Entangling two macroscopic mechanical mirrors in a two-cavity optomechanical system

We propose a simple method to generate quantum entanglement between two macroscopic mechanical resonators in a two-cavity optomechanical system. This entanglement is induced by the radiation pressure of a single photon hopping between the two cavities. Our results are analytical, so that the entangled states are explicitly shown. Up to local operations, these states are two-mode three-component states, and hence the degree of entanglement can be well quantified by the concurrence. By analyzing the system parameters, we find that, to achieve a maximum average entanglement, the system should work in the single-photon strong-coupling regime and the deep-resolved-sideband regime.Comment: 5 pages, 3 figures, Phys. Rev. A in pres

Visual Saliency Maps Can Apply to Facial Expression Recognition

Human eyes concentrate different facial regions during distinct cognitive activities. We study utilising facial visual saliency maps to classify different facial expressions into different emotions. Our results show that our novel method of merely using facial saliency maps can achieve a descent accuracy of 65\%, much higher than the chance level of $1/7$. Furthermore, our approach is of semi-supervision, i.e., our facial saliency maps are generated from a general saliency prediction algorithm that is not explicitly designed for face images. We also discovered that the classification accuracies of each emotional class using saliency maps demonstrate a strong positive correlation with the accuracies produced by face images. Our work implies that humans may look at different facial areas in order to perceive different emotions

Reducing Noise for PIC Simulations Using Kernel Density Estimation Algorithm

Noise is a major concern for Particle-In-Cell (PIC) simulations. We propose a new theoretical and algorithmic framework to evaluate and reduce the noise level for PIC simulations based on the Kernel Density Estimation (KDE) theory, which has been widely adopted in machine learning and big data science. According to this framework, the error on particle density estimation for PIC simulations can be characterized by the Mean Integrated Square Error (MISE), which consists of two parts, systematic error and noise. A careful analysis shows that in the standard PIC methods noise is the dominate error, and the noise level can be reduced if we select different shape functions that are capable of balancing the systematic error and the noise. To improve performance, we use the von Mises distribution as the shape function and seek an optimal particle width that minimizes the MISE, represented by a Cross-Validation (CV) function. This procedure significantly reduces both the noise and the MISE for PIC simulations. A particle-wise width adjustment algorithm and a width update algorithm are further developed to reduce the MISE. Simulations using the examples of Langmuir wave and Landau Damping demonstrate that the KDE algorithm developed in the present study reduces the noise level on density estimation by 98%, and gives a much more accurate result on the linear damping rate compared to the standard PIC methods. Meanwhile, it is computational efficient that can save 40% time to achieve the same accuracy.Comment: 28 pages, 8 figure

Quantum logic gates with controllable and selective interaction for superconducting charge qubits via a nanomechanical resonator

In this paper, we propose a scheme to implement two-qubit logic gates with a controllable and selective interaction in a scalable superconducting circuit of charge qubits. A nanomechanical resonator is used as a data bus to connect qubits. It is indicated that a controllable interaction between qubits can be obtained by making use of the data bus. It is shown that a selective interaction between qubits can be realized when many qubits are involved in the system under our consideration.Comment: 4 pages, 2 figure

Baryon Distribution in Galaxy Clusters as a Result of Sedimentation of Helium Nuclei

Heavy particles in galaxy clusters tend to be more centrally concentrated than light ones according to the Boltzmann distribution. An estimate of the drift velocity suggests that it is possible that the helium nuclei may have entirely or partially sedimented into the cluster core within the Hubble time. We demonstrate the scenario using the NFW profile as the dark matter distribution of clusters and assuming that the intracluster gas is isothermal and in hydrostatic equilibrium. We find that a greater fraction of baryonic matter is distributed at small radii than at large radii, which challenges the prevailing claim that the baryon fraction increases monotonically with cluster radius. It shows that the conventional mass estimate using X-ray measurements of intracluster gas along with a constant mean molecular weight may have underestimated the total cluster mass by $\sim 20$, which in turn leads to an overestimate of the total baryon fraction by the same percentage. Additionally, it is pointed out that the sedimentation of helium nuclei toward cluster cores may at least partially account for the sharp peaks in the central X-ray emissions observed in some clusters.Comment: 4 pages + 3 figures, minor changes, ApJ Lett., 2000, 529, L

