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Mapping the electrostatic potential (ESP) distribution around ions in electrolyte solution is crucial for the establishment of a microscopic understanding of electrolyte solution properties. For solutions in the bulk phase, it has not been possible to measure the ESP distribution on Angstrom scale. Here we show that liquid electron scattering experiment using state-of-the-art relativistic electron beam can be used to measure the Debye screening length of aqueous LiCl, KCl, and KI solutions across a wide range of concentrations. We observe that the Debye screening length is long-ranged at low concentration and short-ranged at high concentration, providing key insight into the decades-long debate over whether the impact of ions in water is long-ranged or short-ranged. In addition, we show that the measured ESP can be used to retrieve the non-local dielectric function of electrolyte solution, which can serve as a promising route to investigate the electrostatic origin of special ion effects. Our observations show that, interaction, as one of the two fundamental perspectives for understanding electrolyte solution, can provide much richer information than structure.

Neural interactions occur on different levels and scales. It is of particular importance to understand how they are distributed among different neuroanatomical and physiological relevant brain regions. We investigated neural cross-frequency couplings between different brain regions according to the Desikan-Killiany brain parcellation. The adaptive dynamic Bayesian inference method was applied to EEG measurements of healthy resting subjects in order to reconstruct the coupling functions. It was found that even after averaging over all subjects, the mean coupling function showed a characteristic waveform, confirming the direct influence of the delta-phase on the alpha-phase dynamics in certain brain regions and that the shape of the coupling function changes for different regions. While the averaged coupling function within a region was of similar form, the region-averaged coupling function was averaged out, which implies that there is a common dependence within separate regions across the subjects. It was also found that for certain regions the influence of delta on alpha oscillations is more pronounced and that oscillations that influence other are more evenly distributed across brain regions than the influenced oscillations. When presenting the information on brain lobes, it was shown that the influence of delta emanating from the brain as a whole is greatest on the alpha oscillations of the cingulate frontal lobe, and at the same time the influence of delta from the cingulate parietal brain lobe is greatest on the alpha oscillations of the whole brain.

Two-dimensional (2D) heterostructures integrated into nanophotonic cavities have emerged as a promising approach towards novel photonic and opto-electronic devices. However, the thickness of the 2D heterostructure has a strong influence on the resonance frequency of the nanocavity. For a single cavity, the resonance frequency shifts approximately linearly with the thickness. Here, we propose to use the inherent non-linearity of the mode coupling to render the cavity mode insensitive to the thickness of the 2D heterostructure. Based on the coupled mode theory, we reveal that this goal can be achieved using either a homoatomic molecule with a filtered coupling or heteroatomic molecules. We perform numerical simulations to further demonstrate the robustness of the eigenfrequency in the proposed photonic molecules. Our results render nanophotonic structures insensitive to the thickness of 2D materials, thus owing appealing potential in energy- or detuning-sensitive applications such as cavity quantum electrodynamics.

Spin defects in hexagonal Boron Nitride (hBN) attract increasing interest for quantum technology since they represent optically-addressable qubits in a van der Waals material. In particular, negatively-charged boron vacancy centers (${V_B}^-$) in hBN have shown promise as sensors of temperature, pressure, and static magnetic fields. However, the short spin coherence time of this defect currently limits its scope for quantum technology. Here, we apply dynamical decoupling techniques to suppress magnetic noise and extend the spin coherence time by nearly two orders of magnitude, approaching the fundamental $T_1$ relaxation limit. Based on this improvement, we demonstrate advanced spin control and a set of quantum sensing protocols to detect electromagnetic signals in the MHz range with sub-Hz resolution. This work lays the foundation for nanoscale sensing using spin defects in an exfoliable material and opens a promising path to quantum sensors and quantum networks integrated into ultra-thin structures.

The airline industry was severely hit by the COVID-19 crisis with an average demand decrease of about $64\%$ (IATA, April 2020) which triggered already several bankruptcies of airline companies all over the world. While the robustness of the world airline network (WAN) was mostly studied as an homogeneous network, we introduce a new tool for analyzing the impact of a company failure: the `airline company network' where two airlines are connected if they share at least one route segment. Using this tool, we observe that the failure of companies well connected with others has the largest impact on the connectivity of the WAN. We then explore how the global demand reduction affects airlines differently, and provide an analysis of different scenarios if its stays low and does not come back to its pre-crisis level. Using traffic data from the Official Aviation Guide (OAG) and simple assumptions about customer's airline choice strategies, we find that the local effective demand can be much lower than the average one, especially for companies that are not monopolistic and share their segments with larger companies. Even if the average demand comes back to $60\%$ of the total capacity, we find that between $46\%$ and $59\%$ of the companies could experience a reduction of more than $50\%$ of their traffic, depending on the type of competitive advantage that drives customer's airline choice. These results highlight how the complex competitive structure of the WAN weakens its robustness when facing such a large crisis.

