SOME CONVERGENCE PROBLEMS REGARDING THE FRACTIONAL SCHRODINGER PROPAGATOR ON NONCOMPACT MANIFOLDS

Let L be the Laplace-Beltrami operator.On an n-dimensional(n≥2),complete,noncompact Riemannian manifold M,we prove that if 0<α<1,s>α/2 and f∈Hs(M),then the fractional Schr?dinger propagator e(it|L|α/2)(f)(x)→f(x)a.e.as t→0.In addition,for when M is a Lie group,the rate of the convergence is also studied.These results are a non-trivial extension of results on Euclidean spaces and compact manifolds.

Evaluation of Different Substrates Compositions for Acclimatization of Tissue Culture Taro Plantlets in a Propagator

Taro is cultivated in most Regions of Cameroon and it is affected by taro leaf blight disease since 2010 which has decreased its production. Lack of disease-free planting materials has been a main problem to farmers. This study was carried out at International Institute of Tropical Agriculture (IITA) Yaounde and Institute of Agricultural Research for Development (IRAD) Bambui to assess different substrates for acclimatization of tissue culture taro plantlets in apropagator. No information is available on acclimatization of Cameroonian taro plantlets in different substrates. Taro plantlets from tissue culture were acclimatised in a propagator for six weeks under different substrates, the first substrate consisted of sterile three parts of soil and one part of river sand mixed together (3:1), the second substrate consisted of sterile two parts of soil and two parts of river sand mixed together (2:2), the third substrate consisted of sterile two parts of soil, one part of rice husk and one part of river sand mixed together (2:1:1) and the fourth substrate consisted of sterile one part of soil and three parts of river sand mixed together (1:3). After acclimatisation of the different taroplantlets (Dark green petiole with small leaves (L1), Red petiole with small leaves (L2), Light green petiole with large leaves (L3) and Light green petiole with small leaves (L4) in these four substrates, it was observed that the best growth rate of plant was recorded on substrate sand + soil (1:3). The other substrates showed moderate growth of plants. Substrate sand + soil (1:3) can be recommended for acclimatization of Cameroonian taro plantlets.

A Generalized Propagator Algorithm for Localization of Non-circular Sources Using Arbitrary Array Geometry

A propagator-based algorithm for direction of arrival(DOA)estimation of noncoherent one-dimensional(1-D)non-circular sources is presented such as binary phase shift keying(BPSK)and amplitude modulation(AM).The algorithm achieves DOA estimation through searching a 1-D spectrum,which is newly formed on the basis of the rank reduction criterion,and works well without knowledge of the non-circular phases.And then,a search-free implementation of the algorithm is also developed by using the polynomial rooting technique.According to the non-circular property,the algorithm can virtually enlarge the array aperture,thus significantly improving its estimation accuracy and enabling it to handle more sources than the number of sensors.Moreover,the algorithm requires no rotational invariance,so it can be applied to arbitrary array geometry and dispense with the high-complexity procedure of the eigen-decomposition of the correlation sample matrix.Finally,numerical simulations verify the performance and effectiveness of the proposed algorithm.

Alternative Derivation of the Propagator in Polar Coordinates by Feynman's Physical Interpretation of the Characteristic Function

This article revisits Feynman's characteristic function, and points out the insight and usefulness of hisphysical interpretation. As an example, the tedious and rather long derivation of the propagator in polar coordinatescan be easily and clearly obtained by merely using Feynman's physical intepretation of the characteristic function andsome well-known results of central force problem.

Configuration of propagator method for calculation of electron velocity distribution function in gas under crossed electric and magnetic fields

This paper presents a self-contained description on the configuration of propagator method(PM)to calculate the electron velocity distribution function(EVDF) of electron swarms in gases under DC electric and magnetic fields crossed at a right angle. Velocity space is divided into cells with respect to three polar coordinates v,θ and f. The number of electrons in each cell is stored in three-dimensional arrays. The changes of electron velocity due to acceleration by the electric and magnetic fields and scattering by gas molecules are treated as intercellular electron transfers on the basis of the Boltzmann equation and are represented using operators called the propagators or Green’s functions. The collision propagator, assuming isotropic scattering, is basically unchanged from conventional PMs performed under electric fields without magnetic fields. On the other hand, the acceleration propagator is customized for rotational acceleration under the action of the Lorentz force. The acceleration propagator specific to the present cell configuration is analytically derived. The mean electron energy and average electron velocity vector in a model gas and SF6 were derived from the EVDF as a demonstration of the PM under the Hall deflection and they were in a fine agreement with those obtained by Monte Carlo simulations. A strategy for fast relaxation is discussed, and extension of the PM for the EVDF under AC electric and DC/AC magnetic fields is outlined as well.

