Non-integer Quantum Transition, a True Non-perturbation Effect in Laser-Atom Interaction

We show that in the quantum transition of an atom interacting with an intense laser of circular frequency ω, the energy difference between the initial and the final states of the atom is not necessarily an integer multiple of the quantum energy hω. This kind of non-integer transition is a true non-perturbation effect in laser-atom interaction.

Non-perturbative Aspects of QCD and Parameterized Quark Propagator

Based on the Global Color Symmetry Model, the non-perturbative Q, CD vacuum is investigated in the parameterized fully dressed quark propagator. Our theoretical predictions for various quantities characterized the QCD vacuum are in agreement with those predicted by many other phenomenologieal QCD inspired models. The successful predictions clearly indicate the extensive validity of our parameterized quark propagator used here. A detailed discussion on the arbitrariness in determining the integration cut-off parameter ofμ in calculating QCD vacuum condensates and a good method, which avoided the dependence of calculating results on the cut-off parameter is also strongly recommended to readers.

Non-perturbative multiphoton excitation studies in an excitonic coupled quantum well system using high-intensity THz laser fields

Multiphoton excitations and nonlinear optical properties of exciton states in GaAs/AlxGa1-xAs coupled quantum well structure have been theoretically investigated under the influence of a time-varying high-intensity terahertz(THz)laser field.Non-perturbative Floquet theory is employed to solve the time-dependent equation of motion for the laser-driven excitonic quantum well system.The response to the field parameters,such as intensity and frequency of the laser electric field on the state populations,can be used in various optical semiconductor device applications,such as photodetectors,sensors,all-optical switches,and terahertz emitters.

Non-perturbative QCD Effect on K-Factor of Drell-Yan Process

By using a non-perturbative quark propagator with the lowest-dimensional condensate contributions from the QCD vacuum, the non-perturbative egect to K-factor of the Drell-Yan process is numerically investigated for 6^12C- 6^12C collision at the center-of-mass energy √s- 200 GeV, 630 GeV respectively. Calculated results show that the non-perturbative QCD effect has just a weak influence on K-factor in the two cases.

Pair Production in Non-Perturbative QCD

In this paper, a method to calculate the vacuum to vacuum transition amplitude in the presence of a non-abelian background field is introduced. The number of non-perturbative quark-antiquark produced per unit time, per unit volume and per unit transverse momentum from a given constant chromo-electric field is calculated and its application to quark-gluon plasma is presented.

Stability analysis of a time-delayed Van der Pol–Helmholtz–Duffing oscillator in fractal space with a non-perturbative approach

The time-delayed fractal Van der Pol–Helmholtz–Duffing(VPHD)oscillator is the subject of this paper,which explores its mechanisms and highlights its stability analysis.While time-delayed technologies are currently garnering significant attention,the focus of this research remains crucially relevant.A non-perturbative approach is employed to refine and set the stage for the system under scrutiny.The innovative methodologies introduced yield an equivalent linear differential equation,mirroring the inherent nonlinearities of the system.Notably,the incorporation of quadratic nonlinearity into the frequency formula represents a cutting-edge advancement.The analytical solution's validity is corroborated using a numerical approach.Stability conditions are ascertained through the residual Galerkin method.Intriguingly,it is observed that the delay parameter,in the context of the fractal system,reverses its stabilizing influence,impacting both the amplitude of delayed velocity and the position.The analytical solution's precision is underscored by its close alignment with numerical results.Furthermore,the study reveals that fractal characteristics emulate damping behaviors.Given its applicability across diverse nonlinear dynamical systems,this non-perturbative approach emerges as a promising avenue for future research.

Searching for Odderon with ^-pp and pp Elastic Scattering at High Energies

Based on the assumption that the Pomeron is a sum of Regge multipoles, each of which corresponds to a finite gluon ladder, we suggest a way to search the Odderon by studying the diffractive processes of ^-pp and pp elastic scattering. From our theoretical calculations and fits to the corresponding experimental data at high energies and all available momentum transfer, we find that the Odderon plays a significant role in the description of differential cross section dσ/ dt in the whole experimental domain. Accordingly, we can claim that the ^-pp and pp diffractive processes at high energies s and moderate momentum transfer t could be a good tool to search for Odderon and to test QCD since the processes are purely non-perturbative QCD phenomena. Therefore, the experimental measurements are urgently demanded.