The dynamical and structural aspects of cluster synchronization (CS) in complex systems have been intensively investigated in recent years. Here, we study CS of dynamical systems with intra and inter-cluster couplings. We propose new metrics that describe the performance of such systems and evaluate them as a function of the strength of the couplings within and between clusters. We obtain analytical results that indicate that spectral differences between the Laplacian matrices associated with the partition between intra and inter-couplings directly affect the proposed metrics of system performance. Our results show that the dynamics of the system might exhibit an optimal balance that optimizes its performance. Our work provides new insights into the way specific symmetry properties relate to collective behavior, and could lead to new forms to increase the controllability of complex systems and to optimize their stability.

In this paper, we focus on the emergence of diverse neuronal oscillations arising in a mixed population of neurons with different excitability properties. These properties produce mixed mode oscillations (MMOs) characterized by the combination of large amplitudes and alternate subthreshold or small amplitude oscillations. Considering the biophysically plausible, Izhikevich neuron model, we demonstrate that various MMOs, including MMBOs (mixed mode bursting oscillations) and synchronized tonic spiking appear in a randomly connected network of neurons, where a fraction of them is in a quiescent (silent) state and the rest in self-oscillatory (firing) states. We show that MMOs and other patterns of neural activity depend on the number of oscillatory neighbors of quiescent nodes and on electrical coupling strengths. Our results are verified by constructing a reduced-order network model and supported by systematic bifurcation diagrams as well as for a small-world network. Our results suggest that, for weak couplings, MMOs appear due to the de-synchronization of a large number of quiescent neurons in the networks. The quiescent neurons together with the firing neurons produce high frequency oscillations and bursting activity. The overarching goal is to uncover a favorable network architecture and suitable parameter spaces where Izhikevich model neurons generate diverse responses ranging from MMOs to tonic spiking.

Understanding how interurban movements can modify the spatial distribution of the population is important for transport planning but is also a fundamental ingredient for epidemic modeling. We focus here on vacation trips (for all transportation modes) during the Chinese Lunar New Year and compare the results for 2019 with the ones for 2020 where travel bans were applied for mitigating the spread of a novel coronavirus (COVID-19). We first show that these travel flows are broadly distributed and display both large temporal and spatial fluctuations, making their modeling very difficult. When flows are larger, they appear to be more dispersed over a larger number of origins and destinations, creating de facto hubs that can spread an epidemic at a large scale. These movements quickly induce (in about a week) a very strong population concentration in a small set of cities. We characterize quantitatively the return to the initial distribution by defining a pendular ratio which allows us to show that this dynamics is very slow and even stopped for the 2020 Lunar New Year due to travel restrictions. Travel restrictions obviously limit the spread of the diseases between different cities, but have thus the counter-effect of keeping high concentration in a small set of cities, a priori favoring intra-city spread, unless individual contacts are strongly limited. These results shed some light on how interurban movements modify the national distribution of populations, a crucial ingredient for devising effective control strategies at a national level.

In dark matter direct detection experiments, neutron is a serious source of background, which can mimic the dark matter-nucleus scattering signals. In this paper, we present an improved evaluation of the neutron background in the PandaX-II dark matter experiment by a novel approach. Instead of fully relying on the Monte Carlo simulation, the overall neutron background is determined from the neutron-induced high energy signals in the data. In addition, the probability of producing a dark-matter-like background per neutron is evaluated with a complete Monte Carlo generator, where the correlated emission of neutron(s) and $\gamma$(s) in the ($\alpha$, n) reactions and spontaneous fissions is taken into consideration. With this method, the neutron backgrounds in the Run 9 (26-ton-day) and Run 10 (28-ton-day) data sets of PandaX-II are estimated to be 0.66$\pm$0.24 and 0.47$\pm$0.25 events, respectively.

