Mutual transformations between the P–Q,Q–P,and generalized Weyl ordering of operators

Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok （p, q） with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 （p - P） （q - Q）, （q - Q） 3 （p - P）, and （p, q）, which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of （p, q） are also derived, which helps us to put the operators into their - and - ordering, respectively.     

A New Type of Seiberg-Witten Map and Its Application

Deformation quantization is a powerful tool to deal with systems in noncommutative space to get their energy spectra and corresponding Wigner functions, especially for the ease of both coordinates and momenta being noneommutative. In order to simplify solutions of the relevant .-genvalue equation, we introduce a new kind of Seiberg Witten-like map to change the variables of the noncommutative phase space into ones of a commutative phase space, and demonstrate its role via an example of two-dimensional oscillator with both kinetic and elastic couplings in the noneommutative phase space.     

Double coherence resonance of the FitzHugh Nagumo neuron driven by harmonic velocity noise

The effect of noise frequency on the FitzHugh–Nagumo neuron is investigated by the use of the harmonic velocity noise, which has a direct frequency parameter and no zero frequency part of the power spectrum. It is shown that the neuron has the resonance characteristic strongly responding to the noise with a certain frequency at fixed power, and there is double coherence resonance related to the frequency and the intensity. If the harmonic velocity noise lacks low frequency ingredients, there is no synchronization between the frequency of the neuron and that of the noise. Thus the low frequency part of the noise plays an important role in creating the synchronization.     

Calculations for shortening the bunch length in storage rings using a harmonic cavity

Using the Hefei Light Source phase Ⅱ project （HLS- Ⅱ） as an example, a theoretical analysis of shortening the bunch lengths using a higher harmonic cavity （HHC） is given. The threshold voltage of an active HHC and the threshold tuning angle of a passive HHC are first analysed. The optimum tuning angle for the constant detuning scenario and the optimum harmonic voltage for the constant voltage scenario are presented. The calculated results show that the reduced bunch length is about half that of the nominal bunch. The bunch lengths vary from 11 mm at 0.1 A to 7 mm at 0.4 A for the constant detuning scenario, while the bunch lengths are around 7 mm over the beam current range for the constant voltage scenario. In addition, the synchrotron frequency spread is increased. It indicates that HHC may be used to reduce the bunch length and increase the Landau damping of synchrotron oscillations in a storage ring.     

A proposed method to characterize high harmonic microbunching in EEHG operation of SDUV-FEL

The echo-enabled harmonic generation （EEHG） scheme offers remarkable efficiency for generating high harmonic microbunching with a relatively small energy modulation. A proof of principle experiment of the EEHG scheme has been proposed at the Shanghai deep ultraviolet （SDUV） free electron laser （FEL） facility, where the 4th harmonic of the seed laser is amplified in the 9 m long radiator. To explore the advantages of the EEHG scheme, in this paper, a method of measuring the coherent high harmonic radiation of the radiator is proposed to investigate the electron beam microbunching corresponding to the 10th-20th harmonics of the seed laser. The principle of the proposed method, comparisons with existing methods and the simulation results are presented and discussed.     

Quantum Systems Connected by a Time-Dependent Canonical Transformation

We study both classical and quantum relation between two Hamiltonian systems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other is timedependent Hamiltonian system. The quantum unitary operator relevant to classical canonical transformation between the two systems are obtained through rigorous evaluation. With the aid of the unitary operator, we have derived quantum states of the time-dependent Hamiltonian system through transforming the quantum states of the conservative system. The invariant operators of the two systems are presented and the relation between them are addressed. We showed that there exist numerous Hamiltonians, which gives the same classical equation of motion. Though it is impossible to distinguish the systems described by these Hamiltonians within the realm of classical mechanics, they can be distinguishable quantum mechanically.     

Solutions of the Schrodinger Equation with Quantum Mechanical Gravitational Potential Plus Harmonic Oscillator Potential

The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained.     

Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrodinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special eases like （i） a confined free particle, （ii） a confined time-independent harmonic oscillator, and （iii） an aging oscillator are examined, and the corresponding time- dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well.     

Application of wavelet-based active magnet power supply filter in accelerator

Since modern accelerators demand excellent stability to magnet power supply （PS）, it is necessary to decrease harmonic currents passing magnets. Aiming at depressing the rappel current from the PS in the Beijing electron-positron collider Ⅱ, a wavelet-based active power filter （APF） is proposed in this paper. An APF is an effective device to improve the quality of currents. As a countermeasure to these harmonic currents, the APF circuit generates a harmonic current, countervailing harmonic current from PS. An active power filter based on wavelet transformation is proposed. Discrete wavelet transformation is used to analyze the harmonic components in the supply current, and an active power filter circuit works according to the analysis results. Our simulation and experiment results are given to prove the effect of the APF.     

Production of CH （A2△） by multi-photon dissociation of （CH3）2CO,CH3NO2, CH2Br2, and CHBr3 at 213 nm

In order to realize electrostatic Stark deceleration of CH radicals and study cold chemistry, the fifth harmonic of a YAG laser is used to prepare CH(A2△) molecules through using the multi-photon dissociation of(CH3)2CO, CH3NO2, CH2Br2,and CHBr3 at ～ 213 nm. The CH product intensity is measured by using the emission spectrum of CH(A2△→ X2Π). The dependence of fluorescence intensity on laser power is studied, and the probable dissociation channels are analyzed. The relationship between the fluorescence intensity and some parameters, such as the temperature of the beam source, stagnation pressure, and the time delay between the opening of pulse valve and the photolysis laser, are also studied. The influence of three different carrier gases on CH signal intensity is investigated. The vibrational and rotational temperatures of the CH(A2△) product are obtained by comparing experimental data with the simulated ones from the LIFBASE program.     

Generalized Harmonic Oscillator and the SchrSdinger Equation with Position-Dependent Mass

We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties corresponding effective potentials for several mass functions, for the system with PDM are also discussed. We give the the systems with such potentials are isospectral to the usual harmonic oscillator.     

Re-explanation of Weyl Quantization Scheme via Weyl Ordering Approach

We re-explain the Weyl quantization scheme by virtue of the technique of integration within Weyl ordered product of operators, i.e., the Weyl correspondence rule can be reconstructed by classical functions＇ Fourier transformation followed by an inverse Fourier transformation within Weyl ordering of operators. As an application of this reconstruction, we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave.     

High-efficiency S-band harmonic tuning GaN amplifier

In this paper, we present a high-efficiency S-band gallium nitride （GaN） power amplifier （PA）. This amplifier is fabri- cated based on a self-developed GaN high-electron-mobility transistor （HEMT） with 10 mm gate width on SiC substrate. Harmonic manipulation circuits are presented in the amplifier. The matching networks consist of microstrip lines and discrete components. Open-circuited stub lines in both input and output are used to tune the 2rid harmonic wave and match the GaN HEMT to the highest efficiency condition. The developed amplifier delivers an output power of 48.5 dBm （70 W） with a power-added efficiency （PAE） of 72.2% at 2 GHz in pulse condition. When operating at 1.8-2.2 GHz （20% relative bandwidth）, the amplifier provides an output power higher than 48 dBm （,-~ 65 W）, with a PAE over 70% and a power gain above 15 dB. When operating in continuous-wave （CW） operating conditions, the amplifier gives an output power over 46 dBm （40 W） with PAE beyond 60% over the whole operation frequency range.     

Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation

A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-invariant transition probability amplitudes is derived.     

