The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function $g(t) \sim t^{\gamma}$, $0 \le \gamma < 2$, and the probability density function $\omega(t)$ of a particle's waiting time $t$ follows a power law form for large $t$: $\omega(t) \sim t^{-(1+\alpha)}$, $0 < \alpha < 1$. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent $\gamma$ and the long-tailed index $\alpha$ of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.

We discuss the equivalent form of the Lévy-Leblond equation such that the nilpotent matrices are two-dimensional. We show that this equation can be obtained in the non-relativistic limit of the (2+1)-dimensional Dirac equation. Furthermore, we analyze the case with four-dimensional matrices, propose a Hamiltonian for the equation in (3+1) dimensions, and solve it for a Coulomb potential. The quantized energy levels for the hydrogen atom are obtained, and the result is consistent with the non-relativistic quantum mechanics.

We propose an effective mechanism to couple superconducting charge and flux qubits by using a quantized nanomechanical resonator. The coupling between the charge and flux qubits can be controlled by the external flux of the charge qubit. Under the strong coupling limit, an iSWAP gate can be generated by this scheme. The experimental feasibility in our scheme is also presented.

The Bronnikov regular magnetic black hole as a gravitational lens is studied. In nonlinear electrodynamics, photons do not follow null geodesics of background geometry, but move along null geodesics of a corresponding effective geometry. To study the Bronnikov regular magnetic black hole gravitational lensing in the strong deflection limit, the corresponding effective geometry should be obtained firstly. This is the most important and key step. We obtain the deflection angle in the strong deflection limit, and further calculate the angular positions and magnifications of relativistic images as well as the time delay between different relativistic images. The influence of the magnetic charge on the black hole gravitational lensing is also discussed.

The identification between chaotic systems and stochastic processes is not easy since they have numerous similarities. In this study, we propose a novel approach to distinguish between chaotic systems and stochastic processes based on the component reordering procedure and the visibility graph algorithm. It is found that time series and their reordered components will show diverse characteristics in the 'visibility domain'. For chaotic series, there are huge differences between the degree distribution obtained from the original series and that obtained from the corresponding reordered component. For correlated stochastic series, there are only small differences between the two degree distributions. For uncorrelated stochastic series, there are slight differences between them. Based on this discovery, the well-known Kullback–Leible divergence is used to quantify the difference between the two degree distributions and to distinguish between chaotic systems, correlated and uncorrelated stochastic processes. Moreover, one chaotic map, three chaotic systems and three different stochastic processes are utilized to illustrate the feasibility and effectiveness of the proposed method. Numerical results show that the proposed method is not only effective to distinguish between chaotic systems, correlated and uncorrelated stochastic processes, but also easy to operate.

The contribution of this work is twofold: (1) a multimodality prediction method of chaotic time series with the Gaussian process mixture (GPM) model is proposed, which employs a divide and conquer strategy. It automatically divides the chaotic time series into multiple modalities with different extrinsic patterns and intrinsic characteristics, and thus can more precisely fit the chaotic time series. (2) An effective sparse hard-cut expectation maximization (SHC-EM) learning algorithm for the GPM model is proposed to improve the prediction performance. SHC-EM replaces a large learning sample set with fewer pseudo inputs, accelerating model learning based on these pseudo inputs. Experiments on Lorenz and Chua time series demonstrate that the proposed method yields not only accurate multimodality prediction, but also the prediction confidence interval. SHC-EM outperforms the traditional variational learning in terms of both prediction accuracy and speed. In addition, SHC-EM is more robust and insusceptible to noise than variational learning.

We investigate the critical behavior and the duality property of the ferromagnetic $q$-state clock model on the square lattice based on the tensor-network formalism. From the entanglement spectra of local tensors defined in the original and dual lattices, we obtain the exact self-dual points for the model with $q \leq 5 $ and approximate self-dual points for $q \geq 6$. We calculate accurately the lower and upper critical temperatures for the six-state clock model from the fixed-point tensors determined using the higher-order tensor renormalization group method and compare with other numerical results.