We report the Neutrino-less Double Beta Decay (NLDBD) search results from PandaX-II dual-phase liquid xenon time projection chamber. The total live time used in this analysis is 403.1 days from June 2016 to August 2018. With NLDBD-optimized event selection criteria, we obtain a fiducial mass of 219 kg of natural xenon. The accumulated xenon exposure is 242 kg$\cdot$yr, or equivalently 22.2 kg$\cdot$yr of $^{136}$Xe exposure. At the region around $^{136}$Xe decay Q-value of 2458 keV, the energy resolution of PandaX-II is 4.2%. We find no evidence of NLDBD in PandaX-II and establish a lower limit for decay half-life of 2.4 $ \times 10^{23} $ yr at the 90% confidence level, which corresponds to an effective Majorana neutrino mass $m_{\beta \beta} < (1.3 - 3.5)$ eV. This is the first NLDBD result reported from a dual-phase xenon experiment.

Excessively high, neural synchronisation has been associated with epileptic seizures, one of the most common brain diseases worldwide. A better understanding of neural synchronisation mechanisms can thus help control or even treat epilepsy. In this paper, we study neural synchronisation in a random network where nodes are neurons with excitatory and inhibitory synapses, and neural activity for each node is provided by the adaptive exponential integrate-and-fire model. In this framework, we verify that the decrease in the influence of inhibition can generate synchronisation originating from a pattern of desynchronised spikes. The transition from desynchronous spikes to synchronous bursts of activity, induced by varying the synaptic coupling, emerges in a hysteresis loop due to bistability where abnormal (excessively high synchronous) regimes exist. We verify that, for parameters in the bistability regime, a square current pulse can trigger excessively high (abnormal) synchronisation, a process that can reproduce features of epileptic seizures. Then, we show that it is possible to suppress such abnormal synchronisation by applying a small-amplitude external current on less than 10% of the neurons in the network. Our results demonstrate that external electrical stimulation not only can trigger synchronous behaviour, but more importantly, it can be used as a means to reduce abnormal synchronisation and thus, control or treat effectively epileptic seizures.

Self-sustained activity in the brain is observed in the absence of external stimuli and contributes to signal propagation, neural coding, and dynamic stability. It also plays an important role in cognitive processes. In this work, by means of studying intracellular recordings from CA1 neurons in rats and results from numerical simulations, we demonstrate that self-sustained activity presents high variability of patterns, such as low neural firing rates and activity in the form of small-bursts in distinct neurons. In our numerical simulations, we consider random networks composed of coupled, adaptive exponential integrate-and-fire neurons. The neural dynamics in the random networks simulate regular spiking (excitatory) and fast-spiking (inhibitory) neurons. We show that both the connection probability and network size are fundamental properties that give rise to self-sustained activity in qualitative agreement with our experimental results. Finally, we provide a more detailed description of the self-sustained activity in terms of lifetime distributions, synaptic conductances, and synaptic currents.

The PandaX-4T experiment, a four-ton scale dark matter direct detection experiment, is being planned at the China Jinping Underground Laboratory. In this paper we present a simulation study of the expected background in this experiment. In a 2.8-ton fiducial mass and the signal region between 1 to 10 keV electron equivalent energy, the total electron recoil background is found to be 4.9x10^-5 /(kg day keV). The nuclear recoil background in the same region is 2.8x10^-7/(kg day keV). With an exposure of 5.6 ton-years, the sensitivity of PandaX-4T could reach a minimum spin-independent dark matter-nucleon cross section of 6x10^-48 cm^2 at a dark matter mass of 40 GeV/c^2.

We report the first observation of multi-photon photoluminescence excitation (PLE) below the resonant energies of nitrogen vacancy (NV) centers in diamond. The quadratic and cubic dependence of the integrated fluorescence intensity as a function of excitation power indicate a two-photon excitation pathway for the NV- charge state and a three-photon process involved for the neutral NV0 charge state respectively. Comparing the total multi-photon energy with its single-photon equivalent, the PLE spectra follows the absorption spectrum of single photon excitation. We also observed that the efficiency of photoluminescence for different charge states, as well as the decay time constant, was dependent on the excitation wavelength and power.

The femtosecond laser pulse heating of silver film is investigated by performing quantum mechanics (QM), molecular dynamics (MD) and two temperature model (TTM) integrated multiscale simulation. The laser excitation dependent electron thermophysical parameters (electron heat capacity, electron thermal conductivity, and effective electron-phonon coupling factor) are determined from ab initio QM calculation, and implemented into TTM description of electron thermal excitation, heat conduction, as well as electron-phonon coupled thermal energy transport. The kinetics of atomic motion is modeled by MD simulation. Energy evolution of excited electron subsystem is described by TTM in continuum. The MD and TTM are coupled by utilizing the effective electron-phonon coupling factor. Laser heating with varying laser fluence is systematically studied to determine the thresholds of the homogeneous melting and ablation. The thermal ablation induced by faster expansion of locally and excessively superheated silver is reported. This paper provides a basis for interpreting the phase change process induced by laser heating, and facilitates the advancement of femtosecond laser pulse processing of material.

