We present a detailed study of the spherically symmetric solutions in Lorentz breaking massive gravity. There is an undetermined function $mathcal{F}(X, w_1, w_2, w_3)$ in the action of St{u}ckelberg fields $S_{phi}=Lambda^4int{d^4xsqrt{-g}mathcal{F}
}$, which should be resolved through physical means. In the general relativity, the spherically symmetric solution to the Einstein equation is a benchmark and its massive deformation also play a crucial role in Lorentz breaking massive gravity. $mathcal{F}$ will satisfy the constraint equation $T_0^1=0$ from the spherically symmetric Einstein tensor $G_0^1=0$, if we maintain that any reasonable physical theory should possess the spherically symmetric solutions. The St{u}ckelberg field $phi^i$ is taken as a hedgehog configuration $phi^i=phi(r)x^i/r$, whose stability is guaranteed by the topological one. Under this ans{a}tz, $T_0^1=0$ is reduced to $dmathcal{F}=0$. The functions $mathcal{F}$ for $dmathcal{F}=0$ form a commutative ring $R^{mathcal{F}}$. We obtain a general expression of solution to the functional differential equation with spherically symmetry if $mathcal{F}in R^{mathcal{F}}$. If $mathcal{F}in R^{mathcal{F}}$ and $partialmathcal{F}/partial X=0$, the functions $mathcal{F}$ form a subring $S^{mathcal{F}}subset R^{mathcal{F}}$. We show that the metric is Schwarzschild, AdS or dS if $mathcal{F}in S^{mathcal{F}}$. When $mathcal{F}in R^{mathcal{F}}$ but $mathcal{F} otin S^{mathcal{F}}$, we will obtain some new metric solutions. Using the general formula and the basic property of function ring $R^{mathcal{F}}$, we give some analytical examples and their phenomenological applications. Furthermore, we also discuss the stability of gravitational field by the analysis of Komar integral and the results of QNMs.
We consider testing for two-sample means of high dimensional populations by thresholding. Two tests are investigated, which are designed for better power performance when the two population mean vectors differ only in sparsely populated coordinates.
The first test is constructed by carrying out thresholding to remove the non-signal bearing dimensions. The second test combines data transformation via the precision matrix with the thresholding. The benefits of the thresholding and the data transformations are showed by a reduced variance of the test thresholding statistics, the improved power and a wider detection region of the tests. Simulation experiments and an empirical study are performed to confirm the theoretical findings and to demonstrate the practical implementations.
In this paper, we study the electron spin decoherence of single defects in silicon carbide (SiC) nuclear spin bath. We find that, although the natural abundance of $^{29}rm{Si}$ ($p_{rm{Si}}=4.7%$) is about 4 times larger than that of $^{13}{rm C}$ (
$p_{rm{C}}=1.1%$), the electron spin coherence time of defect centers in SiC nuclear spin bath in strong magnetic field ($B>300~rm{Gauss}$) is longer than that of nitrogen-vacancy (NV) centers in $^{13}{rm C}$ nuclear spin bath in diamond. The reason for this counter-intuitive result is the suppression of heteronuclear-spin flip-flop process in finite magnetic field. Our results show that electron spin of defect centers in SiC are excellent candidates for solid state spin qubit in quantum information processing.
For $J/psi$ pair production at hadron colliders, we present the full next-to-leading order (NLO) calculations with the color-singlet channel in nonrelativistic QCD. We find that the NLO result can reasonably well describe the LHCb measured cross sect
ion, but exhibits very different behaviors from the CMS data in the transverse momentum distribution and mass distribution of $J/psi$ pair. Moreover, by adding contributions of gluon fragmentation and quark fragmentation, which occur at even higher order in $alpha_s$, it is still unable to reduce the big differences. In particular, the observed flat distribution in the large invariant mass region is hard to explain. New processes or mechanisms are needed to understand the CMS data for $J/psi$ pair production.
