Exact Solution to Spin Squeezing of the Arbitrary-Range Spin Interaction and Transverse Field Model

We investigate spin squeezing effects of trapped ions in an off-resonance optical potential system using the arbitrary range spin spin interaction and transverse field model. The collective spin noises at any time are analyzed exactly. The general expression of spin squeezing factor is presented for arbitrary-range spin interaction. For the nearest-neighbor and next-nearest neighbor spin interaction model, the analytic solutions are reduced from the general expressions. It is shown that the maximum spin squeezing is enhanced for the general arbitrary-range spin interaction compared with the nearest-neighbor interaction model as the long-range interaction with arbitrary sites enforces stronger correlation.

Effects of Transverse Field on Internal Energy and Specific Heat of a Molecular-Based Materials

The molecular-based magnetic materials AFe11 Fe111（C2O4）3 have a honeycomb structure in which FeII （S = 2） and FeIH （S= 5/2） occupy sites alternately. They can be described as mixed spin-2 and spin-5/2 Ising model with ferrimagnetic interlayer coupling. The influences of the transverse field on the internal energy and the specific heat of the molecalar-based magnetic system have been studied numerically by using the effective-field theory with self-spin correlations and the differential operator technique.

Critical Properties of Mixed Ising Spin System with Different Trimodal Transverse Fields in the Presence of Single-Ion Anisotropy

Within the framework of an effective field approximation, the effects of single-ion anisotropy and different trimodal transverse fields of two sublattices on the critical properties of the mixed spin-1/2 and spin-1 Ising system are investigated on the simple cubic lattice. A smaller single-lon anisotropy can magnify magnetic ordering phases and a larger one can depress magnetic ordering phase for T-Ω1/2 space at low temperatures, while a smaller single-ion anisotropy can hardly change the value of critical transverse field for T-Ω1 space. On the other hand, influences of two different trimodal transverse fields concentrations on tricritical points and magnetic ordering phases take on some interesting results in T-D space. The main reason comes from the common action of single-ion anisotropy, different transverse fields and two trimodal distributions.

Reduced Fidelity Susceptibility in One-Dimensional Transverse Field Ising Model

We study critical behaviors of the reduced fidelity susceptibility for two neighboring sites in the onedimensional transverse field Ising model. It is found that the divergent behaviors of the susceptibility take the form of square of logarithm, in contrast with the global ground-state fidelity susceptibility which is power divergence. In order to perform a scaling analysis, we take the square root of the susceptibility and determine the scaling exponent analytically and the result is further confirmed by numerical calculations.

Influence of the Transverse Field Component on the Edge Efect in a Short-Gap Discharge

In a general plane-parallel electrode system the edge of the electrode will undermine the uniformity of the dielectric barrier discharge （DBD） because of the influence of the distorted electrical field. In this paper, the influence of the non-uniform electrical field on the edge effect of DBDs in a short-gap is investigated. We present some o.f the experimental results of DBDs produced by three kinds of convex-spherical electrodes. The results show that there is a dark area （the homogeneous discharge） in the central region of the electrode and a bright halo （the filamentary discharge） in the outer peripheral region, and the radius of the dark region is determined by the electrode geometry. The calculated results of the transverse （radial） field component distribution on the surface of the electrodes show that the edge effect does not come from the electrode edge, but the transverse field. The discharge has enough space to be fully developed and then format the filamentary discharge in the outer peripheral region because the streamer of the filamentary discharge is driven to move along the direction of the longer path by the transverse field. Thus, the homogeneous discharge （the Townsend DBD or a glow DBD） could not be produced in this area.

Structure of continuous matrix product operator for transverse field Ising model:An analytic and numerical study

We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.