By combining ab initio quantum mechanics calculation and Drude model, electron temperature and lattice temperature dependent electron thermal conductivity is calculated and implemented into a multiscale model of laser material interaction, which couples the classical molecular dynamics and two-temperature model. The results indicated that the electron thermal conductivity obtained from ab initio calculation leads to faster thermal diffusion than that using the electron thermal conductivity from empirical determination, which further induces deeper melting region, larger number of density waves travelling inside the copper film and more various speeds of atomic clusters ablated from the irradiated film surface.

A two-dimensional axisymmetric transient laser drilling model is used to analyze the effects of laser beam diameter and laser pulse duration on the laser drilling process. The model includes conduction and convection heat transfer, melting, solidification and vaporization, as well as material removal resulting from the vaporization and melt ejection. The validated model is applied to study the effects of laser beam size and pulse duration on the geometry of the drilled hole. It is found that the ablation effect decrease with the increasing beam diameter due to the effect of increased vaporization rate, and deeper hole is observed for the larger pulse width due to the higher thermal ablation efficiency.

Understanding heat transfer characteristics of phase change and enhancing thermal energy transport in nanoscale are of great interest in both theoretical and practical applications. In the present study, we investigated the nanoscale vaporization and condensation by using molecular dynamics simulation. A cuboid system is modeled by placing hot and cold walls in the bottom and top ends and filling with working fluid between the two walls. By setting two different high temperatures for the hot wall, we showed the normal and explosive vaporizations and their impacts on thermal transport. For the cold wall, the cuboid nanostructures with fixed height, varied length, width ranging from 4 to 20 layers, and an interval of 4 layers are constructed to study the effects of condensation induced by different nanostructures. For vaporization, the results showed that higher temperature of the hot wall led to faster transport of the working fluid as a cluster moving from the hot wall to the cold wall. However, excessive temperature of the hot wall causes explosive boiling, which seems not good for the transport of heat due to the less phase change of working fluid. For condensation, the results indicate that nanostructure facilitates condensation, which could be affected not only by the increased surface area but also by the distances between surfaces of the nanostructures and the cold end. There is an optimal nanosctructure scheme which maximizes the phase change rate of the entire system.

The electron temperature dependent electron density of states, Fermi-Dirac distribution, and electron-phonon spectral function are computed as prerequisites before achieving effective electron-phonon coupling factor. The obtained coupling factor is implemented into a molecular dynamics (MD) and two-temperature model (TTM) coupled simulation of femtosecond laser heating. By monitoring temperature evolutions of electron and lattice subsystems, the result utilizing coupling factor from ab initio calculation, shows a faster decrease of electron temperature and increase of lattice temperature than those using coupling factor from phenomenological treatment. The approach of calculating coupling factor and its implementation into MD-TTM simulation is applicable to other metals.

On the basis of ab initio quantum mechanics (QM) calculation, the obtained electron heat capacity is implemented into energy equation of electron subsystem in two temperature model (TTM). Upon laser irradiation on the copper film, energy transfer from the electron subsystem to the lattice subsystem is modeled by including the electron-phonon coupling factor in molecular dynamics (MD) and TTM coupled simulation. The results show temperature and thermal melting difference between the QM-MD-TTM integrated simulation and pure MD-TTM coupled simulation. The successful construction of the QM-MD-TTM integrated simulation provide a general way that is accessible to other metals in laser heating.

First-principles molecular dynamics simulation based on a plane wave/pseudopotential implementation of density functional theory is adopted to investigate atomic scale energy transport for semiconductors (silicon and germanium). By imposing thermostats to keep constant temperatures of the nanoscale thin layers, initial thermal non-equilibrium between the neighboring layers is established under the vacuum condition. Models with variable gap distances with an interval of lattice constant increment of the simulated materials are set up and statistical comparisons of temperature evolution curves are made. Moreover, the equilibration time from non-equilibrium state to thermal equilibrium state of different silicon or/and germanium layers combinations are calculated. The results show significant distinctions of heat transfer under different materials and temperatures combinations. Further discussions on the equilibrium time are made to explain the simulation results. As the first work of the atomic scale energy transport spanning from heat conduction to thermal radiation, the simulation results here highlights the promising application of the first-principles molecular dynamics in thermal engineering.

