High-order harmonic generation of ZnO crystals in chirped and static electric fields

High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduced, the interference structure becomes obvious while the harmonic cutoff is not extended. Furthermore, the harmonic efficiency is improved when the static electric field is included. These phenomena are demonstrated by the classical recollision model in real space affected by the waveform of laser field and inversion symmetry. Specifically, the electron motion in k-space shows that the change of waveform and the destruction of the symmetry of the laser field lead to the incomplete X-structure of the crystal-momentum-resolved(k-resolved) inter-band harmonic spectrum. Furthermore, a pre-acceleration process in the solid four-step model is confirmed.

Constructing Hopf Insulator from Geometric Perspective of Hopf Invariant

We propose a method to construct Hopf insulators based on the study of topological defects from the geometric perspective of Hopf invariant I.Firstly,we prove two types of topological defects naturally inhering in the inner differential structure of the Hopf mapping.One type is the four-dimensional point defects.

Weak Merging Scenario of CLASH Cluster A209

We study the structural and dynamical properties of A209 based on Chandra and XMM-Newton observations.We obtain detailed temperature,pressure,and entropy maps with the contour binning method,and find a hot region in the NW direction.The X-ray brightness residual map and corresponding temperature profiles reveal a possible shock front in the NW direction and a cold front feature in the SE direction.Combined with the galaxy luminosity density map we propose a weak merger scenario.A young sub-cluster passing from the SE to NW direction could explain the optical subpeak,the intracluster medium temperature map,the X-ray surface brightness excess,and the X-ray peak offset together.

Production of the X(4014)as the Spin-2 Partner of X(3872)in e^(+)e^(-)Collisions

In 2021,the Belle collaboration reported the first observation of a new structure in theψ(2S)γfinal state produced in the two-photon fusion process.In the hadronic molecule picture,this new structure can be associatedwith the shallow isoscalar D*D* bound state and as such is an excellent candidate for the spin-2 partner of the X(3872)with the quantum numbers J^(PC)=2^(++)conventionally named X_(2).

Statistical physics of hard combinatorial optimization:Vertex cover problem

Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomi＇al （NP）-complete combinatorial opti- mization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.

Steady state equilibrium condition of npe~± gas and its application to astrophysics

The steady equilibrium conditions for a mixed gas of neutrons, protons, electrons, positrons and radiation fields （abbreviated as npe^± gas） with or without external neutrino flux are investigated, and a general chemical potential equilibrium equation μn = μp ＋ Cμe is obtained to describe the steady equilibrium at high temperatures （T 〉 10^9 K）. An analytic fitting formula of coefficient C is presented for the sake of simplicity, when neutrinos and antineutrinos are transparent. It is a simple method to estimate the electron fraction for the steady equilibrium npe^± gas that adopts the corresponding equilibrium condition. As an example, we apply this method to the GRB accretion disk and confirm that the composition in the inner region is approximately in equilibrium when the accretion rate is low. For the case with external neutrino flux, we calculate the initial electron fraction of neutrino-driven wind from the proto-neutron star model M15-l1-r1. The results show that the improved equilibrium condition makes the electron fraction decrease significantly more than the case μn = μp ＋ μe when the time is less than 5s post bounce, which may be useful for r-process nucleosynthesis models.

Effects of sequential decay on collective flows and nuclear stopping power in heavy-ion collisions at intermediate energies

In this study, the rapidity distribution, collective flows, and nuclear stopping power in ^(197)Au+^(197)Au collisions at intermediate energies were investigated using the ultrarelativistic quantum molecular dynamics(UrQMD) model with GEMINI++ code. The UrQMD model was adopted to simulate the dynamic evolution of heavy-ion collisions, whereas the GEMINI++ code was used to simulate the decay of primary fragments produced by UrQMD. The calculated results were compared with the INDRA and FOPI experimental data. It was found that the rapidity distribution, collective flows, and nuclear stopping power were affected to a certain extent by the decay of primary fragments, especially at lower beam energies. Furthermore, the experimental data of the collective flows and nuclear stopping power at the investigated beam energies were better reproduced when the sequential decay effect was included.

Estimation of far-field wavefront error of tilt-to-length distortion coupling in space-based gravitational wave detection

In space-based gravitational wave detection, the estimation of far-field wavefront error of the distorted beam is the precondition for the noise reduction. Zernike polynomials are used to describe the wavefront error of the transmitted distorted beam. The propagation of a laser beam between two telescope apertures is calculated numerically. Far-field wavefront error is estimated with the absolute height of the peak-to-valley phase deviation between the distorted Gaussian beam and a reference distortion-free Gaussian beam. The results show that the pointing jitter is strongly related to the wavefront error. Furthermore, when the jitter decreases 10 times from 100 nrad to 10 nrad, the wavefront error reduces for more than an order of magnitude. In the analysis of multi-parameter minimization, the minimum of wavefront error tends to Z[5,3] Zernike in some parameter ranges. Some Zernikes have a strong correlation with the wavefront error of the received beam. When the aperture diameter increases at Z[5,3] Zernike, the wavefront error is not monotonic and has oscillation.Nevertheless, the wavefront error almost remains constant with the arm length increasing from 10-1Mkm to 10~3Mkm.When the arm length decreases for three orders of magnitude from 10-1Mkm to 10-4Mkm, the wavefront error has only an order of magnitude increasing. In the range of 10-4Mkm to 10~3Mkm, the lowest limit of the wavefront error is from 0.5 fm to 0.015 fm at Z[5,3] Zernike and 10 nrad jitter.