The effects of the Dzyaloshinskii-Moriya interaction on the ground-state properties of the XY chain in a transverse field

The effects of the Dzyaloshinski-Moriya （DM） interaction on the ground-state properties of the anisotropic XY chain in a transverse field have been studied by means of correlation functions and entanglement. Different from the case without the DM interaction, the excitation spectra ek of this model are not symmetrical in the momentum space and are not always positive. As a result, besides the ferromagnetic （FM） and the paramagnetic （PM） phases, a gapless chiral phase is induced. In the chiral phase, the von Neumann entropy is proportional to log2 L （L is the length of a subchain） with the coefficient A ~ 1/3, which is the same as that of the XY chain in a transverse field without the DM interaction for 7 = 0 and 0 〈 h 〈 1. And in the vicinity of the critical point between the chiral phase and the FM （or PM） phase, the behaviors of the nearest- neighbor concurrence and its derivative are like those for the anisotropy transition.

Suppression of stimulated Brillouin and Raman scatterings using an alternating frequency laser and transverse magnetic fields

A novel scheme to suppress both stimulated Brillouin scattering(SBS) and stimulated Raman scattering(SRS) by combining an alternating frequency(AF) laser and a transverse magnetic field is proposed. The AF laser allows the laser frequency to change discretely and alternately over time. The suppression of SBS is significant as long as the AF difference is greater than the linear growth rate of SBS or the alternating time of the laser frequency is shorter than the linear growth time of SBS. However, the AF laser proves ineffective in suppressing SRS, which usually has a much higher linear growth rate than SBS. To remedy that, a transverse magnetic field is included to suppress the SRS instability. The electrons trapped in the electron plasma waves(EPWs) of SRS can be accelerated by the surfatron mechanism in a transverse magnetic field and eventually detrapped. While continuously extracting energy from EPWs, the EPWs are dissipated and the kinetic inflation of SRS is suppressed. The one-dimensional particle-in-cell simulation results show that both SBS and SRS can be effectively suppressed by combining the AF laser with a transverse magnetic field with tens of Tesla. The total reflectivity can be dramatically reduced by more than one order of magnitude. These results provide a potential reference for controlling SBS and SRS under the related parameters of inertial confinement fusion.

Spin-1 Blume-Capel model with longitudinal random crystal and transverse magnetic fields:A mean-field approach

The spin-1 Blume–Capel model with transverse and longitudinal external magnetic fields h, in addition to a longitudinal random crystal field D, is studied in the mean-field approximation. It is assumed that the crystal field is either turned on with probability p or turned off with probability 1 p on the sites of a square lattice. Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of γ=Ω/J and p at zero h. Thus, the effect of changing γ and p are illustrated on the phase diagrams in great detail and interesting results are observed.

A NEW MODEL AND IMPROVED CABLE FUNCTION FOR REPRESENTING THE ACTIVATING PERIPHERAL NERVES BY A TRANSVERSE ELECTRIC FIELD DURING MAGNETIC STIMULATION

Objective Previous studies of peripheral nerves activation during magnetic stimulation have focused almost exclusively on the cause of high external parallel electric field along the nerves, whereas the effect of the transverse component has been ignored. In the present paper, the classical cable function is modified to represent the excitation of peripheral nerves stimulated by a transverse electric field during magnetic stimulation. Methods Responses of the Ranvier nodes to a transverse-field are thoroughly investigated by mathematic simulation. Results The simulation demonstrates that the excitation results from the net inward current driven by an external field. Based on a two-stage process, a novel model is introduced to describe peripheral nerves stimulated by a transverse-field. Based on the new model, the classical cable function is modified. Conclusion Using this modified cable equation, the excitation threshold of peripheral nerves in a transverse field during MS is obtained. The modified cable equation can be used to represent the response of peripheral nerves by an arbitrary electric field.

The Dynamic Volt-Ampere Characteristics of a Vacuum Arc at Intermediate-Frequency Under a Transverse Magnetic Field

In this study, the changes of a vacuum arc＇s appearance were observed and the volt-ampere characteristics of the vacuum arc at intermediate frequency were analyzed under a transverse magnetic field （TMF）. The TMF and phase shift time were calculated by using the TMF contact model and the large phase shift of the magnetic field at a higher frequency was conductive to the dispersion process of residual plasma. The arc velocity was higher at 800 Hz than at 400 Hz. It can be inferred that TMF will encourage arc movement at 800 Hz. Moreover, the arc movement has an impact on the arc voltage. Because of the increasing length of the arc column with a high arc velocity, the elongated arc causes the arc voltage to increase. Specifically, the volt-ampere characteristics of the vacuum arc are divided into three stages in this paper. The higher the frequency, the greater the initial rate of rise in the arc voltage and the larger the area surrounded by arc volt-ampere characteristics. The correlations between the arc voltage and the amplitude and frequency of the current are also presented.

