The harmonic product of δ(x1,...,xn)\delta (x_{1},..., x_{n}) and δ(x1)\delta (x_{1}) and two combinatorial identities

In the framework of nonstandard analysis, Bang-He Li and the author defined the product of any two distributions on $R^n$ via their harmonic representations. The product of $\delta (x_{1},..., x_{n})$ and $\delta (x_{1})$ was calculated by Kuribayashi and the author in [LK]. In this paper, the result of [LK] is improved to $$\delta (x_{1},..., x_{n})\circ \delta (x_{1}) =\dfrac{1}{2\pi\rho} \delta (x_{1},..., x_{n}) {mod} {infinitesimals}$$ where $\rho$ is a positive infinitesimal. Moreover two combinatorial identities are obtained as byproducts.Comment: Latex. To appear in Hiroshima Math.

Amending the Vafa-Witten Theorem

The strong version of the Vafa-Witten theorem is shown may not to hold because the zero condensate from a direct computation of the order parameter is found to be a result on the symmetric vacuum. The validity of the Vafa-Witten theorem relies then on its weak version, that the Goldstone boson is absent in vector-like gauge theories with vanishing \theta-angle. The existence of a charged \rho-meson condensate, which violates electromagnetic gauge symmetry, is consistent with this weak version of the Vafa-Witten theorem when applied to strong magnetic fields in QCD.Comment: 6 page

Quantum control gates with weak cross-Kerr nonlinearity

In this paper, with the weak cross-Kerr nonlinearity, we first present a special experimental scheme called C-path gate with which the realization of all possible bipartite POVMs of two-photon polarization states can be simpler and nearly deterministic. Following the same technique, the schemes of the realization of quantum control gates have been proposed, including the CNOT gate (1/2), Fredkin gate (1/8), Toffoli gate (2/23), CU gate and even MCU gate. All these gates are scalable with the certain probabilities which are larger than those gates in linear optics. Less resource are required and the structures of these gates are so simple that we think they are feasible with current technology and may be useful for the realization of universal computation in optics.Comment: 12 pages, 4 figure

Unpaired Multi-Domain Image Generation via Regularized Conditional GANs

In this paper, we study the problem of multi-domain image generation, the goal of which is to generate pairs of corresponding images from different domains. With the recent development in generative models, image generation has achieved great progress and has been applied to various computer vision tasks. However, multi-domain image generation may not achieve the desired performance due to the difficulty of learning the correspondence of different domain images, especially when the information of paired samples is not given. To tackle this problem, we propose Regularized Conditional GAN (RegCGAN) which is capable of learning to generate corresponding images in the absence of paired training data. RegCGAN is based on the conditional GAN, and we introduce two regularizers to guide the model to learn the corresponding semantics of different domains. We evaluate the proposed model on several tasks for which paired training data is not given, including the generation of edges and photos, the generation of faces with different attributes, etc. The experimental results show that our model can successfully generate corresponding images for all these tasks, while outperforms the baseline methods. We also introduce an approach of applying RegCGAN to unsupervised domain adaptation

Static Equilibria of Charged Particles Around Charged Black Holes: Chaos Bound and Its Violations

We study the static equilibrium of a charged massive particle around a charged black hole, balanced by the Lorentz force. For a given black hole, the equilibrium surface is determined by the charge/mass ratio of the particle. By investigating a large class of charged black holes, we find that the equilibria can be stable, marginal or unstable. We focus on the unstable equilibria which signal chaotic motions and we obtain the corresponding Lyapunov exponents $\lambda$. We find that although $\lambda$ approaches universally the horizon surface gravity $\kappa$ when the equilibria are close to the horizon, the proposed chaotic motion bound $\lambda<\kappa$ is satisfied only by some specific black holes including the RN and RN-AdS black holes. The bound can be violated by a large number of black holes including the RN-dS black holes or black holes in Einstein-Maxwell-Dilaton, Einstein-Born-Infeld and Einstein-Gauss-Bonnet-Maxwell gravities. We find that unstable equilibria can even exist in extremal black holes, implying that the ratio $\lambda/\kappa$ can be arbitrarily large for sufficiently small $\kappa$. Our investigation does suggest a universal bound for sufficiently large $\kappa$, namely $\lambda/\kappa <{\cal C}$ for some order-one constant ${\cal C}$.Comment: Latex, 29 pages, 1 figur

