10,451 research outputs found
Ad-nilpotent ideals and The Shi arrangement
We extend the Shi bijection from the Borel subalgebra case to parabolic
subalgebras. In the process, the -deleted Shi arrangement
naturally emerges. This arrangement interpolates between the Coxeter
arrangement and the Shi arrangement , and breaks
the symmetry of in a certain symmetrical way. Among other
things, we determine the characteristic polynomial
of explicitly for and . More generally, let
be an arbitrary arrangement between and
. Armstrong and Rhoades recently gave a formula for
for . Inspired by their result, we obtain
formulae for for , and .Comment: The third version, quasi-antichains are shown to be in bijection with
elements of L(Cox). arXiv admin note: text overlap with arXiv:1009.1655 by
other author
Implementation of quantum algorithms with resonant interactions
We propose a scheme for implementing quantum algorithms with resonant
interactions. Our scheme only requires resonant interactions between two atoms
and a cavity mode, which is simple and feasible. Moreover, the implementation
would be an important step towards the fabrication of quantum computers in
cavity QED system.Comment: 4 pages, 3 figure
First-principles calculations of phase transition, elasticity, and thermodynamic properties for TiZr alloy
tructural transformation, pressure dependent elasticity behaviors, phonon,
and thermodynamic properties of the equiatomic TiZr alloy are investigated by
using first-principles density-functional theory. Our calculated lattice
parameters and equation of state for and phases as well as
the phase transition sequence of
are
consistent well with experiments. Elastic constants of and
phases indicate that they are mechanically stable. For cubic phase,
however, it is mechanically unstable at zero pressure and the critical pressure
for its mechanical stability is predicted to equal to 2.19 GPa. We find that
the moduli, elastic sound velocities, and Debye temperature all increase with
pressure for three phases of TiZr alloy. The relatively large values
illustrate that the TiZr alloy is rather ductile and its ductility is more
predominant than that of element Zr, especially in phase. Elastic wave
velocities and Debye temperature have abrupt increase behaviors upon the
transition at around 10 GPa and exhibit
abrupt decrease feature upon the
transition at higher pressure. Through Mulliken population analysis, we
illustrate that the increase of the \emph{d}-band occupancy will stabilize the
cubic phase. Phonon dispersions for three phases of TiZr alloy are
firstly presented and the phase phonons clearly indicate its
dynamically unstable nature under ambient condition. Thermodynamics of Gibbs
free energy, entropy, and heat capacity are obtained by quasiharmonic
approximation and Debye model.Comment: 9 pages, 10 figure
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