Evaluation of the angular spectrum approach for simulations of near-field pressures

The implementation of the angular spectrum approach based on the two-dimensional fast Fourier transform is evaluated for near-field pressure simulations of square ultrasound transducers, where the three-dimensional pressure field is calculated from the normal velocity distribution on the transducer surface. The pressure field is propagated in the spatial frequency domain with the spatial propagator or the spectral propagator. The spatial propagator yields accurate results in the central portion of the computational grid while significant errors are produced near the edge due to the finite extent of the window applied to the spatial propagator. Likewise, the spectral propagator is inherently undersampled in the spatial frequency domain, and this causes high frequency errors in the computed pressure field. This aliasing problem is alleviated with angular restriction. The results show that, in nonattenuating media, the spatial propagator achieves smaller errors than the spectral propagator after the region of interest is truncated to exclude the windowing error. For pressure calculations in attenuating media or with apodized pistons as sources, the spatial and spectral propagator achieve similar accuracies. In all simulations, the angular spectrum calculations with the spatial propagator take more time than calculations with the spectral propagator.     

Validity of Parametrized Quark Propagator

Based on an extensively study of the Dyson-Schwinger equations for a fully dressed quark propagator in the “rainbow”approximation, a parametrized fully dressed quark propagator is proposed in this paper. The parametrized propagator describes a confining quark propagator in hadron since it is analytic everywhere in complex p2-plane and has no Lemmann representation. The validity of the new propagator is discussed by comparing its predictions on selfenergy functions A/(p2), Bl(p2) and effective mass M$(p2) of quark with flavor f to their corresponding theoretical results produced by Dyson-Schwinger equations. Our comparison shows that the parametrized quark propagator is a good approximation to the fully dressed quark propagator given by the solutions of Dyson-Schwinger equations in the rainbow approximation and is convenient to use in any theoretical calculations.     

Numerically Solving Quark-Loop Effects on Dressed Gluon Propagator in Chiral Limit

We do a numerical calculation on the quark-loop effects on the dressed gluon propagator in the chiral limit. It is found that the quark-loop effects on the dressed gluon propagator are significant in solving the quark propagator in the rainbow approximation of the Dyson-Schwinger equation. The approach we used here is quite general and can also be used to calculate both the chemical potential and current quark mass dependence of the dressed gluon propagator.     

The Effective Gluon Propagator in the Global Color Symmetry Model

It is shown that the effective gluon propagator in the global color symmetry model can be calculated in the instanton dilute liquid approximation. The calculated effective gluon propagator is consistent with the general command on the qualitative features of the gluon propagator, i.e., (i) the gluon propagator is significantly enhanced at small space-like k², and (ii) for k² > 1.5 GeV² the perturbative results are quantitatively reliable.     

Infrared effects on the axial gauge quark propagator

The axial gauge quark propagator is studied when only the most singular infrared part of the gluon propagator is retained in the Dyson-Schwinger equation. With a new representation for the quark-gluon vertex a simple configuration space propagator and a momentum space form valid for all values of the gauge variable n · p are obtained. The propagator has no poles. The effective potential is minimized when there is no chiral symmetry breaking.     

Optical propagator of quantum systems in the probability representation

The evolution equation for the propagator of the quantum system in the optical probability representation (optical propagator) is obtained. The relations between the optical and quantum propagators for the Schrödinger equation and the optical propagator of an arbitrary quadratic system are found explicitly.     

