2,171 research outputs found
Einstein Manifolds As Yang-Mills Instantons
It is well-known that Einstein gravity can be formulated as a gauge theory of
Lorentz group where spin connections play a role of gauge fields and Riemann
curvature tensors correspond to their field strengths. One can then pose an
interesting question: What is the Einstein equations from the gauge theory
point of view? Or equivalently, what is the gauge theory object corresponding
to Einstein manifolds? We show that the Einstein equations in four dimensions
are precisely self-duality equations in Yang-Mills gauge theory and so Einstein
manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R
gauge theory. Specifically, we prove that any Einstein manifold with or without
a cosmological constant always arises as the sum of SU(2)_L instantons and
SU(2)_R anti-instantons. This result explains why an Einstein manifold must be
stable because two kinds of instantons belong to different gauge groups,
instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay
into a vacuum. We further illuminate the stability of Einstein manifolds by
showing that they carry nontrivial topological invariants.Comment: v4; 17 pages, published version in Mod. Phys. Lett.
Nonchaotic Nonlinear Motion Visualized in Complex Nanostructures by Stereographic 4D Electron Microscopy
Direct electron imaging with sufficient time resolution is a powerful tool for visualizing the three-dimensional (3D) mechanical motion and resolving the four-dimensional (4D) trajectories of many different components of a nanomachine, e.g., a NEMS device. Here, we report a nanoscale nonchaotic motion of a nano- and microstructured NiTi shape memory alloy in 4D electron microscopy. A huge amplitude oscillatory mechanical motion following laser heating is observed repetitively, likened to a 3D motion of a conductor’s baton. By time-resolved 4D stereographic reconstruction of the motion, prominent vibrational frequencies (3.0, 3.8, 6.8, and 14.5 MHz) are fully characterized, showing evidence of nonlinear behavior. Moreover, it is found that a stress (fluence)−strain (displacement) profile shows nonlinear elasticity. The observed resonances of the nanostructure are reminiscent of classical molecular quasi-periodic behavior, but here both the amplitude and frequency of the motion are visualized using ultrafast electron microscopy
Application of Artificial Neural Network to Search for Gravitational-Wave Signals Associated with Short Gamma-Ray Bursts
We apply a machine learning algorithm, the artificial neural network, to the
search for gravitational-wave signals associated with short gamma-ray bursts.
The multi-dimensional samples consisting of data corresponding to the
statistical and physical quantities from the coherent search pipeline are fed
into the artificial neural network to distinguish simulated gravitational-wave
signals from background noise artifacts. Our result shows that the data
classification efficiency at a fixed false alarm probability is improved by the
artificial neural network in comparison to the conventional detection
statistic. Therefore, this algorithm increases the distance at which a
gravitational-wave signal could be observed in coincidence with a gamma-ray
burst. In order to demonstrate the performance, we also evaluate a few seconds
of gravitational-wave data segment using the trained networks and obtain the
false alarm probability. We suggest that the artificial neural network can be a
complementary method to the conventional detection statistic for identifying
gravitational-wave signals related to the short gamma-ray bursts.Comment: 30 pages, 10 figure
Atomic-Scale Imaging in Real and Energy Space Developed in Ultrafast Electron Microscopy
In this contribution, we report the development of ultrafast electron microscopy (UEM) with atomic-scale real-, energy-, and Fourier-space resolutions. This second-generation UEM provides images, diffraction patterns, and electron energy spectra, and here we demonstrate its potential with applications for nanostructured materials and organometallic crystals. We clearly resolve the separation between atoms in the direct images and the Bragg spots/Debye−Scherrer rings in diffraction and obtain the electronic structure and elemental energies in the electron energy loss spectra (EELS) and energy filtered transmission electron microscopy (EFTEM)
Formation of Five-Dimensional String Solutions from the Gravitational Collapse
We study the formation of five-dimensional string solutions including the
Gregory-Laflamme (GL) black string, the Kaluza-Klein (KK) bubble, and the
geometry with a naked singularity from the gravitational collapse. The interior
solutions of five-dimensional Einstein equations describe collapsing
non-isotropic matter clouds. It is shown that the matter cloud always forms the
GL black string solution while the KK bubble solution cannot be formed. The
numerical study seems to suggest that the collapsing matter forms the
geometries with timelike naked curvature singularities, which should be taken
cautiously as the general relativity is not reliable in the strong curvature
regime.Comment: 17 pages, 10 figures, LaTeX, to appear in Class. Quant. Grav., a
appendix and some discussions added, title change
Current and noise expressions for radio-frequency single-electron transistors
We derive self-consistent expressions of current and noise for
single-electron transistors driven by time-dependent perturbations. We take
into account effects of the electrical environment, higher-order co-tunneling,
and time-dependent perturbations under the two-charged state approximation
using the Schwinger-Kedysh approach combined with the generating functional
technique. For a given generating functional, we derive exact expressions for
tunneling currents and noises and present the forms in terms of transport
coefficients. It is also shown that in the adiabatic limit our results
encompass previous formulas. In order to reveal effects missing in static
cases, we apply the derived results to simulate realized radio-frequency
single-electron transistor. It is found that photon-assisted tunneling affects
largely the performance of the single-electron transistor by enhancing both
responses to gate charges and current noises. On various tunneling resistances
and frequencies of microwaves, the dependence of the charge sensitivity is also
discussed.Comment: 18 pages, 9 figure
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