Model of energy spectrum parameters of ground level enhancement events in solar cycle 23

Mewaldt et al. 2012 fitted the observations of the ground level enhancement (GLE) events during solar cycle 23 to the double power-law equation to obtain the four energy spectra parameters, the normalization parameter $C$, low-energy power-law slope $\gamma_1$, high-energy power-law slope $\gamma_2$, and break energy $E_0$. There are 16 GLEs from which we select $13$ for study by excluding some events with complicated situation. We analyze the four parameters with conditions of the corresponding solar events. According to solar event conditions we divide the GLEs into two groups, one with strong acceleration by interplanetary (IP) shocks and another one without strong acceleration. By fitting the four parameters with solar event conditions we obtain models of the parameters for the two groups of GLEs separately. Therefore, we establish a model of energy spectrum of solar cycle 23 GLEs which may be used in prediction in the future.Comment: 42 pages, 19 figures, 3 table

Decoherence and Energy Relaxation in the Quantum-Classical Dynamics for Charge Transport in Organic Semiconducting Crystals: an Instantaneous Decoherence Correction Approach

We explore an instantaneous decoherence correction (IDC) approach for the decoherence and energy relaxation in the quantum-classical dynamics of charge transport in organic semiconducting crystals. These effects, originating from environmental fluctuations, are essential ingredients of the carrier dynamics. The IDC is carried out by measurement-like operations in the adiabatic representation. While decoherence is inherent in the IDC, energy relaxation is taken into account by considering the detailed balance through the introduction of energy-dependent reweighing factors, which could be either Boltzmann (IDC-BM) or Miller-Abrahams (IDC-MA) type. For a non-diagonal electron-phonon coupling model, it is shown that the IDC tends to enhance diffusion while energy relaxation weakens this enhancement. As expected, both the IDC-BM and IDC-MA achieve a near-equilibrium distribution at finite temperatures in the diffusion process, while the Ehrenfest dynamics renders system tending to infinite temperature limit. The resulting energy relaxation times with the two kinds of factors lie in different regimes and exhibit different dependence on temperature, decoherence time and electron-phonon coupling strength, due to different dominant relaxation process.Comment: 8 pages, 4 figure

Further factorization of xn−1x^n-1 over a finite field

Let $\Bbb F_q$ be a finite field with $q$ elements and $n$ a positive integer. Mart\'inez, Vergara and Oliveira \cite{MVO} explicitly factorized $x^{n} - 1$ over $\Bbb F_q$ under the condition of $rad(n)|(q-1)$. In this paper, suppose that $rad(n)\nmid (q-1)$ and $rad(n)|(q^w-1)$, where $w$ is a prime, we explicitly factorize $x^{n}-1$ into irreducible factors in $\Bbb F_q[x]$ and count the number of its irreducible factors

Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data

We present a numerical approach for approximating unknown Hamiltonian systems using observation data. A distinct feature of the proposed method is that it is structure-preserving, in the sense that it enforces conservation of the reconstructed Hamiltonian. This is achieved by directly approximating the underlying unknown Hamiltonian, rather than the right-hand-side of the governing equations. We present the technical details of the proposed algorithm and its error estimate in a special case, along with a practical de-noising procedure to cope with noisy data. A set of numerical examples are then presented to demonstrate the structure-preserving property and effectiveness of the algorithm.Comment: 27 pages, 19 figure

High-dimensional covariance matrix estimation using a low-rank and diagonal decomposition

We study high-dimensional covariance/precision matrix estimation under the assumption that the covariance/precision matrix can be decomposed into a low-rank component L and a diagonal component D. The rank of L can either be chosen to be small or controlled by a penalty function. Under moderate conditions on the population covariance/precision matrix itself and on the penalty function, we prove some consistency results for our estimators. A blockwise coordinate descent algorithm, which iteratively updates L and D, is then proposed to obtain the estimator in practice. Finally, various numerical experiments are presented: using simulated data, we show that our estimator performs quite well in terms of the Kullback-Leibler loss; using stock return data, we show that our method can be applied to obtain enhanced solutions to the Markowitz portfolio selection problem