The Al$^+$ ion optical clock is a very promising optical frequency standard candidate due to its extremely small black-body radiation shift. It has been successfully demonstrated with the indirect cooled, quantum-logic-based spectroscopy technique. Its accuracy is limited by second-order Doppler shift, and its stability is limited by the number of ions that can be probed in quantum logic processing. We propose a direct laser cooling scheme of Al$^+$ ion optical clocks where both the stability and accuracy of the clocks are greatly improved. In the proposed scheme, two Al$^+$ traps are utilized. The first trap is used to trap a large number of Al$^+$ ions to improve the stability of the clock laser, while the second trap is used to trap a single Al$^+$ ion to provide the ultimate accuracy. Both traps are cooled with a continuous wave 167 nm laser. The expected clock laser stability can reach $9.0\times10^{-17}/\sqrt{\tau}$. For the second trap, in addition to 167 nm laser Doppler cooling, a second stage pulsed 234 nm two-photon cooling laser is utilized to further improve the accuracy of the clock laser. The total systematic uncertainty can be reduced to about $1\times10^{-18}$. The proposed Al$^+$ ion optical clock has the potential to become the most accurate and stable optical clock.

In the context of unified hydrodynamics, we discuss the pseudorapidity distributions of the charged particles produced in Au-Au and Cu-Cu collisions at the low RHIC energies of $\sqrt {s_{\rm NN}}=19.6$ and 22.4 GeV, respectively. It is found that the unified hydrodynamics alone can give a good description to the experimental measurements. This is different from the collisions at the maximum RHIC energy of $\sqrt {s_{\rm NN}}=200$ GeV or at LHC energy of $\sqrt {s_{\rm NN}}=2.76$ TeV, in which the leading particles must be taken into account so that we can properly explain the experimental observations.

Bubble evolution in low energy and high dose He-implanted 6H-SiC upon thermal annealing is studied. The $\langle0001\rangle$-oriented 6H-SiC wafers are implanted with 15 keV helium ions at a dose of 1$\times$10$^{17}$ cm$^{-2}$ at room temperature. The samples with post-implantation are annealed at temperatures of 1073, 1173, 1273, and 1473 K for 30 min. He bubbles in the wafers are examined via cross-sectional transmission electron microscopy (XTEM) analysis. The results present that nanoscale bubbles are almost homogeneously distributed in the damaged layer of the as-implanted sample, and no significant change is observed in the He-implanted sample after 1073 K annealing. Upon 1193 K annealing, almost full recrystallization of He-implantation-induced amorphization in 6H-SiC is observed. In addition, the diameters of He bubbles increase obviously. With continually increasing temperatures to 1273 K and 1473 K, the diameters of He bubbles increase and the number density of lattice defects decreases. The growth of He bubbles after high temperature annealing abides by the Ostwald ripening mechanism. The mean diameter of He bubbles located at depths of 120–135 nm as a function of annealing temperature is fitted in terms of a thermal activated process which yields an activation energy of 1.914+0.236 eV.

A compact laser plasma accelerator that is a novel accelerator based on the interaction of ultra-intense laser and plasmas is being built now at Peking University. According to the results of experiments and numerical simulations, a beam line combining the advantages of quadrupole and analyzing magnets is designed to deliver proton beams with energy ranging from 1 to 44 MeV, energy spread within $\pm$5% and $10^{6-8}$ protons per pulse. It turns out that the existence of space charge force of protons can be ignored for the increase of transverse and longitudinal envelopes even in the case of 10$^{9}$ protons in one pulse. To cope with the challenge to obtain a uniform distribution of protons at the final experiment target in laser acceleration, we manipulate the envelope beam waist in the $Y$ direction to a proper position and obtain a relatively good distribution uniformity of protons with an energy spread of 0–$\pm$5%.