Nearfield acoustic holography in a moving medium based on particle velocity input using nonsingular propagator

Nearfield acoustic holography in a moving medium is a technique which is typically suitable for sound sources identification in a flow.In the process of sound field reconstruction,sound pressure is usually used as the input,but it may contain considerable background noise due to the interactions between microphones and flow moving at a high velocity.To avoid this problem,particle velocity is an alternative input,which can be obtained by using laser Doppler velocimetry in a non-intrusive way.However,there is a singular problem in the conventional propagator relating the particle velocity to the pressure,and it could lead to significant errors or even false results.In view of this,in this paper,nonsingular propagators are deduced to realize accurate reconstruction in both cases that the hologram is parallel to and perpendicular to the flow direction.The advantages of the proposed method are analyzed,and simulations are conducted to verify the validation.The results show that the method can overcome the singular problem effectively,and the reconstruction errors are at a low level for different flow velocities,frequencies,and signal-to-noise ratios.

Instanton Effects on Gluon Propagator

Gluon propagator is investigated for pure Yang-Mills SU(3) gauge theory in field-strength approach. It isfound that instantohs provide a homogeneous solid-like medium background which generates finite nonzero momentumgluon propagator and gluon receives effective mass.

Gluon Propagator in a New Perturbative Expansion of Quantum Chromodynamics with a Non-Perturbative Background

Using a new perturbative expansion method in Quantum Chromodynamics with a non-perturbative gluon background, the gluon propagator is calculated up to the one-loop level, and renormalized in the modified minimal subtraction scheme. The resultant renormalization constants of the quantum gluon field and the gauge parameter receive a non-perturbative contribution coming from the gluon condensate <FF> besides the usual perturbative one, respectively.

Semiclassical propagator and van Vleck in a mixed position-momentum determinant space

In this paper a semiclassical propagator in a mixed position-momentum space is derived in the formalism of Maslov＇s multi-dimensional semiclassical theory. The corresponding mixed van Vleck determinant is also given explicitly. The propagator can be used to locally fix semiclassical divergences in singular regions of configuration space. It is shown that when a semicla^sical propagator is transformed from one representation to another, its form is invariant.

Exact propagator for an electron in a quadratic saddle-point potential and a magnetic field

We study the propagator for an electron moving in a two-dimensional （2D） quadratic saddle-point potential, in the presence of a perpendicular uniform magnetic field. A closed-form expression for the propagator is derived using the Feynmann path integrals.

Reverse-feeding effect of epidemic by propagators in two-layered networks

Epidemic spreading has been studied for a long time and is currently focused on the spreading of multiple pathogens,especially in multiplex networks. However, little attention has been paid to the case where the mutual influence between different pathogens comes from a fraction of epidemic propagators, such as bisexual people in two separated groups of heterosexual and homosexual people. We here study this topic by presenting a network model of two layers connected by impulsive links, in contrast to the persistent links in each layer. We let each layer have a distinct pathogen and their interactive infection is implemented by a fraction of propagators jumping between the corresponding pairs of nodes in the two layers. By this model we show that（i） the propagators take the key role to transmit pathogens from one layer to the other,which significantly influences the stabilized epidemics;（ii） the epidemic thresholds will be changed by the propagators;and（iii） a reverse-feeding effect can be expected when the infective rate is smaller than its threshold of isolated spreading.A theoretical analysis is presented to explain the numerical results.

Elastic one-return boundary element method and hybrid elastic thin-slab propagator for strong-contrast media with sharp boundaries

In this paper, we developed the theory and algorithm of an elastic one-way boundary element method（BEM） and a corresponding hybrid elastic thin-slab propagator for earth media with sharp boundaries between strong contrast media. This approach can takes the advantage of accurate boundary condition of BEM and completely overcomes the weak contrast limitation of the perturbationtheory based one-way operator approach. The one-way BEM is a smooth boundary approximation, which avoids huge matrix operations in exact full BEM. In addition, the one-way BEM can model the primary-only transmitted and reflected waves and therefore is a valuable tool in elastic imaging and inversion. Through numerical tests for some simple models,we proved the validity and efficiency of the proposed method.

Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator

Abstract We develop a highly efficient scheme for numerically solving the three-dimensional time-dependent Schrödinger equation of the single-active-electron atom in the field of laser pulses by combining smooth exterior complex scaling(SECS)absorbing method and Arnoldi propagation method.Such combination has not been reported in the literature.The proposed scheme is particularly useful in the applications involving long-time wave propagation.The SECS is a wonderful absorber,but its application results in a non-Hermitian Hamiltonian,invalidating propagators utilizing the Hermitian symmetry of the Hamiltonian.We demonstrate that the routine Arnoldi propagator can be modified to treat the non-Hermitian Hamiltonian.The efficiency of the proposed scheme is checked by tracking the time-dependent electron wave packet in the case of both weak extreme ultraviolet(XUV)and strong infrared(IR)laser pulses.Both perfect absorption and stable propagation are observed.

