Controllable Fano resonance and fast to slow light in a hybrid semiconductor/superconductor ring device mediated by Majorana fermions

We demonstrate theoretically the Fano resonance and the conversion from fast to slow light in a hybrid quantum dot-semiconductor/superconductor ring device, where the QD is coupled to a pair of MFs appearing in the hybrid S/S ring device. The absorption spectra of the weak probe field can exhibit a series of asymmetric Fano line shapes and their related propagation properties such as fast and slow light effects are investigated based on the hybrid system for suitable parametric regimes. The positions of the Fano resonances can be determined by the parameters, such as different detuning regimes and QD-MFs coupling strengths. Further, the transparency windows (the absorption dip approaches zero) in the probe absorption spectra are accompanied by the rapid dispersion, which indicates the slow or fast light effect, and tunable fast-to-slow light propagation (or vice versa) can be achieved by controlling different parameter regimes. Our study may provide an all-optical means to investigate MFs and open up promising applications in quantum information processing based on MFs in solid state devices

Randomized Algorithms for Large-scale Inverse Problems with General Regularizations

We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then apply randomized algorithms to reduce large-scale systems of standard form to much smaller-scale systems and seek their regularized solutions in combination with some popular choice rules for regularization parameters. Then we will propose a second approach to solve large-scale ill-posed systems with general regularizations. This involves a new randomized generalized SVD algorithm that can essentially reduce the size of the original large-scale ill-posed systems. The reduced systems can provide approximate regularized solutions with about the same accuracy as the ones by the classical generalized SVD, and more importantly, the new approach gains obvious robustness, stability and computational time as it needs only to work on problems of much smaller size. Numerical results are given to demonstrated the efficiency of the algorithms

Finite Element Methods For Interface Problems On Local Anisotropic Fitting Mixed Meshes

A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new finite element method is proposed for second order elliptic interface problems based on the resulting mesh. Optimal approximation capabilities on anisotropic elements are proved in both the $H^1$ and $L^2$ norms. The discrete system is usually ill-conditioned due to anisotropic and small elements near the interface. Thereupon, a multigrid method is presented to handle this issue. The convergence rate of the multigrid method is shown to be optimal with respect to both the coefficient jump ratio and mesh size. Numerical experiments are presented to demonstrate the theoretical results

The next-to-leading order corrections to B→ρB \to \rho transition in the kTk_T factorization

In this paper, we investigate the factorization hypothesis step by step for the exclusive process $B \to \rho$ at next-to-leading order (NLO) with the collinear factorization approach, and then we extend our results to the $k_T$ factorization frame. We show that the soft divergence from the specific NLO diagrams will cancel each other at the quark level, while the remaining collinear divergence can be absorbed into the NLO wave functions. The full NLO amplitudes can be factorized into two parts: the NLO $B$ and $\rho$ meson wave functions containing the collinear divergence and the leading order (LO) finite hard kernels. We give the general form of the nonlocal hadron matrix for the NLO $B$ and $\rho$ meson wave functions and all results of factorization for different twists' combinations.Comment: 22 pages, 7 figure

Top-quark forward-backward asymmetry in e+e- annihilation at NNLO in QCD

We report on a complete calculation of electroweak production of top quark pairs in $e^+e^-$ annihilation at next-to-next-to-leading order in Quantum Chromodynamics. Our setup is fully differential and can be used to calculate any infrared-safe observable. Especially we calculated the next-to-next-to-leading order corrections to top-quark forward-backward asymmetry and found sizable effects. Our results show a large reduction of the theoretical uncertainties in predictions of the forward-backward asymmetry, and allow a precision determination of the top quark electroweak couplings at future $e^+e^-$ colliders.Comment: 6 pages, 5 figures. arXiv admin note: text overlap with arXiv:1408.515