A THEORETICAL CALCULATION OF THE LOW-LYING BRANCHES OF PHONON DISPERSION RELATIONS FOR α-LiIO_(3)

A preliminary calculation for the low-lying branches of phonon dispersion relations of α-LiIO3 in directions [001], [100] and [110] using a simplified model are reported. In addition, we point out that coupling between different vibration modes may be important in lattice dynamics of such crystals.

Topological properties of tetratomic Su-Schrieffer-Heeger chains with hierarchical long-range hopping

We propose a new generalized Su–Schrieffer–Heeger model with hierarchical long-range hopping based on a onedimensional tetratomic chain. The properties of the topological states and phase transition, which depend on the cointeraction of the intracell and intercell hoppings, are investigated using the phase diagram of the winding number. It is shown that topological states with large positive/negative winding numbers can readily be generated in this system. The properties of the topological states can be verified by the ring-type structures in the trajectory diagram of the complex plane. The topological phase transition is strongly related to the opening(closure) of an energy bandgap at the center(boundaries) of the Brillouin zone. Finally, the non-zero-energy edge states at the ends of the finite system are revealed and matched with the bulk–boundary correspondence.

Ground-state phase diagram,symmetries,excitation spectra and finite-frequency scaling of the two-mode quantum Rabi model

We investigate the two-mode quantum Rabi model(QRM)describing the interaction between a two-level atom and a two-mode cavity field.The quantum phase transitions are found when the ratioηof transition frequency of atom to frequency of cavity field approaches infinity.We apply the Schrieffer–Wolff(SW)transformation to derive the low-energy effective Hamiltonian of the two-mode QRM,thus yielding the critical point and rich phase diagram of quantum phase transitions.The phase diagram consists of four regions:a normal phase,an electric superradiant phase,a magnetic superradiant phase and an electromagnetic superradiant phase.The quantum phase transition between the normal phase and the electric(magnetic)superradiant phase is of second order and associates with the breaking of the discrete Z_(2) symmetry.On the other hand,the phase transition between the electric superradiant phase and the magnetic superradiant phase is of first order and relates to the breaking of the continuous U(1)symmetry.Several important physical quantities,for example the excitation energy and average photon number in the four phases,are derived.We find that the excitation spectra exhibit the Nambu–Goldstone mode.We calculate analytically the higher-order correction and finite-frequency exponents of relevant quantities.To confirm the validity of the low-energy effective Hamiltonians analytically derived by us,the finite-frequency scaling relation of the averaged photon numbers is calculated by numerically diagonalizing the two-mode quantum Rabi Hamiltonian.

Three-dimensional numerical simulation of heating and melting behaviors of cerium oxide powders in radio frequency thermal plasma

The present study aims at the numerical simulations of the melting process of cerium oxide particles in RF thermal plasma.The physical model and the calculating method were described firstly;the interaction between cerium oxide particles and plasma was analyzed;specific attention was given to the effects of particle initial size,injection velocity on the particle melting and trajectory in plasma.The influence of the temperature field and velocity field distribution of the plasma around the particle trajectory on the melting effect is analyzed,and the relationship between the heat absorption efficiency of the particles and the particle size reduction process is further determined.It is also found that there exists an optimal particle initial injection velocity which led to a more concentrated final particle size distribution and a more significant reduction of particle size.The results could provide effective guidance for understanding the plasma spheroidization process of uranium dioxide and cerium dioxide powder particles.

Effects of quantum quench on entanglement dynamics in antiferromagnetic Ising model

We study the relationship between quench dynamics of entanglement and quantum phase transition in the antiferromagnetic Ising model with the Dzyaloshinskii–Moriya(DM)interaction by using the quantum renormalization-group method and the definition of negativity.Two types of quench protocols(i)adding the DM interaction suddenly and(ii)rotating the spins around x axis are considered to drive the dynamics of the system,respectively.By comparing the behaviors of entanglement in both types of quench protocols,the effects of quench on dynamics of entanglement are studied.It is found that there is the same characteristic time at which the negativity firstly reaches its maximum although the system shows different dynamical behaviors.Especially,the characteristic time can accurately reflect the quantum phase transition from antiferromagnetic to saturated chiral phases in the system.In addition,the correlation length exponent can be obtained by exploring the nonanalytic and scaling behaviors of the derivative of the characteristic time.