Measurement of weak static magnetic fields with nitrogen-vacancy color center

We propose a strategy to measure weak static magnetic fields with nitrogen-vacancy color center in diamond. Inspired by avian magnetoreception models, we consider the feasibility of utilizing quantum coherence phenomena to measure weak static magnetic fields. Nitrogen-vacancy (NV) color centers are regarded as the ideal platform to study quantum sciences as a result of its long coherence time up to a millisecond timescale. In high-purity diamond, hyperfine interaction with 13C nuclear spins dominates the decoherence process. In this paper, we numerically simulate the decoherence process between 0 and +1 of the individual NV color center spin in 13C nuclear baths with various of magnitudes of external magnetic fields. By applying Hahn echo into the system, we obtain the coherence of NV color center spin as a function of total evolution time and magnetic field. Furthermore we obtain the high-accuracy relationship between the three decoherence-characteristic timescales, i.e. T_W, T_R, T_2, and magnetic field B. And we draw a conclusion that T_R has the highest sensitivity about magnetic field among the three time-scales. Thus, for a certain NV color center, T_R can be the scale for the magnitude of magnetic field, or rather, the component along the NV electronic spin axis. When measuring an unknown magnetic field, we adjust the NV axis to three mutually orthogonal directions respectively. By this means, we obtain the three components of the magnetic field and thus the magnitude and direction of the actual magnetic field. The accuracy could reach 60 nT/Hz^{1/2},and could be greatly improved by using an ensemble of NV color centers or diamond crystals purified with 12C atoms.Comment: 17 pages, 5 figures, 1 tabl

Impacts on Cosmological Constraints from Degeneracies

In this paper, we study the degeneracies among several cosmological parameters in detail and discuss their impacts on the determinations of these parameters from the current and future observations. By combining the latest data sets, including type-Ia supernovae "Union2.1" compilation, WMAP seven-year data and the baryon acoustic oscillations from the SDSS Data Release Seven, we perform a global analysis to determine the cosmological parameters, such as the equation of state of dark energy w, the curvature of the universe \Omega_k, the total neutrino mass \sum{m_\nu}, and the parameters associated with the power spectrum of primordial fluctuations (n_s, \alpha_s and r). We pay particular attention on the degeneracies among these parameters and the influences on their constraints, by with or without including these degeneracies, respectively. We find that $w$ and \Omega_k or \sum{m_\nu} are strongly correlated. Including the degeneracies will significantly weaken the constraints. Furthermore, we study the capabilities of future observations and find these degeneracies can be broken very well. Consequently, the constraints of cosmological parameters can be improved dramatically.Comment: 9 figures, 6 tables, Accepted for publication in JCA

Wilson Line Response of Holographic Superconductors in Gauss-Bonnet Gravity

We study the Wilson line response in the holographic superconducting phase transitions in Gauss-Bonnet gravity. In the black brane background case, the Little-Parks periodicity is independent of the Gauss-Bonnet parameter, while in the AdS soliton case, there is no evidence for the Little-Parks periodicity. We further study the impact of the Gauss-Bonnet term on the holographic phase transitions quantitatively. The results show that such quantum corrections can effectively affect the occurrence of the phase transitions and the response to the Wilson line.Comment: 19 pages, 6 figures, 2 tables, references adde

On-off intermittency in small-world networks of chaotic maps

Small-world networks are highly clustered networks with small average distance among the nodes. There are many natural and technological networks that present this kind of connections. The on-off intermittency is investigated in small-world networks of chaotic maps in this paper. We show how the small-world topology would affect the on-off intermittency behavior. The distributions of the laminar phase are calculated numerically. The results show that the laminar phases obey power-law distributions.Comment: 7 pages, 6 figure

Constraints on Dark Energy Parameters from Correlations of CMB with LSS

In this paper, we combine the the latest observational data, including the WMAP five-year data (WMAP5), the baryon acoustic oscillations (BAO) and type Ia supernovae (SN) "union" compilation, and use the Markov Chain Monte Carlo method to determine the dark energy parameters. We pay particular attention to the Integrated Sache-Wolfe (ISW) data from the cross-correlations of cosmic microwave background (CMB) and large scale structure (LSS). In the \Lambda CDM model, we find that the ISW data, as a complement to the WMAP data, could significantly improve the constraint of curvature \Omega_k. We also check the improvement of constraints from the new prior on the Hubble constant and find this new prior could improve the constraint of \Omega_k by a factor of 2. Finally, we study the dynamical evolving EoS of dark energy from the current observational data. Based on the dynamical dark energy model, parameterizing as w(a)=w_0+w_a(1-a), we find that the \Lambda CDM model remains a good fit to the current data. When taking into account the ISW data, the error bars of w_0 and w_a could be shrunk slightly. Current constraints on the dynamical dark energy model are not conclusive. The future precision measurements are needed.Comment: 6 pages, 4 figures, accepted for publication in JCA