Exact Propagator of a Two Dimensional Anisotropic Harmonic Oscillator in the Presence of a Magnetic Field

In this paper we solve exactly the problem of the spectrum and Feynman propagator of a charged particle submitted to both an anharmonic oscillator in the plane and a constant and homogeneous magnetic field of arbitrary strength aligned with the perpendicular direction to the plane. As we shall see in the beginning of the letter, the Hamiltonian, being a quadratic form, is easily diagonalizable and the Classical Action can be used to construct the exact Feynman Propagator using the Stationary Phase Approximation. The result is useful for the treatment of quasi two dimensional samples in the field of magnetic effects in nano-structures and quantum optics. The presented solution, after minor extensions, can also be used for motion in three dimensions, and in fact it has been used for years in such cases. Also it can be used as a good exercise of a Feynman Path Integral that can be calculated easily with just the help of the Classical Action.

How to Explicitly Calculate Feynman and Wheeler Propagators in the ADS/CFT Correspondence

We discuss, giving all necessary details, the boundary-bulk propagators. We do it for a scalar field, with and without mass, for both the Feynman and the Wheeler cases. Contrary to standard procedure, we do not need here to appeal to any unfounded conjecture (as done by other authors). Emphasize that we do not try to modify standard ADS/CFT procedures, but use them to evaluate the corresponding Feynman and Wheeler propagators. Our present calculations are original in the sense of being the first ones undertaken explicitly using distributions theory (DT). They are carried out in two instances: 1) when the boundary is a Euclidean space and 2) when it is of Minkowskian nature. In this last case we compute also three propagators: Feynman’s, Anti-Feynman’s, and Wheeler’s (half advanced plus half retarded). For an operator corresponding to a scalar field we explicitly obtain, for the first time ever, the two points’ correlations functions in the three instances above mentioned. To repeat, it is not our intention here to improve on ADS/CFT theory but only to employ it for evaluating the corresponding Wheeler’s propagators.

Angular Decomposition and Sign Solved Propagator of the 2D and 3D Helium Atom Path Integrals

In the present paper on the one hand we apply the central limit theorem to the solution of the sign problem of a path integral of two-interacting particles in potential and give an expression for the sign solved propagator (SSP) derived from that solution and on the other hand we perform the angular decomposition of the path integrals of the 2D and 3D Helium atoms. Finally, we combine those two results and derive the SSPs of the 2D and 3D Helium atoms.

The Dirac Propagator for One-Dimensional Finite Square Well

The solution of Dirac particles confined in a one-dimensional finite square well potential is solved by using the path-integral formalism for Dirac equation. The propagator of the Dirac equation in case of the bounded Dirac particles is obtained by evaluating an appropriate path integral, directly constructed from the Dirac equation. The limit of integration techniques for evaluating path integral is only valid for the piecewise constant potential. Finally, the Dirac propagator is expressed in terms of standard special functions.

Dynamics of a Quantum Dissipative System Coupled with an Oscillator

We study the dynamics of a quantum dissipative system. Besides its linear coupling with a harmonic bath modelling the dissipation, we suppose that it is coupled with an oscillator with an interaction of the form s 2 x 2 . In our study, we integrate over the bath and the oscillator, extract the corresponding influence functionals and then solve the system’s sign problem. We apply the theory to the case of a double well and study the time evolution of the expectation value of the position.

基于Cornell的自适应电离层闪烁强度的模型研究

针对Cornell模型在同一闪烁条件下,数据更新周期越长,估计和模型输入的幅度闪烁指数S4的偏差越大,并随着电离层闪烁的增强而增强的问题,提出基于Cornell模型的自适应S4的电离层闪烁模型即AS4-Cornell模型。模型以S4的偏差作为BP(back propagation)神经网络比例积分微分(proportional integral derivative,PID)算法的反馈,自动调整输入的复高斯白噪声的区段权值,使最终产生的闪烁信号满足模型输入的闪烁指数S4的指标。结果表明:仿真时,AS4-Cornell模型的幅度和相位闪烁序列概率分布均符合电离层闪烁理论,估算得到的电离层幅度指数S4与模型输入S4指数的最大偏差为0.001;全球定位系统(global positioning system,GPS)电离层闪烁模拟器测试时,AS4-Cornell模型估算得到的电离层幅度指数S4与模型输入S4指数的最大偏差为0.09;相比Cornell模型,AS4-Cornell模型产生的电离层闪烁信号更能够很好地反映模型输入的电离层闪烁指数S4的强度。