This work reports on the use of the holmium oxide (Ho$_{2}$O$_{3})$ polymer film as a saturable absorber (SA) for generating stable Q-switching pulses operating in a 2-μm region in a thulium-doped fiber laser cavity. The SA is prepared by diluting a commercial Ho$_{3}$O$_{2}$ powder and then mixing it with polyvinyl alcohol (PVA) solution to form a Ho$_{2}$O$_{3}$-PVA film. A tiny part of the film about 1 mm$\times$1 mm in size is sandwiched between two fiber ferrules with the help of index matching gel. When incorporated in a laser cavity driven by a 1552-nm pump, stable Q-switching pulses are observed at 1955 nm within the pump power range of 363–491 mW. As the pump power increases within this range, the repetition rate rises from 26 kHz to 39 kHz, as the pulse width drops from 4.22 μs to 2.57 μs. The laser operates with a signal-to-noise ratio of 47 dB, and the maximum output power and the pulse energy obtained are 2.67 mW and 69 nJ, respectively. Our results successfully demonstrate that the Ho$_{2}$O$_{3 }$ film can be used as a passive SA to generate a 2-μm pulse laser.

Amplifying the attosecond pulse by the chirp pulse amplification method is impossible. Furthermore, the intensity of attosecond pulse is low in the interaction of laser pulse and underdense plasma. This motivates us to propose using a multi-color pulse to produce the high intense attosecond pulse. In the present study, the relativistic interaction of a three-color linearly-polarized laser-pulse with highly overdense plasma is studied. We show that the combination of $\omega_{1}$, $\omega_{2}$ and $\omega_{3}$ frequencies decreases the instance full width at half maximum reflected attosecond pulse train from the overdense plasma surface. Moreover, we show that the three-color pulse increases the intensity of generated harmonics, which is explained by the relativistic oscillating mirror model. The obtained results demonstrate that if the three-color laser pulse interacts with overdense plasma, it will enhance two orders of magnitude of intensity of ultra short attosecond pulses in comparison with monochromatic pulse.

We propose a new approach for generating a multiple focal spot segment of subwavelength size, by tight focusing of a phase modulated radially polarized Laguerre Bessel Gaussian beam. The focusing properties are investigated theoretically by vector diffraction theory. We observe that the focal segment with multiple focal structures is separated with different axial distances and a super long dark channel can be generated by properly tuning the phase of the incident radially polarized Laguerre Bessel Gaussian beam. We presume that such multiple focal patterns and high intense beam may find applications in atom optics, optical manipulations and multiple optical trapping.

Based on the frequency-to-time mapping relation of the linearly chirped pulse, the temporal phase shift induced by a laser-excited wake in a helium gas jet is measured using a chirped-pulse spectral interferometry with $\sim$140 fs resolution over a temporal region of 1 ps in a single shot. In this measurement, the image of the wake is obtained with one-dimensional spatial resolution and temporal resolution limited only by the bandwidth and chirp of the pulse. The 'bubbles' feature of the wake structure, along with multiple wakes excited by the main lobe and the side lobe of a laser focal-spot, is captured simultaneously.

We present a new method to achieve an optical vector network analyzer (OVNA) based on a polarization multiplexing electro-optic modulator (PM-EOM) without an optical bandpass filter. Optical single sideband (OSSB) modulated signals with a tunable optical carrier-sideband ratio (OCSR) are obtained at the output of the PM-EOM. The OCSR can be flexibly tuned by controlling bias voltages of the PM-EOM. The dynamic range of the OVNA is expanded by taking the improvement of the OCSR into account. The transmission response of an optical device under test (ODUT) is measured based on one-to-one mapping from optical domain to electrical domain. By optimizing the OCSR of the OSSB modulated signals, the dynamic range of the OVNA can be effectively improved with 3.7 dB. An analytical model is derived to describe the transfer function of the ODUT. The magnitude and phase responses of a fiber Bragg grating are characterized with a large dynamic range.