Motion and Splitting of Vacuum Arc Column in Transverse Magnetic Field Contacts at Intermediate—Frequency

Arc motion and splitting of vacuum arc at intermediate frequency（400-800 Hz） were investigated under transverse magnetic field（TMF）.The experiment was performed on cup-type TMF contacts with contact diameter of 40 mm and a contact gap of 4 mm in a single-frequency circuit.With high-speed photography we characterized the arc appearance at different arc currents from 3.3 kA-rms to 10 kA-rms at intermediate frequencies.As arc current increases from3.3 kA-rms to 10 kA-rms the arc appearance changes obviously.When current value is 3.3 kArms（current frequency 400-800 Hz）,there is almost no splitting arc;when the current exceeds5 kA-rms（current frequency 400-800 Hz）,the arc rotates at a speed above 20 m/s,accompanied by an observable splitting arc.The splitting arc could be observed at different frequencies and the arc-voltage had no noises when splitting occurred.The motion direction and the velocity of arc column were studied.Finally,the formation of a split arc was discussed.

Phase Transition for a Mixed Spin-1／2 and Spin-sB System with a Transverse CrystalField

The critical behaviors of a mixed spin-1/2 and spin-sB Ising system with a transverse crystal field are studiedby use of the effective-field theory with correlations. The effect of the transverse crystal field on transition temperaturesis investigated numerically for the honeycomb (z = 3) and square (z = 4) lattices. The results show that there is notricritical point for the system.

Perturbation solution to unsteady flow in a porous channel with expanding or contracting walls in the presence of a transverse magnetic field

An incompressible flow in a porous channel with expanding or contacting walls in the presence of a transverse magnetic field is considered. Using similarity transformations, the governing equations are reduced to the nonlinear ordinary differential equations. The exact similar solutions for the different cases of the expansion ratio and the Hartmann number are obtained with a singular perturbation method, and the associated behavior is discussed in detail.

Arc characteristics during the instability stage on transverse magnetic field contacts

The arcing process greatly affects the breaking ability after current zero.The instability stage is the transition stage from the ignition to the movement stage,which affects the arc movement characteristics.In this paper,the arc characteristics during the instability stage on spiral-type contacts were investigated using a high-speed video camera.A multi-column parallel instability mode and a single-column instability mode were found during the instability stage.The arc appearance and constriction degree changed rapidly.The arc voltage usually increased accompanied by fluctuations.In addition,it was found that the current significantly influenced the arc mode and duration in the instability stage.With increased peak current,the probability of a single-column instability mode increased,and the fluctuation range and average time decreased.

Investigation of cathode spot characteristics in vacuum under transverse magnetic field (TMF) contacts

With the continuous improvement of current levels in power systems, the demands on the breaking capacity requirements of vacuum circuit breakers are getting higher and higher. The breaking capacity of vacuum breakers is determined by cathode spots, which provide electrons and metal vapor to maintain the arc. In this paper, experiments were carried out on two kinds of transverse magnetic field（TMF） contacts in a demountable vacuum chamber, the behavior of the cathode spots was recorded by a high-speed charge-coupled device（CCD） video camera, and the characteristics of the cathode spots were analyzed through the image processing method. The phenomenon of cathode spot groups and the star-shaped pattern of the spots were both discovered in the experiment. The experimental results show that with the condition of TMF contacts the initial expansion speed of cathode spots is influenced by some parameters, such as the tested current, contact gap, the structure of the contact, the contact diameter, the number of slots, etc. In addition, the influence of the magnetic field on the formation of the cathode spot groups, the distribution, and the dynamic characteristics of the cathode spots were analyzed. It is concluded that the characteristics of the cathode spots are due to the effect of the magnetic field on the near-cathode plasma. The study of the characteristics of cathode spots in this paper would be helpful in the exploration of the physical process of vacuum arcs, and would be of guiding significance in optimizing the design of vacuum circuit breakers.