Background modeling is a critical component for various vision-based applications. Most traditional methods tend to be inefficient when solving large-scale problems. In this paper, we introduce sparse representation into the task of large scale stabl
e background modeling, and reduce the video size by exploring its discriminative frames. A cyclic iteration process is then proposed to extract the background from the discriminative frame set. The two parts combine to form our Sparse Outlier Iterative Removal (SOIR) algorithm. The algorithm operates in tensor space to obey the natural data structure of videos. Experimental results show that a few discriminative frames determine the performance of the background extraction. Further, SOIR can achieve high accuracy and high speed simultaneously when dealing with real video sequences. Thus, SOIR has an advantage in solving large-scale tasks.
The spin-orbit coupling (SOC) can mediate electric-dipole spin resonance (EDSR) in an a.c. electric field. In this letter, the EDSR is essentially understood as an spin precession under an effective a.c. magnetic field induced by the SOC in the refer
ence frame, which is exactly following the classical trajectory of the electron and obtained by applying a quantum linear coordinate transformation. With this observation for one-dimensional (1D) case, we find a upper limit for the spin-flipping speed in the EDSR-based control of spin, which is given by the accessible data from the current experiment. For two-dimensional case, the azimuthal dependence of the effective magnetic field can be used to measure the ratio of the Rashba and Dresselhause SOC strengths.
For a bosonic (fermionic) open system in a bath with many bosons (fermions) modes, we derive the exact non-Markovian master equation in which the memory effect of the bath is reflected in the time dependent decay rates. In this approach, the reduced
density operator is constructed from the formal solution of the corresponding Heisenberg equations. As an application of the exact master equation, we study the active probing of non-Markovianity of the quantum dissipation of a single boson mode of electromagnetic (EM) field in a cavity QED system. The non-Markovianity of the bath of the cavity is explicitly reflected by the atomic decoherence factor.
We study the quantum transitions of a central spin surrounded by a collective-spin environment. It is found that the influence of the environmental spins on the absorption spectrum of the central spin can be explained with the analog of the Franck-Co
ndon (FC) effect in conventional electron-phonon interaction system. Here, the collective spins of the environment behave as the vibrational mode, which makes the electron to be transitioned mainly with the so-called vertical transitions in the conventional FC effect. The vertical transition for the central spin in the spin environment manifests as, the certain collective spin states of the environment is favored, which corresponds to the minimal change in the average of the total spin angular momentum.
Some chemical reactions are described by electron transfer (ET) processes. The underlying mechanism could be modeled as a polaron motion in the molecular crystal-the Holstein model. By taking spin degrees of freedom into consideration, we generalize
the Holstein model (molecular crystal model) to microscopically describe an ET chemical reaction. In our model, the electron spins in the radical pair simultaneously interact with a magnetic field and their nuclear-spin environments. By virtue of the perturbation approach, we obtain the chemical reaction rates for different initial states. It is discovered that the chemical reaction rate of the triplet state demonstrates its dependence on the direction of the magnetic field while the counterpart of the singlet state does not. This difference is attributed to the explicit dependence of the triplet state on the direction when the axis is rotated. Our model may provide a possible candidate for the microscopic origin of avian compass.
Due to the stochastic nature of biochemical processes, the copy number of any given type of molecule inside a living cell often exhibits large temporal fluctuations. Here, we develop analytic methods to investigate how the noise arising from a bursti
ng input is reshaped by a transport reaction which is either linear or of the Michaelis-Menten type. A slow transport rate smoothes out fluctuations at the output end and minimizes the impact of bursting on the downstream cellular activities. In the context of gene expression in eukaryotic cells, our results indicate that transcriptional bursting can be substantially attenuated by the transport of mRNA from nucleus to cytoplasm. Saturation of the transport mediators or nuclear pores contributes further to the noise reduction. We suggest that the mRNA transport should be taken into account in the interpretation of relevant experimental data on transcriptional bursting.