Applicability of Parametrized Form of Fully Dressed Quark Propagator

According to extensive study of the Dyson-Schwinger equations for a fully dressed quark propagator in the ＂rainbow＂ approximation with an effective gluon propagator, a parametrized fully dressed confining quark propagator is suggested in this paper. The parametrized quark propagator describes a confined quark propagation in hadron, and is analytic everywhere in complex p^2-plane and has no Lehmann representation. The vector and scalar self-energy functions [1 - Af（p^2）] and [Bf（p^2） - mf], dynamlcally running effective mass of quark Mf（p^2） and the structure of non-local quark vacuum condensates as well as local quark vacuum condensates are predicted by use of the parametrized quark propagator. The results axe compatible with other theoretical calculations,

Mode structure symmetry breaking of reversed shear Alfvén eigenmodes and its impact on the generation of parallel velocity asymmetries in energetic particle distribution

In this work,the gyrokinetic eigenvalue code LIGKA,the drift-kinetic/MHD hybrid code HMGC and the gyrokinetic full-f code TRIMEG-GKX are employed to study the mode structure details of reversed shear Alfvén eigenmodes(RSAEs).Using the parameters from an ASDEXUpgrade plasma,a benchmark with the three different physical models for RSAE without and with energetic particles(EPs)is carried out.Reasonable agreement has been found for the mode frequency and the growth rate.Mode structure symmetry breaking(MSSB)is observed when EPs are included,due to the EPs’non-perturbative effects.It is found that the MSSB properties are featured by a finite radial wave phase velocity,and the linear mode structure can be well described by an analytical complex Gaussian expressionФ(s)=e^(-σ(s-s_(0))^(2))with complex parametersσand s_(0),where s is the normalized radial coordinate.The mode structure is distorted in opposite manners when the EP drive shifted from one side of qminto the other side,and specifically,a non-zero average radial wave number with opposite signs is generated.The initial EP density profiles and the corresponding mode structures have been used as the input of HAGIS code to study the EP transport.The parallel velocity of EPs is generated in opposite directions,due to different values of the average radial wave number,corresponding to different initial EP density profiles with EP drive shifted away from the qmin.

A new non-perturbative approach in quantum mechanics for time-independent Schr?dinger equations

A new non-perturbative approach is proposed to solve time-independent Schr?dinger equations in quantum mechanics.It is based on the homotopy analysis method(HAM)that was developed by the author in 1992 for highly nonlinear equations and has been widely applied in many fields.Unlike perturbative methods,this HAM-based approach has nothing to do with small/large physical parameters.Besides,convergent series solution can be obtained even if the disturbance is far from the known status.A nonlinear harmonic oscillator is used as an example to illustrate the validity of this approach for disturbances that might be one thousand times larger than the possible superior limit of the perturbative approach.This HAM-based approach could provide us rigorous theoretical results in quantum mechanics,which can be directly compared with experimental data.Obviously,this is of great benefit not only for improving the accuracy of experimental measurements but also for validating physical theories.

Estimating proton radius and proportion of other non-perturbative components in the proton by the maximum entropy method

In this paper,we apply the Maximum Entropy Method to estimate the proton radius and determine the valence quark distributions in the proton at extremely low resolution scale Q02.Using the simplest functional form of the valence quark distribution and standard deviations of quark distribution functions in the estimation of the proton radius,we obtain a quadratic polynomial for the relationship between the proton radius and the momentum fraction of other non-perturbative components in the proton.The proton radii are approximately equal to the muonic hydrogen experimental result rp = 0.841 fm and the CODATA analysis rp = 0.877 fm when the other non-perturbative components account for 17.5% and 22.3% respectively.We propose ＂ghost matter＂ to explain the difference in other non-perturbative components（4.8%） that the electron can detect.

An innovative technique to solve a fractal damping Duffing-jerk oscillator

The idea of the present article is to look into the nonlinear dynamics and vibration of a damping Duffing-jerk oscillator in fractal space exhibiting the non-perturbative approach.Using a new analytical technique,namely,the modification of a He’s fractal derivative that converts the fractal derivative to the traditional derivative in continuous space,this study provides an effective and easy-to-apply procedure that is dependent on the He’s fractal derivative approach.The analytic approximate solution has a significant match with the results of the numerical simulation as the fractal parameter is very closer to unity,which proves the reliability of the method.Stability behavior is discussed and illustrated graphically.These new powerful analytical tools are developed in an attempt to obtain effective analytical tools,valid for any fractal nonlinear problems.

Algebro-geometrical orientifold and IR dualities

Orientifold projections are an important ingredient in the geometrical engineering of Quantum Field Theory.However,an orientifold can break down the superconformal symmetry and no new superconformal fixed points are admitted(scenario Ⅱ);nevertheless,in some cases,dubbed scenarios Ⅰ and Ⅲ orientifold,a new IR fixed point is achieved and,for scenario Ⅲ examples,some still not fully understood IR duality seems to emerge.Here we give an algebro-geometrical point of view of orientifold for toric varieties and we propose the existence of relevant operators that deform the starting oriented Conformal Field Theory triggering a flow.We briefly discuss a possible holographic description of this flow.

