8,705 research outputs found
New gap theorem on complete Riemannian manifolds
In this short note, we find a new gap phenomena on Riemannian manifolds,
which says that for any complete noncompact Riemannian manifold with
nonnegative Ricci curvature, if the scalar curvature decays faster than
quadratically, then it is Ricci flat.Comment: This paper has been withdrawn by the author due to some crucial
error
A double inequality for bounding Toader mean by the centroidal mean
In the paper, the authors find the best numbers and such
that for all with , where
and
denote respectively the centroidal mean and Toader mean of two positive numbers
and .Comment: 5 page
Exact holographic mapping in free fermion systems
In this paper, we shall perform a detailed analysis of the Exact Holographic
Mapping first introduced in arXiv:1309.6282, which was proposed as an explicit
example of holographic duality between quantum many-body systems and
gravitational theories. We obtain analytic results for free-fermion systems
that not only confirm previous numerical results, but also elucidate the exact
relationships between the various physical properties of the bulk and boundary
systems. Our analytic results allow us to study the asymptotic properties that
are difficult to probe numerically, such as the near horizon regime of the
black hole geometry. We shall also explore a few interesting but hitherto
unexplored bulk geometries, such as that corresponding to a boundary critical
fermion with nontrivial dynamic critical exponent. Our analytic framework also
allows us to study the holographic mapping of some of these boundary theories
in dimensions 2+1 or higher.Comment: 32 pages, 7 figure
On the M-eigenvalues of elasticity tensor and the strong ellipticity condition
Strong ellipticity is an important property in the elasticity theory. In
2009, M-eigenvalues were introduced for the elasticity tensor. It was shown
that M-eigenvalues are invariant under coordinate system choices, and the
strong ellipticity condition holds if and only if all the M-eigenvalues of the
elasticity tensor are positive. Thus, M-eigenvalues are some intrinsic
parameters of the elasticity tensor. In this paper, we show that the
M-eigenvalues of the elasticity tensor are closely related with some elastic
moduli, such as the bulk modulus, the shear modulus, Lam\'e's first parameter,
the P-wave modulus, etc, and the positiveness of the M-eigenvalues are
corresponding to some existing conditions for strong ellipticity in some
special cases, such as the isotropic case, the cubic case, the polar
anisotropic case and the tetragonal case. We also present new sufficient
conditions for the strong ellipticity of the orthotropic case. These, in a
certain sense, further reveal the physical meanings of M-eigenvalues
Lattice construction of pseudopotential Hamiltonians for Fractional Chern Insulators
Fractional Chern insulators are new realizations of fractional quantum Hall
states in lattice systems without orbital magnetic field. These states can be
mapped onto conventional fractional quantum Hall states through the Wannier
state representation (Phys. Rev. Lett. 107, 126803 (2011)). In this paper, we
use the Wannier state representation to construct the pseudopotential
Hamiltonians for fractional Chern insulators, which are interaction
Hamiltonians with certain ideal model wavefunctions as exact ground states. We
show that these pseudopotential Hamiltonians can be approximated by
short-ranged interactions in fractional Chern insulators, and that their range
will be minimized by an optimal gauge choice for the Wannier states. As
illustrative examples, we explicitly write down the form of the lowest
pseudopotential for several fractional Chern insulator models including the
lattice Dirac model and the checkerboard model with Chern number 1, and the
d-wave model and the triangular lattice model with Chern number 2. The proposed
pseudopotential Hamiltonians have the 1/3 Laughlin state as their groundstate
when the Chern number C=1, and a topological nematic (330) state as their
groundstate when C=2. Also included are the results of an interpolation between
the d-wave model and two decoupled layers of lattice Dirac models, which
explicitly demonstrate the relation between C=2 fractional Chern insulators and
bilayer fractional quantum Hall states. The proposed states can be verified by
future numerical works, and in particular provide a model Hamiltonian for the
topological nematic states that have not been realized numerically.Comment: 16 pages, 9 figure
Uncovering the community structure associated with the diffusion dynamics of networks
As two main focuses of the study of complex networks, the community structure
and the dynamics on networks have both attracted much attention in various
scientific fields. However, it is still an open question how the community
structure is associated with the dynamics on complex networks. In this paper,
through investigating the diffusion process taking place on networks, we
demonstrate that the intrinsic community structure of networks can be revealed
by the stable local equilibrium states of the diffusion process. Furthermore,
we show that such community structure can be directly identified through the
optimization of the conductance of network, which measures how easily the
diffusion occurs among different communities. Tests on benchmark networks
indicate that the conductance optimization method significantly outperforms the
modularity optimization methods at identifying the community structure of
networks. Applications on real world networks also demonstrate the
effectiveness of the conductance optimization method. This work provides
insights into the multiple topological scales of complex networks, and the
obtained community structure can naturally reflect the diffusion capability of
the underlying network.Comment: 10 pages, 5 figure
Breather-to-soliton and rogue wave-to-soliton transitions in a resonant erbium-doped fiber system with higher-order effects
Under investigation in this paper is the higherorder nonlinear Schrodinger
and Maxwell-Bloch (HNLSMB) system which describes the wave propagation in an
erbium-doped nonlinear fiber with higher-order effects including the
fourth-order dispersion and quintic nonKerr nonlinearity. The breather and
rogue wave (RW) solutions are shown that they can be converted into various
soliton solutions including the multipeak soliton, periodic wave, antidark
soliton, M-shaped soliton, and W-shaped soliton. In addition, under different
values of higher-order effect, the locus of the eigenvalues on the complex
plane which converts breathers or RWs into solitons is calculated
Quantum Anomalous Hall Effect in a Perovskite and Inverse-Perovskite Sandwich Structure
Based on first-principles calculations, we propose a sandwich structure
composed of a G-type anti-ferromagnetic (AFM) Mott insulator LaCrO grown
along the [001] direction with one atomic layer replaced by an
inverse-perovskite material SrPbO. We show that the system is in a
topologically nontrivial phase characterized by simultaneous nonzero charge and
spin Chern numbers, which can support a spin-polarized and dissipationless edge
current in a finite system. Since these two materials are stable in bulk and
match each other with only small lattice distortions, the composite material is
expected easy to synthesize.Comment: 4 pages, 4 figure
Electrically Tunable Topological State in [111] Perovskite Materials with Antiferromagnetic Exchange Field
A topological state with simultaneous nonzero Chern number and spin Chern
number is possible for electrons on honeycomb lattice based on band engineering
by staggered electric potential and antiferromagnetic exchange field in
presence of intrinsic spin-orbit coupling. With first principles calculation we
confirm that the scheme can be realized by material modification in perovskite
G-type antiferromagnetic insulators grown along [111] direction, where d
electrons hop on a single buckled honeycomb lattice. This material is ideal for
spintronics applications, since it provides a spin-polarized quantized edge
current, robust to both nonmagnetic and magnetic defects, with the spin
polarization tunable by inverting electric field.Comment: 5 pages, 5 figure
Resonance interaction of two dipoles in optically active surroundings
We study the resonance interaction between two quantum electric dipoles
immersed in optically active surroundings. Quantum electrodynamics is employed
to deal with dipole-vacuum interaction. Our results show that the optical
activity of surroundings will not change the single atom behaviors while it can
change the collective behaviors of the two dipoles, as well as greatly affect
the dipole-dipole resonance interaction. Especially, if the orientations of two
dipoles are orthogonal and respectively perpendicular to the interdipole axis,
the interdipole resonance interaction can be established with the help of
optically active surroundings while there is no resonance interaction in
vacuum.Comment: 13 pages, 3 figure
- …