The Width-Flux Relation of the Broad Iron KαLine during the State Transitions of the Black Hole X-Ray Binaries

The observations of varying broad iron lines during the state transition of the black hole X-ray binaries have been accumulating.In this work,the relation between the normalized intensity and the width of iron lines is investigated,in order to understand better the variation of iron lines and possibly its connection to state transition.Considering the uncertainties due to ionization and illuminating X-rays,only the effects of geometry and gravity are taken into account.Three scenarios were studied,i.e.,the continuous disk model,the innermost annulus model,and the cloud model.As shown by our calculations,at given iron width,the line flux of the cloud model is smaller than that of the continuous disk model;while for the innermost annulus model,the width is almost unrelated with the flux.The range of the line strength depends on both the BH spin and the inclination of the disk.We then apply to the observation of MAXI J1631-479 by Nuclear Spectroscopic Telescope Array during its decay from the soft state to the intermediate state.We estimated the relative line strength and width according to the spectral fitting results in Xu et al.,and then compared with our theoretical width-flux relation.It was found that the cloud model was more favored.We further modeled the iron line profiles,and found that the cloud model can explain both the line profile and its variation with reasonable parameters.

The Year-scale X-Ray Variations in the Core of M87

The analysis of light variation of M87 can help us understand the disk evolution.In the past decade,M87 has experienced several short-term light variabilities related to flares.We also find that there are year-scale X-ray variations in the core of M87.Their light variability properties are similar to clumpy-ADAF.By re-analyzing 56Chandra observations from 2007 to 2019,we distinguish the“non-flaring state”from“flaring state”in the light variability.After removing flaring state data,we identify four gas clumps in the nucleus and all of them can be well fitted by the clumpy-ADAF model.The average mass accretion rate is~0.16M⊙yr^(-1).We analyze the photon index(Γ)-flux(2-10 keV)correlation between the non-flaring state and flaring state.For the non-flaring states,the flux is inversely proportional to the photon index.For the flaring states,we find no obvious correlation between the two parameters.In addition,we find that the flare always occurs at a high mass accretion rate,and after the luminosity of the flare reaches the peak,it will be accompanied by a sudden decrease in luminosity.Our results can be explained as that the energy released by magnetic reconnection destroys the structure of the accretion disk,thus the luminosity decreases rapidly and returns to normal levels thereafter.

Dynamics of Fokker-Planck Equation with Logarithmic Coefficients and Its Application in Econophysics

We demonstrate that Fokker Planck equations with logarithmic factors in diffusion and drift terms can be straightforwardly derived from the class of ＂constant elasticity of variance＂ stochastic processes without appealing to any symmetry argument, Analytical closed-form solutions are available for some special cases of this class of Fokker-Planck equations. The dynamics of the underlying stochastic variables are examined. These Fokker-Planck equations have found a rather wide range of applications in various contexts. In particular, in the field of econophysics we have demonstrated their immediate relevance to modelling the exchange rate dynamics in a target zone, e.g. the linked exchange rate system of the Hong Kong dollar. Furthermore, the knowledge of exact solutions in some special cases can be useful as a benchmark to test approximate numerical or analytical procedures.

Erratum:Cobalt-Dimer Nitrides:A Potential Novel Family of High-Temperature Superconductors[Chin.Phys.Lett.39,097401(2022)]

Fig.1.(a)Structure of Co_(2)N_(2) dimer.(b)Structure;of Co_(2)N_(2) layer.The dashed black lines show the mirror symmetries.X,Y coordinates are defined according to the direction of the Co Co bond,and x,y are the global coordinates in the conventional crystal structure.

Pulsation Analysis of High-AmplitudeδScuti Stars with TESS

In this work,the pulsation analysis is performed on 83 high-amplitudeδScuti stars(HADS),which have been observed by the Transiting Exoplanet Survey Satellite.The results show that 49 of these HADS show single-mode pulsation,27 of them show radial double-modes pulsation(in which 22 of them pulsate with the fundamental and first overtone modes and five of them pulsate with the first and second overtone modes),and seven of them show radial triple-modes pulsation(three of which are newly confirmed triple-mode HADS).The histogram of the fundamental periods and the ratios between the fundamental and first overtone periods show bimodal structures,which might be caused by the stellar evolution in this specific phase.Most of the radial triple-mode HADS have a fundamental amplitude of 41-54 mmag,and 50%of them have similar amplitudes of the fundamental and first overtone pulsation modes.All these hints require further confirmation not only in observations with more HADS samples,but also in theoretical models with suitable treatments of stellar evolution and pulsation.

Variational quantum simulation of thermal statistical states on a superconducting quantum processer

Quantum computers promise to solve finite-temperature properties of quantum many-body systems,which is generally challenging for classical computers due to high computational complexities.Here,we report experimental preparations of Gibbs states and excited states of Heisenberg X X and X X Z models by using a 5-qubit programmable superconducting processor.In the experiments,we apply a hybrid quantum–classical algorithm to generate finite temperature states with classical probability models and variational quantum circuits.We reveal that the Hamiltonians can be fully diagonalized with optimized quantum circuits,which enable us to prepare excited states at arbitrary energy density.We demonstrate that the approach has a self-verifying feature and can estimate fundamental thermal observables with a small statistical error.Based on numerical results,we further show that the time complexity of our approach scales polynomially in the number of qubits,revealing its potential in solving large-scale problems.