In traditional ghost imaging, the entangled photon pairs produced from the spontaneous parametric down conversion (SPDC) process are used. There is an intrinsic disadvantage that the utilization efficiency of the photon pairs is very low. Inasmuch as all the correlated photon pairs produced by the degenerate SPDC process can be used to record the image of an object, the ghost imaging scheme we present here has a higher utilization efficiency of the photon pairs. We also investigate the robustness of our experimental scheme. The experimental results show that, no matter whether the photon-pair source is two light cones or two beam-like spots, the clear image of the object can be obtained. The slight rotation of the nonlinear crystal has no influence on the imaging quality. Our experimental results also demonstrate that when the part of the photon-pair source in the signal path or the idler path is blocked by unwanted things, the clear ghost image of the object can still be recorded.

We present a terahertz (THz) real-time digital holographic system with zoom function worked at 0.17 THz. The magnification factor ranges from 1 to 2. In the imaging experiment, the resolution is 2 mm with the magnification factor of 1.2. A metal sheet with F-shaped hollow is used as a sample, and its THz holograms are reconstructed by our developed algorithm based on the angular spectrum theorem, and the qualities of the THz images under different conditions are compared.

The direct initiation of detonations in one-dimensional (1D) and two-dimensional (2D) cylindrical geometries is investigated through numerical simulations. In comparison of 1D and 2D simulations, it is found that cellular instability has a negative effect on the 2D initiation and makes it more difficult to initiate a sustaining 2D cylindrical detonation. This effect associates closely with the activation energy. For the lower activation energy, the 2D initiation of cylindrical detonations can be achieved through a subcritical initiation way. With increasing the activation energy, the 2D cylindrical detonation has increased difficulty in its initiation due to the presence of unreacted pockets behind the detonation front and usually requires rather larger source energy.

Marangoni–Bénard convection, which is mainly driven by the thermocapillary (Marangoni) effect, occurs in a thin liquid layer heated uniformly from the bottom. The wavenumber of supercritical convection is studied experimentally in a $160\times160$-mm$^{2}$ cavity that is heated from the bottom block. The convection pattern is visualized by an infrared thermography camera. It is shown that the onset of the Bénard cell is consistent with theoretical analysis. The wavenumber decreases obviously with increasing temperature, except for a slight increase near the onset. The wavenumber gradually approaches the minimum when the supercritical number $\varepsilon$ is larger than 10. Finally, a formula is devised to describe the wavenumber selection in supercritical convection.

The hydrodynamic effects of molten surface of titanium alloy on the morphology evolution by intense pulsed ion beam (IPIB) irradiation are studied. It is experimentally revealed that under irradiation of IPIB pulses, the surface morphology of titanium alloy in a spatial scale of μm exhibits an obvious smoothening trend. The mechanism of this phenomenon is explained by the mass transfer caused by the surface tension of molten metal. Hydrodynamic simulation with a combination of the finite element method and the level set method reveals that the change in curvature on the molten surface leads to uneven distribution of surface tension. Mass transfer is caused by the relief of surface tension, and meanwhile a flattening trend in the surface morphology evolution is achieved.

The spallation behaviors of Al+0.2 wt% $^{10}$B targets and neutron irradiated Al+0.2 wt% $^{10}$B targets with 5 nm radius helium bubble subjected to direct laser ablation are presented. It is found that the spall strength increases significantly with the tensile strain rate, and the helium bubble or boron inclusions in aluminum reduces the spall strength of materials by 34%. However, slight difference is observed in the spall strength of unirradiated samples compared with the irradiated sample with helium bubbles.

The capillary force of a liquid bridge with a pinned contact line between a small disk and a parallel plate is investigated by simulation and experiments. The numerical minimization simulation method is utilized to calculate the capillary force. The results show excellent agreement with the Young–Laplace equation method. An experimental setup is built to measure the capillary force. The experimental results indicate that the simulation results agree well with the measured forces at large separation distances, while some deviation may occur due to the transition from the advancing contact angle to the receding one at small distances. It is also found that the measured rupture distance is slightly larger than the simulation value due to the effect of the viscous interaction inside the liquid bridge.

