14,775 research outputs found
Variational formulas of higher order mean curvatures
In this paper, we establish the first variational formula and its
Euler-Lagrange equation for the total -th mean curvature functional
of a submanifold in a general Riemannian manifold
for . As an example, we prove that closed
complex submanifolds in complex projective spaces are critical points of the
functional , called relatively -minimal submanifolds,
for all . At last, we discuss the relations between relatively -minimal
submanifolds and austere submanifolds in real space forms, as well as a special
variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201
Site symmetry dependence of repulsive interactions between chemisorbed oxygen atoms on Pt{100}-(1×1)
[[abstract]]Ab initio total energy calculations using density functional theory with the generalized gradient
approximation have been performed for the chemisorption of oxygen atoms on a Pt$100%-~131!
slab. Binding energies for the adsorption of oxygen on different high-symmetry sites are presented.
The bridge site is the most stable at a coverage of 0.5 ML, followed by the fourfold hollow site. The
atop site is the least stable. This finding is rationalized by analyzing the ‘‘local structures’’ formed
upon oxygen chemisorption. The binding energies and heats of adsorption at different oxygen
coverages show that pairwise repulsive interactions are considerably stronger between oxygen
atoms occupying fourfold sites than those occupying bridge sites. Analysis of the partial charge
densities associated with Bloch states demonstrates that the O–Pt bond is considerably more
localized at the bridge site. These effects cause a sharp drop in the heats of adsorption for oxygen
on hollow sites when the coverage is increased from 0.25 to 0.5 ML. Mixing between oxygen p
orbitals and Pt d orbitals can be observed over the whole metal d-band energy range.[[notice]]補正完畢[[journaltype]]國內[[booktype]]紙
Graded reflection equation algebras and integrable Kondo impurities in the one-dimensional t-J model
Integrable Kondo impurities in two cases of the one-dimensional model
are studied by means of the boundary -graded quantum inverse
scattering method. The boundary matrices depending on the local magnetic
moments of the impurities are presented as nontrivial realizations of the
reflection equation algebras in an impurity Hilbert space. Furthermore, these
models are solved by using the algebraic Bethe ansatz method and the Bethe
ansatz equations are obtained.Comment: 14 pages, RevTe
Application of Instantons: Quenching of Macroscopic Quantum Coherence and Macroscopic Fermi-Particle Configurations
Starting from the coherent state representation of the evolution operator
with the help of the path-integral, we derive a formula for the low-lying
levels of a quantum spin
system. The quenching of macroscopic quantum coherence is understood as the
vanishing of in disagreement with the suppression of tunneling
(i.e. ) as claimed in the literature. A new
configuration called the macroscopic Fermi-particle is suggested by the
character of its wave function. The tunneling rate
() does not vanish, not for integer spin s nor for
a half-integer value of s, and is calculated explicitly (for the position
dependent mass) up to the one-loop approximation.Comment: 13 pages, LaTex, no figure
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Tuning magnetic anisotropy of epitaxial Ag/Fe/Fe0.5Co0.5/MgO(001) films
Single crystalline Ag/Fe/Fe0.5Co0.5/MgO(001) films were grown by Molecular Beam Epitaxy and investigated by Magneto-Optic Kerr Effect (MOKE). We find that even though the 4-fold magnetic anisotropies of Ag/Fe/MgO(001) and Ag/Fe0.5Co0.5/MgO(001) films are different from the corresponding bulk values, their opposite signs allow a fine tuning of the 4-fold magnetic anisotropy in Ag/Fe/Fe0.5Co0.5/MgO(001) films by varying the Fe and Fe0.5Co0.5 film thicknesses. In particular, the critical point of zero anisotropy can be achieved in a wide range of film thicknesses. Using Rotational MOKE, we determined and constructed the anisotropy phase diagram in the Fe and Fe0.5Co0.5 thickness plane from which the zero anisotropy exhibits a linear relation between the Fe and Fe0.5Co0.5 thickness
Approximating the partition function of the ferromagnetic Potts model
We provide evidence that it is computationally difficult to approximate the
partition function of the ferromagnetic q-state Potts model when q>2.
Specifically we show that the partition function is hard for the complexity
class #RHPi_1 under approximation-preserving reducibility. Thus, it is as hard
to approximate the partition function as it is to find approximate solutions to
a wide range of counting problems, including that of determining the number of
independent sets in a bipartite graph. Our proof exploits the first order phase
transition of the "random cluster" model, which is a probability distribution
on graphs that is closely related to the q-state Potts model.Comment: Minor correction
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