The structural, dynamic, and vibrational properties during the heat transfer process in Si/Ge superlattices, are studied by analyzing the trajectories generated by the ab initio Car-Parrinello molecular dynamics simulation. The radial distribution functions and mean square displacements are calculated and further discussions are made to explain and probe the structural changes relating to the heat transfer phenomenon. Furthermore, the vibrational density of states of the two layers (Si/Ge) are computed and plotted to analyze the contributions of phonons with different frequencies to the heat conduction. Coherent heat conduction of the low frequency phonons is found and their contributions to facilitate heat transfer are confirmed. The Car-Parrinello molecular dynamics simulation outputs in the work show reasonable thermophysical results of the thermal energy transport process and shed light on the potential applications of treating the heat transfer in the superlattices of semiconductor materials from a quantum mechanical molecular dynamics simulation perspective.

An ab initio molecular dynamics study of femtosecond laser processing of germanium is presented in this paper. The method based on the finite temperature density functional theory is adopted to probe the structural change, thermal motion of the atoms, dynamic property of the velocity autocorrelation, and the vibrational density of states. Starting from a cubic system at room temperature (300 K) containing 64 germanium atoms with an ordered arrangement of 1.132 nm in each dimension, the femtosecond laser processing is simulated by imposing the Nose Hoover thermostat to the electronic subsystem lasting for ~100 fs and continuing with microcanonical ensemble simulation of ~200 fs. The simulation results show solid, liquid and gas phases of germanium under adjusted intensities of the femtosecond laser irradiation. We find the irradiated germanium distinguishes from the usual germanium crystal by analyzing their melting and dynamic properties.

Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.

We present a simple and effective method of loading particles into an optical trap in air at atmospheric pressure. Material which is highly absorptive at the trapping laser wavelength, such as tartrazine dye, is used as media to attach photoluminescent diamond nanocrystals. The mix is burnt into a cloud of air-borne particles as the material is swept near the trapping laser focus on a glass slide. Particles are then trapped with the laser used for burning or transferred to a second laser trap at a different wavelength. Evidence of successfully loading diamond nanocrystals into the trap presented includes high sensitivity of the photoluminecscence (PL) to an excitation laser at 520~nm wavelength and the PL spectra of the optically trapped particles. This method provides a convenient technique for the study of the nitrogen-vacancy (NV) centers contained in optically trapped diamond nanocrystals.

In this paper we analyze the second-order Kuramoto model presenting a positive correlation between the heterogeneity of the connections and the natural frequencies in scale-free networks. We numerically show that discontinuous transitions emerge not just in disassortative but also in assortative networks, in contrast with the first-order model. We also find that the effect of assortativity on network synchronization can be compensated by adjusting the phase damping. Our results show that it is possible to control collective behavior of damped Kuramoto oscillators by tuning the network structure or by adjusting the dissipation related to the phases movement.

We have collected and cleaned two network data sets: Coauthorship and Citation networks for statisticians. The data sets are based on all research papers published in four of the top journals in statistics from $2003$ to the first half of $2012$. We analyze the data sets from many different perspectives, focusing on (a) centrality, (b) community structures, and (c) productivity, patterns and trends. For (a), we have identified the most prolific/collaborative/highly cited authors. We have also identified a handful of "hot" papers, suggesting "Variable Selection" as one of the "hot" areas. For (b), we have identified about $15$ meaningful communities or research groups, including large-size ones such as "Spatial Statistics", "Large-Scale Multiple Testing", "Variable Selection" as well as small-size ones such as "Dimensional Reduction", "Objective Bayes", "Quantile Regression", and "Theoretical Machine Learning". For (c), we find that over the 10-year period, both the average number of papers per author and the fraction of self citations have been decreasing, but the proportion of distant citations has been increasing. These suggest that the statistics community has become increasingly more collaborative, competitive, and globalized. Our findings shed light on research habits, trends, and topological patterns of statisticians. The data sets provide a fertile ground for future researches on or related to social networks of statisticians.