We present a theoretical study of quantum charge pumping in metallic armchair graphene nanoribbons using the Floquet–Green function method. A central part of the ribbon acting as the scattering region is supposed to have staggered sublattice potential to open a finite band gap. A single ac gate is asymmetrically applied to a part of the scattering region to drive the pumping. Corresponding to the gap edges, there are two pumped current peaks with opposite current directions, which can be reversed by changing the position of the ac gate relative to the scattering region. The effects of the parameters, such as the staggered sublattice potential, the driving frequency and the geometric parameters of the structure, on the pumping are discussed.

Positive bias temperature instability stress induced interface trap density in a buried InGaAs channel metal-oxide-semiconductor field-effect transistor with a InGaP barrier layer and Al$_{2}$O$_{3}$ dielectric is investigated. Well behaved split $C$–$V$ characteristics with small capacitance frequency dispersion are confirmed after the insertion of the InGaP barrier layer. The direct-current $I_{\rm d}$–$V_{\rm g}$ measurements show both degradations of positive gate voltage shift and sub-threshold swing in the sub-threshold region, and degradation of positive $\Delta V_{\rm g}$ in the on-current region. The $I_{\rm d}$–$V_{\rm g}$ degradation during the positive bias temperature instability tests is mainly contributed by the generation of near interface acceptor traps under stress. Specifically, the stress induced acceptor traps contain both permanent and recoverable traps. Compared with surface channel InGaAs devices, stress induced recoverable donor traps are negligible in the buried channel ones.

Recently, the concept of topological insulators has been generalized to topological semimetals, including three-dimensional (3D) Weyl semimetals, 3D Dirac semimetals, and 3D node-line semimetals (NLSs). In particular, several compounds (e.g., certain 3D graphene networks, Cu$_{3}$PdN, Ca$_{3}$P$_{2}$) were discovered to be 3D NLSs, in which the conduction and valence bands cross at closed lines in the Brillouin zone. Except for the two-dimensional (2D) Dirac semimetal (e.g., graphene), 2D topological semimetals are much less investigated. Here we propose a new concept of a 2D NLS and suggest that this state could be realized in a new mixed lattice (named as HK lattice) composed by Kagome and honeycomb lattices. It is found that A$_{3}$B$_{2}$ (A is a group-IIB cation and B is a group-VA anion) compounds (such as Hg$_{3}$As$_{2})$ with the HK lattice are 2D NLSs due to the band inversion between the cation Hg-$s$ orbital and the anion As-$p_{z}$ orbital with respect to the mirror symmetry. Since the band inversion occurs between two bands with the same parity, this peculiar 2D NLS could be used as transparent conductors. In the presence of buckling or spin-orbit coupling, the 2D NLS state may turn into a 2D Dirac semimetal state or a 2D topological crystalline insulating state. Since the band gap opening due to buckling or spin-orbit coupling is small, Hg$_{3}$As$_{2}$ with the HK lattice can still be regarded as a 2D NLS at room temperature. Our work suggests a new route to design topological materials without involving states with opposite parities.

Fluorene is a polycyclic aromatic hydrocarbon, which is a hazardous toxic chemical in the environment. The measurement of low concentrations of fluorene is a subject of intense interest in chemistry and in the environment. Polypyrrole chitosan cobalt ferrite nanoparticles are prepared using the electrochemical method. The prepared layers are characterized using field emission scanning electron microscopy, Fourier transform infrared spectroscopy, and energy dispersive spectroscopy. The layers are used to detect fluorene using the surface plasmon resonance technique at room temperature. The composite layer is evaluated after detection of fluorene using atomic force microscopy. The fluorene is bound on the layer, and the shift of the resonance angle is about 0.0052$^{\circ}$, corresponding to the limitation of 0.01 ppm.