Rational and Periodic Wave Solutions of Two-Dimensional Boussinesq Equation

Two new exact, rational and periodic wave solutions are derived for the two-dimensional Boussinesq equation. For the first solution it is obtained by performing an appropriate limiting procedure on the soliton solutions obtained by Hirota bilinear method. The second one in terms of Riemann theta function is explicitly presented by virtue of Hirota bilinear method and its asymptotic property is also analyzed in detail. Moreover, it is of interest to note that classical soliton solutions can be reduced from the periodic wave solutions.     

Further studies on stability analysis of nonlinear Roesser-type two-dimensional systems

This paper is concerned with further relaxations of the stability analysis of nonlinear Roesser-type two-dimensional （2D） systems in the Takagi-Sugeno fuzzy form. To achieve the goal, a novel slack matrix variable technique, which is homogenous polynomially parameter-dependent on the normalized fuzzy weighting functions with arbitrary degree, is developed and the algebraic properties of the normalized fuzzy weighting functions are collected into a set of augmented matrices. Consequently, more information about the normalized fuzzy weighting functions is involved and the relaxation quality of the stability analysis is significantly improved. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed result.     

High-mobility two-dimensional electron gases at oxide interfaces： Origin and opportunities

Our recent experimental work on metallic and insulating interfaces controlled by interfacial redox reactions in SrTiO3-based heterostructures is reviewed along with a more general background of two-dimensional electron gas(2DEG)at oxide interfaces.Due to the presence of oxygen vacancies at the SrTiO3surface,metallic conduction can be created at room temperature in perovskite-type interfaces when the overlayer oxide ABO3has Al,Ti,Zr,or Hf elements at the B sites.Furthermore,relying on interface-stabilized oxygen vacancies,we have created a new type of 2DEG at the heterointerface between SrTiO3and a spinelγ-Al2O3epitaxial film with compatible oxygen ion sublattices.This 2DEG exhibits an electron mobility exceeding 100000 cm2·V 1·s 1,more than one order of magnitude higher than those of hitherto investigated perovskite-type interfaces.Our findings pave the way for the design of high-mobility all-oxide electronic devices and open a route toward the studies of mesoscopic physics with complex oxides.     

Quantization of a nonlinear oscillator as a model of the harmonic oscillator on spaces of constant curvature: One- and two-dimensional systems

The quantum version of a nonlinear oscillator, previously analyzed at the classical level, is studied first in one dimension and then in two dimensions. This is a problem of quantization of a system with position-dependent mass of the form m = (1 + λx ²)⁻¹ and with a λ-dependent nonpolynomial rational potential. The quantization procedure analyzes the existence of Killing vectors and makes use of an invariant measure. It is proved that this system can be considered as a model of the quantum harmonic oscillator on two-dimensional spaces of constant curvature. The text was submitted by the authors in English.     

Normally-Ordered Time Evolution Operator for Mass-Varying Harmonic Oscillator and Wigner Function of Squeezed Number State

For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integration operator in coherent state representation and then perform this integral by virtue of the technique of integration within an ordered product of operators. The normally ordered time evolution operator is thus obtained. We then derive the Wigner function of u（t）｜n,〉, where ｜n〉 is a Fock state, which exhibits a generalized squeezing, the squeezing effect is related to the varying mass with time.     

Ultra-high order harmonic generation via a free electron laser mechamsm

In this paper, by using the ＂frequency up-conversion＂ principle with a high gain harmonic generation free electron laser and an external seed laser, we consider the possibility of modulating a relativistic electron beam on the attosecond scale, so that it can produce coherent spontaneous radiation from the deep ultraviolet to the hard X-ray spectral region with a very short radiator. Analytical estimation and three-dimensional numerical modeling show the great potential to reach ultra-high harmonics up to several thousand. For an electron bunch with the typical quality as in the free electron laser scheme and a seed laser with 800 nm wave- length, 0.8 nm attosecond trains with alterable duration and GW scale peak power are modeled. The output radiation exhibits good shot-to-shot stability, full coherence and perfect tuning ability between the discrete harmonics of the seed frequency.