Low-dimensional behavior of large systems of globally coupled oscillators has been intensively investigated since the introduction of the Ott-Antonsen ansatz. In this report, we generalize the Ott-Antonsen ansatz to second-order Kuramoto models in complex networks. With an additional inertia term, we find a low-dimensional behavior similar to the first-order Kuramoto model, derive a self-consistent equation and seek the time-dependent derivation of the order parameter. Numerical simulations are also conducted to verify our analytical results.

The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of traditional configuration models, networks generated through these models fail to describe many topological features of real-world networks, in particular non-null values of the clustering coefficient. Here we study effects of cycles of order three (triangles) in network spectra. By using recent advances in random matrix theory, we determine the spectral distribution of the network adjacency matrix as a function of the average number of triangles attached to each node for networks without modular structure and degree-degree correlations. Implications to network dynamics are discussed. Our findings can shed light in the study of how particular kinds of subgraphs influence network dynamics.

The classical nonlinear laser-plasma interaction theory is corrected. Given the effects of vacuum polarization (induced by extreme laser) as nonlinear media response, one-dimensional wave equations of a monochromatic laser field are derived from the Heisenberg-Euler Lagrangian density and a derivative correction with the first order quantum electrodynamic (QED) effects. A more suitable model to formulate the interactions of extreme laser and high-energy-density plasma is developed. In the results, the enhanced effect of vacuum polarization will be discussed and shown.

The emergence of explosive synchronization has been reported as an abrupt transition in complex networks of first-order Kuramoto oscillators. In this Letter, we demonstrate that the nodes in a second-order Kuramoto model, perform a cascade of transitions toward a synchronous macroscopic state, which is a novel phenomenon that we call \textitcluster explosive synchronization. We provide a rigorous analytical treatment using a mean-field analysis in uncorrelated networks. Our findings are in good agreement with numerical simulations and fundamentally deepen the understanding of microscopic mechanisms toward synchronization.

The propagation of emissions in the relativistic streaming pair plasmas of pulsars and magnetars is studied within the framework of Gordon effective metric theory, and the effect of vacuum polarization on the radiation spectra is examined particularly. It is found that the electromagnetic and kinetic effects of streaming magnetized plasmas and the vacuum polarization effect can shift the radiation spectra of stars. The modification of redshifts of spectra can reach the same magnitude as the gravitational redshift in particular cases. Moreover, the redshifts induced by the media are anisotropic and associated with wave modes. For the O-mode, the modification of redshifts is dependent on the frequency of the radiation. For lower-frequency radiation, the modification is dominated by the plasma effect, while for higher-frequency radiations, by the vacuum polarization effect. For the X-mode, the modification is non-dispersive and dominated by the vacuum polarization effect. The vacuum polarization also has a significant effect on the redshifts of X-ray emissions in magnetars.

By means of the optical metric, we investigate the propagation of a polarized light in an inhomogeneous medium in this paper. We find that the evolution of photons is affected by the spin-spin interaction of photons, besides the spin-orbit interaction. Due to the spin-spin interaction, there is a small deflection of the ray trajectory of the polarized light along the direction of the inhomogeneity gradient of the medium. It is different from the transverse deflection described by the spin Hall effect of photons.

On the viewpoint of corpuscular model an electromagnetic radiation can be regarded as a system composed of photons with different energies and momenta, which provides us a method being different from the Maxwell wave theory to describe the interaction of electromagnetic waves with plasmas. In this paper the evolution behavior of a single photon and the collective effect of a photon system in plasma waves are uniformly described in the frame of photon dynamics. In a small-amplitude plasma wave the modulation of photon dynamical behavior by the plasma wave can be treated as perturbation, and the photon acceleration effect and photon Landau damping are investigated in the linear theory. In a plasma wave with arbitrary amplitude the photon evolution trajectories in phase space and coordinate space are obtained by solving the dynamical equations, and the trapping condition and possibility of photons in the given plasma wave are also discussed.

We present a description of the evolution of a polarized Gaussian beam in a smoothly inhomogeneous isotropic medium in frame of the eikonal-based complex geometrical optics which describes the phase front and the cross section of the Gaussian beam using the quadratic expansion of the complex-valued eikonal. The linear complex-valued eikonal components are introduced to describe the influence of the spin-orbit interaction and the deformation of a polarized Gaussian beam on the propagation firstly in this paper. In an inhomogeneous medium, the interaction between the polarization and the rotation deformation of the light beam is presented besides the spin-orbit interaction, it corresponds to the spin-intrinsic orbital angular momentum interaction and makes the correction for the spin Hall effect of a polarized Gaussian light beam.