Spin polarization in ferromagnetic metal/insulator/spin-filter barrier/nonmagnetic metal, referred to as quasi-magnetic tunnel junctions, is studied within the free-electron model. Our results show that large positive or negative spin-polarization can be obtained at high bias in quasi-magnetic tunnel junctions, and within large bias variation regions, the degree of spin-polarization can be linearly tuned by bias. These linear variation regions of spin-polarization with bias are influenced by the barrier thicknesses, barrier heights and molecular fields in the spin-filter (SF) layer. Among them, the variations of thickness and heights of the insulating and SF barrier layers have influence on the value of spin-polarization and the linear variation regions of spin-polarization with bias. However, the variations of molecular field in the SF layer only have influence on the values of the spin-polarization and the influences on the linear variation regions of spin-polarization with bias are slight.

We investigate the influence of Al preflow time on surface morphology and quality of AlN and GaN. The AlN and GaN layers are grown on a Si (111) substrate by metal organic chemical vapor deposition. Scanning electron microscopy, atomic force microscopy, x-ray diffraction and optical microscopy are used for analysis. Consequently, we find significant differences in the epitaxial properties of AlN buffer and the GaN layer, which are dependent on the Al preflow time. Al preflow layers act as nucleation sites in the case of AlN growth. Compact and uniform AlN nucleation sites are observed with optimizing Al preflow at an early nucleation stage, which will lead to a smooth AlN surface. Trenches and AlN grain clusters appear on the AlN surface while melt-back etching occurs on the GaN surface with excessive Al preflow. The GaN quality variation keeps a similar trend with the AlN quality, which is influenced by Al preflow. With an optimized duration of Al preflow, crystal quality and surface morphology of AlN and GaN could be improved.

Based on power modulation of a pump laser and precessional projection detection, we present an all-optical vector magnetometer of cesium, which has a demonstrated magnitude sensitivity of 80 fT/Hz$^{1/2}$ and an orientation sensitivity of 0.1$^{\circ}$/Hz$^{1/2}$. In the device, four main factors are measured experimentally, which are the Larmor precession frequency of a polarized magnetic moment that depends on the modulus of the measured magnetic field only, two phase shifts and amplitude ratio of the precession projection in the two probe directions relative to the magnetic field orientation. This kind of magnetometer with high sensitivity in the range of the spatial angle is suitable for solving the inverse problem and geomagnetic navigation.

Amorphous InGaZnO$_{4}$ neuron transistors based on multi-gate electric-double-layer modulation are fabricated by photolithography processes. The sweeping rate dependent output current and hysteresis loop are observed due to the proton dynamic process in the SiO$_{2}$ nanogranular electrolyte. Temporal summation such as paired-pulse facilitation is mimicked in the neuron transistor with one presynaptic input. At the same time, supralinear spatial summation of two presynaptic inputs is also successfully mimicked in the neuron transistor with two presynaptic inputs. Our InGaZnO$_{4}$ neuron transistors with temporal and spatial summation function are interesting for the brain-inspired neuromorphic system.

The dynamic characteristic of complex network failure and recovery is one of the main research topics in complex networks. Real world systems such as traffic jams and Internet recovery could be described by the complex network theory. We propose a model to study the recovery process in complex networks. Two different recovery mechanisms are considered in three kinds of networks: external recovery and internal recovery. By simulating the process of the nodes recovery in networks, it is found that the system exhibits the feature of first-order phase transition only when the external recovery is considered. Internal recovery cannot induce such a kind of transitions. As external recovery and internal recovery coexist on networks, the systems will retain the most efficient part of external recovery and internal recovery. Meanwhile, a hysteresis could be observed when increasing or decreasing the failure probability. Finally, a largest degree node protection strategy is proposed for improving the robustness of networks.

Empirical data show that most of the degree distribution of airline networks assume a double power law. In this work, firstly, we assume cities as sites, flight between two cities as an edge between two sites, and build a dynamic evolution model for airline networks by improving the BA model, in which the conception of attractiveness plays a decisive role in the course of evolution of the networks. To this end, we discuss whether the attractiveness depends on the site label $s$ or not separately, finally we obtain analytic degree distribution. As a result, if the attractiveness of a site is independent of the degree distribution of sites, which will follow the double power law, otherwise, it will be scale-free. Moreover, degree distribution depends on the parameters of the models, and some parameters are more sensitive than others.