes are free of
any kind of space-time singularities, depending on the choices of the free
parameters of the solutions. We also find several classes of exact static
non-diagonal solutions, which represent similar space-time structures as those
given in the diagonal case. The relevance of these solutions to the
non-relativistic Lifshitz-type gauge/gravity duality is discussed.Comment: revtex4, 5 figures. Typos are correcte
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