Slip-Line Field Theory of Transversely Isotropic Body

A slip-line field theory of transversely isotropic body is proposed in the presentpaper in order to deal with problems in geology and geotechniques.The Goldenblat-Kopnov failure criterion is employed.The parameters in it are treated as functions of tempperature It is applicable to transverse isotropic media in non-uniform temperaturefield.The basic equtions of plastic deformation are developed while the associated ru-les of flow are derived.By means of characteristic line theory,slip-line slope formulasand laws of variation of stress and velocity along slip lines are obtained,The indenta-tion on semi-infinite media is calculated.The theory developed in this paper may be simplified into many classical theories such as Mises,Hill,and Coulomb ones,This complicated theory may be applied to geotechniques,geological structures,petroleumindustry,mining engineering,etc.

Hall Effect on ECF Flow along a Rotating Infinite Porous Plate in the Presence of Transverse Magnetic Field

Unsteady extracellular fluid (ECF) flow along with a rotating infinite vertical porous plate in the presence of a transverse magnetic field has been studied numerically. The dimensional governing equations have been non-dimensionalized by useful dimensionless variables. The explicit finite difference method has been used to solve dimensionless equations. The numerical results have been calculated by studio developer FORTRAN 6.6a and MATLAB 2018a. For perfect conducting case, Magnetic Diffusivity Parameter 5 ≤ Pm ≤ 15 has been taken in induction equation. For good accuracy, stability and convergence analysis have been analyzed. Mesh Sensitivity test, steady-state solution test, and code validation test have been performed. For time step τ = 1, the numerical results have been found for the primary velocity, secondary velocity, angular velocity, primary induced magnetic field, secondary induced magnetic field, temperature as well as shear stresses along x and z direction, couple stress along z direction, current densities along x and z direction and the Nusselt number. Finally, the effects of various parameters have been separately discussed and illustrated graphically.

The Bipolar Field-Effect Transistor:II.Drift-Diffusion Current Theory(Two-MOS-Gates on Pure-Base)

This paper describes the drift-diffusion theory of the bipolar field-effect transistor （BiFET） with two identical and connected metal-oxide-silicon-gates （MOS-gates） on a thin-pure-base. Analytical solution is obtained by partitioning the two-dimensional transistor into two one-dimensional problems coupled by the parametric sur- face-electric-potential. Total and component output and transfer currents and conductances versus D. C. voltages from the drift-diffusion theory, and their deviations from the electrochemical （quasi-Fermi） potential-gradient theory,are presented over practical ranges of thicknesses of the silicon base and gate oxide. A substantial contri- bution from the longitudinal gradient of the square of the transverse electric field is shown.

The influence of weak transverse magnetic field on plasma dissipation process in the post-arc phase in a vacuum interrupter

Transverse magnetic field(TMF)contacts and applying external TMF are often adopted for reducing the ablation of the contact surface,but TMF will also affect the breaking performance of the vacuum interrupters.In this work,we investigated the influence of weak TMF on the expansion of the plasma in the post-arc phase with one-dimensional implicit particle-in-cell/Monte Carlo collision model,and we added an external circuit to the model to ensure the correctness of the calculation results.We simulated multiple magnetic field strengths(<30 mT),compared the plasma expansion process with the TMF strengths of 0 mT and 10 mT,and discussed the influence of metal vapor density on the insulation performance recovery of the vacuum interrupter.From the results,applying TMF with strength below 5 mT has little effect on the expansion of the plasma,and the TMF can increase the plasma density which improve the flow capacity of vacuum circuit breakers when the magnetic field above 10 mT,which is because the particles become more difficult to leave the discharge area under the force of the magnetic field.In general,we find that weak external TMF may adversely affect the breaking performance of the vacuum circuit breakers.