An efficient approach to solving fractional Van der Pol-Duffing jerk oscillator

The motive behind the current work is to perform the solution of the Van der Pol–Duffing jerk oscillator,involving fractional-order by the simplest method.An effective procedure has been introduced for executing the fractional-order by utilizing a new method without the perturbative approach.The approach depends on converting the fractional nonlinear oscillator to a linear oscillator with an integer order.A detailed solving process is given for the obtained oscillator with the traditional system.

Virtualities of quark and gluon in QCD vacuum

The non-local vacuum condensates of quantum chromodynamics (QCD) describe the distributions of quarks and gluons in the non-perturbative QCD vacuum state. Physically, this means that vacuum quarks and gluons have a nonzero mean-squared momentum in the vacuum, called virtuality. The quark virtuality is given by the ratio of the local quark-gluon mixed vacuum condensate to the quark local vacuum condensate. The gluon virtuality is expressed by gluon vacuum condensates and four-quark vacuum condensates. We study the two virtualities by solving Dyson-Schwinger Equations and calculating quark and gluon vacuum condensates. Our theoretical results for quark virtuality are in good agreement with many other theoretical model predictions such as QCD sum rules and lattice QCD calculations. Our calculation on gluon virtuality is initial and the results are quite interesting.

Recent developments in topological string theory

This review summarizes the recent developments in topological string theory from the author’s perspective, mostly focusing on aspects of research in which the author is involved. After a brief overview of the theory, we discuss two aspects of these developments. First, we discuss the computational progress in the topological string partition functions on a class of elliptic Calabi-Yau manifolds. We propose to use Jacobi forms as an ansatz for the partition function. For non-compact models, the techniques often provide complete solutions, while for compact models, though it is still not completely solvable, we compute to higher genus than previous works. Second, we explore a remarkable connection of refined topological strings on a class of non-compact toric Calabi-Yau threefolds with non-perturbative effects in quantum-mechanical systems. The connections provide rarely available exact quantization conditions for quantum systems and new insights on non-perturbative formulations of topological string theory.

Power-law scalings in weakly-interacting Bose gases at quantum criticality

Weakly interacting quantum systems in low dimensions have been investigated for a long time,but there still remain a number of open questions and a lack of explicit expressions of physical properties of such systems.In this work,we find power-law scalings of thermodynamic observables in low-dimensional interacting Bose gases at quantum criticality.We present a physical picture for these systems with the repulsive interaction strength approaching zero;namely,the competition between the kinetic and interaction energy scales gives rise to power-law scalings with respect to the interaction strength in characteristic thermodynamic observables.This prediction is supported by exact Bethe ansatz solutions in one dimension,demonstrating a simple 1/3-power-law scaling of the critical entropy per particle.Our method also yields results in agreement with a non-perturbative renormalization-group computation in two dimensions.These results provide a new perspective for understanding many-body phenomena induced by weak interactions in quantum gases.

Study of spin sum rules (and the strong coupling constant at large distances)

We present recent results from Jefferson Lab on sum rules related to the spin structure of the nucleon. We then discuss how the Bjorken sum rule with its connection to the Gerasimov-Drell-Hearn sum, allows us to conveniently define an effective coupling for the strong force at all distances.

Ratio of a strange quark mass m_s to up or down quark mass m_(u,d) predicted by a quark propagator in the framework of the chiral perturbation theory

Based on the fully dressed quark propagator and chiral perturbation theory, we study the ratio of the strange quark mass ms to up or down quark mass mu,d . The ratio is related to the determination of quark masses which are fundamental input parameters of QCD Lagrangian in the Standard Model of particle physics and can not be directly measured since the quark is confined within a hadron. An accurate determination of these QCD free parameters is extremely important for both phenomenological and theoretical applications. We begin with a brief introduction to the non-perturbation QCD theory, and then study the mass ratio in the framework of the chiral perturbation theory （χPT） with a parameterized fully dressed quark propagator which describes confining fully dressed quark propagation and is analytic everywhere in the finite complex p2-plane and has no Lehmann representation so there are no quark production thresholds in any theoretical calculations of observable data. Our prediction for the ratio ms/mu,d is consistent with other model predictions such as Lattice QCD, instanton model, QCD sum rules and the empirical values used widely in the literature. As a by-product of this study, our theoretical results, together with other predictions of physical quantities that used this quark propagator in our previous publications, clearly show that the parameterized form of the fully dressed quark propagator is an applicable and reliable approximation to the solution of the Dyson-Schwinger Equation of quark propagator in the QCD.

New exotic charmonium states

In the last years many states in the charmonium mass region were discovery by BABAR,Belle and CDF collaborations.I discuss some of these discoveries,and how the QCD Sum Rule approach can be used to understand the structure of these states.