Fast Multi-Instance Multi-Label Learning

In many real-world tasks, particularly those involving data objects with complicated semantics such as images and texts, one object can be represented by multiple instances and simultaneously be associated with multiple labels. Such tasks can be formulated as multi-instance multi-label learning (MIML) problems, and have been extensively studied during the past few years. Existing MIML approaches have been found useful in many applications; however, most of them can only handle moderate-sized data. To efficiently handle large data sets, in this paper we propose the MIMLfast approach, which first constructs a low-dimensional subspace shared by all labels, and then trains label specific linear models to optimize approximated ranking loss via stochastic gradient descent. Although the MIML problem is complicated, MIMLfast is able to achieve excellent performance by exploiting label relations with shared space and discovering sub-concepts for complicated labels. Experiments show that the performance of MIMLfast is highly competitive to state-of-the-art techniques, whereas its time cost is much less; particularly, on a data set with 20K bags and 180K instances, MIMLfast is more than 100 times faster than existing MIML approaches. On a larger data set where none of existing approaches can return results in 24 hours, MIMLfast takes only 12 minutes. Moreover, our approach is able to identify the most representative instance for each label, and thus providing a chance to understand the relation between input patterns and output label semantics

Quantum beat phenomenon presence in coherent spin dynamics of spin-2 87^{87}Rb atoms in a deep optical lattice

Motivated by the recent experimental work (A. Widera, \textit{et al}, Phys. Rev. Lett. 95, 19045), we study the collisional spin dynamics of two spin-2 $^{87}$Rb atoms confined in a deep optical lattice. When the system is initialized as $|0,0>$, three different two-particle Zeeman states are involved in the time evolution due to the conservation of magnetization. For a large magnetic field $B>0.8$ Guass, the spin coherent dynamics reduces to a Rabi-like oscillation between the states $|0,0>$ and $$. However, under a small magnetic field, a general three-level coherent oscillation displays. In particular, around a critical magnetic field $B_{c}\simeq 0.48$ Guass, the probability in the Zeeman states $$ exhibits a novel quantum beat phenomenon, ready to be confirmed in future experiments.Comment: 5 pages, 5 figure

Ultrasensitive Detection of Majorana Fermions via Spin-based Optomechanics with Carbon Nanotubes

We propose a novel optical method to detect the existence of Majorana fermions at the ends of the semiconductor nanowire via the coupling to an electron spin trapped on a carbon nanotube resonator under the control of a strong pump field and a weak probe field. The coupling strength of Majorana fermion to the spin in the carbon nanotube and the decay rate of the Majorana fermion can be easily measured from the probe absorption spectrum via manipulating the spin-mechanical coupling in the suspended\ carbon nanotube. The scheme proposed here will open a good perspective for its applications in all-optical controlled Majorana fermion-based quantum computation and quantum information processing

Entropy evolution law in a laser process

For the first time, we obtain the entropy variation law in a laser process after finding the Kraus operator of the master equation describing the laser process with the use of the entangled state representation. The behavior of entropy is determined by the competition of the gain and damping in the laser process. The photon number evolution formula is also obtained

The ργ∗→π(ρ)\rho \gamma^* \to \pi (\rho) transition form factors in the Perturbative QCD factorization approach

In this paper, we studied the $\rho \gamma^* \to \pi$ and $\rho\gamma^*\to \rho$ transition processes and made the calculations for the $\rho\pi$ transition form factor $Q^4 F_{\rho\pi}(Q^2)$ and the $\rho$ meson electromagnetic form factors, $F_{\rm LL, LT,TT}(Q^2)$ and $F_{1,2,3}(Q^2)$, by employing the perturbative QCD (PQCD) factorization approach. For the $\rho \gamma^* \to \pi$ transition, we found that the contribution to form factor $Q^4 F_{\rho\pi}(Q)$ from the term proportional to the distribution amplitude combination $\phi^T_{\rho}(x_1)\phi^P_{\pi}(x_2)$ is absolutely dominant, and the PQCD predictions for both the size and the $Q^2$-dependence of this form factor $Q^4 F_{\rho\pi}(Q^2)$ agree well with those from the extended ADS/QCD models or the light-cone QCD sum rule. For the $\rho \gamma^* \to \rho$ transition and in the region of $Q^2\geq 3$ GeV$^2$, further more, we found that the PQCD predictions for the magnitude and their $Q^2$-dependence of the $F_1(Q^2)$ and $F_2(Q^2)$ form factors agree well with those from the QCD sum rule, while the PQCD prediction for $F_3(Q^2)$ is much larger than the one from the QCD sum rule.Comment: 11 pages, 3 figure