The sensitivity analysis of propagator for path independent quantum finance model

Quantum finance successfully implements the imperfectly correlated fluctuation of forward interest rates at different maturities, by replacing the Wiener process with a two-dimensional quantum field. Interest rate derivatives can be priced at a more realistic value under this new framework. The quantum finance model requires three main ingredients for pricing: the initial forward interest rates, the volatility of forward interest rates, and the correlation of forward interest rates at different maturities. However, the hedging strategy only focused on fluctuation of forward interest rates. This hedging method is based on the assumption that the propagator, the covariance of forward interest rates, has an ergodic property. Since inserting the propagator is the main characteristic that distinguishes quantum finance from the Libor market model (LMM) and the Heath, Jarrow and Morton (HJM) model, understanding the impact of propagator dynamics on the price of interest rate derivatives is crucial. This research is the first step in developing a hedge strategy with respect to the evolution of the propagator. We analyze the dynamics of the propagator from Libor futures data and the integrated propagator from zero-coupon bond rate data. Then we study the sensitivity of the implied volatility of caplets and swaptions according to the three dominant dynamics of the propagator, and the change of the zero-coupon bond option price according to the two dominant dynamics of the integrated propagator.     

Exact density matrix of an oscillator-bath system: Alternative derivation

Starting from a total Lagrangian describing an oscillator-bath system, an alternative derivation of exact quantum propagator is presented. Having the quantum propagator, the exact density matrix, reduced density matrix of the main oscillator and thermal equilibrium fixed point are obtained. The modified quantum propagator is obtained in the generalised case where the main oscillator is under the influence of a classical external force. By introducing auxiliary classical external fields, the generalised quantum propagator or generating functional of position correlation functions is obtained.     

Remarks on q-space MR propagator in partially restricted,axially-symmetric,and isotropic environments

The problem of reconstruction of an apparent propagator from a series of diffusion-attenuated magnetic resonance (MR) signals is revisited. In nonimaging acquisitions, the inverse Fourier transform of the MR signal attenuation is consistent with the notion of an ensemble average propagator. However, in image acquisitions where one is interested in quantifying a displacement distribution in every voxel of the image, the propagator derived in the traditional way may lead to a counter-intuitive profile when it is nonsymmetric, which could be a problem in partially restricted environments. By exploiting the reciprocity of the diffusion propagator, an alternative is introduced, which implies a forward Fourier transform of the MR signal attenuations yielding a propagator reflected around the origin. Two simple problems were considered as examples. In the case of diffusion in the proximity of a restricting barrier, the reflected propagator yields a more meaningful result, whereas in the case of curving fibers, the original propagator is more intuitive. In the final section of the article, two more one-dimensional transformations are introduced, which enable the reconstruction of two- and three-dimensional propagators in, respectively, axially symmetric and isotropic environments — in both cases, from one-dimensional q-space MR data.     

Quark Loop Effects on Dressed Gluon Propagator in Framework of Global Color Symmetry Model

Based on the global color symmetry model (GCM), a method for obtaining the quark loop effects on the dressed gluon propagator in GCM is developed. In the chiral limit, it is found that the dressed gluon propagator containing the quark loop effects in the Nambu-Goldstone and Wigner phases are quite different. In solving the quark self-energy functions in the two different phases and subsequent study of bag constant one should use the above dressed gluon propagator as input. The above approach for obtaining the current quark mass effects on the dressed gluon propagator is quite general and can also be used to calculate the chemical potential dependence of the dressed gluon propagator.     

The Application of Lie Algebra Method in Induced Heavy Nuclei Fission

The propagator method is efficient in solving the Fokker-Planck equation.with an inharmonic oscillator potential. The propagator is deri;ed by using the Lie algebra method. The fission rate of ²⁴⁰Pu is calculated based on the expression of the propagator. The numerical results show that the rate is reasonable.     

On the eigenvalue problem associated with Feynman path integration

When the lagrangian is not explicit function of time, the Nth approximation to the propagator may be viewed as the Nth power of anitary operator — the infinitesimal time propagator. We solve the eigenvalue problem associated with the operator for some special cases. In the limit of large N the eigenfunctions are shown to be identical to those of the finite time propagator. We also present an elementary method to evaluate the propagator corresponding to an action function encountered in the study of electron gas in a random potential. The evaluation of this propagator within Feynman's polygonal approach was not possible until recently.     

Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)

We study a gauge-invariant order parameter for deconfinement and the chiral condensate in SU(2) and SU(3) Yang–Mills theory in the vicinity of the deconfinement phase transition using the Landau gauge quark and gluon propagators. We determine the gluon propagator from lattice calculations and the quark propagator from its Dyson–Schwinger equation, using the gluon propagator as input. The critical temperature and a deconfinement order parameter are extracted from the gluon propagator and from the dependency of the quark propagator on the temporal boundary conditions. The chiral transition is determined using the quark condensate as order parameter. We investigate whether and how a difference in the chiral and deconfinement transition between SU(2) and SU(3) is manifest.     

经典粒子和量子微观粒子的运动轨道

用量子力学传播子讨论了经典粒子和量子微观粒子沿着不同轨道对传播子的贡献．通过这样的计算可以清楚地看到为什么经典粒子只是沿着满足最小作用原理的轨道，即经典轨道运动，而对于量子微观粒子沿着许多条路径都有可能．这篇短文将一些教科书中的讨论用具体的数学表达出来，使得读者更容易理解．计算表明，对于质量较大的经典粒子，沿着非经典轨道对传播子的贡献和它周围的临近轨道有强烈的抵消．只有在经典轨道附近对传播子的贡献才不为零．对于量子微观粒子没有这种差别，它可以沿着多种可能的轨道运动．     

Reflectance properties of finite-size turbid media

Analytic expressions for the position-dependent reflectance of light were derived from a classical diffusion propagator. A modified transport propagator which describes the crossover from the ballistic to the diffusive propagation, and a cross-polarized component propagator. The theoretical reflectances are compared with the experimental ones and their potential for describing finite-size turbid media is discussed. It is found that the cross-polarized propagator provides the best agreement with the experimental data at the low volume fraction of scatterers, for a wide range of separation distances.     

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 p2-plane and has no Lehmann representation. The vector and scalar self-energy functions [1 - Af(p2)] and [Bf(p2) - mf], dynamically running effective mass of quark Mf(p2) 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 are compatible with other theoretical calculations.     

On analytic formulas of Feynman propagators in position space

We correct an inaccurate result of previous work on the Feynman propagator in position space of a free Dirac field in(3+1)-dimensional spacetime; we derive the generalized analytic formulas of both the scalar Feynman propagator and the spinor Feynman propagator in position space in arbitrary(D+1)-dimensional spacetime; and we further find a recurrence relation among the spinor Feynman propagator in(D+l)-dimensional spacetime and the scalar Feynman propagators in(D+1)-,(D-1)-and(D+3)-dimensional spacetimes.     

Probing Quark Loop Effects on Dressed Gluon Propagator

We study the quark loop effects on the dressed gluon propagator and also on the quark propagator itself. We find that the gluon propagators are different in two phases. The quark mass effects on the gluon propagator are small but not negligible. We also study the current quark mass dependence on the bag constant.     

Infrared gluon and ghost propagators from lattice QCD

We report on the infrared limit of the quenched lattice Landau gauge gluon and ghost propagators as well as the strong-coupling constant computed from large asymmetric lattices. The infrared lattice propagators are compared with the pure power law solutions from Dyson-Schwinger equations (DSE). For the gluon propagator, the lattice data is compatible with the DSE solution. The preferred measured gluon exponent being ∼0.52, favouring a vanishing propagator at zero momentum. The lattice ghost propagator shows finite-volume effects and, for the volumes considered, the propagator does not follow a pure power law. Furthermore, the strong-coupling constant is computed and its infrared behaviour investigated.     

Path integration of a generalized quadratic action

Path integration of a class of generalized quadratic actions first proposed by Feynman is performed within the framework of Feynman's polygonal path approach. The exact propagator has the form of a free particle propagator with an “effective mass” apart from the normalization factor. Relation between the propagator and the usual Van Vleck-Pauli formula is discussed.