Loop vertex expansion for higher-order interactions

This note provides an extension of the constructive loop vertex expansion to stable interactions of arbitrarily high order, opening the way to many applications. We treat in detail the example of the \((\bar{\phi } \phi )^p\) field theory in zero dimension. We find that the important feature to extend the loop vertex expansion is not to use an intermediate field representation, but rather to force integration of exactly one particular field per vertex of the initial action.     

半无界空间上函数的傅里叶-贝塞尔积分展开

柱坐标系中,本征函数族贝塞尔函数构成完备正交系,因此可作为广义傅里叶级数展开的基.本文从定义在有限区间[0,ρ0]上函数的广义傅里叶级数展开出发,利用贝塞尔函数的渐近展开公式以及贝塞尔函数零点的近似公式,讨论了半无界空间上函数的傅里叶-贝塞尔积分展开问题,得到了本征函数模方的近似表达式.当ρ0趋于无穷时,不连续参量变成连续参量,得到了函数的傅里叶-贝塞尔积分及其展开系数公式.     

Loop space solution of two-dimensional QCD

Two-dimensional QCD is reformulated in terms of gauge-invariant loop traces. It is shown that in the $\text{1}\text{N}$ approximation the theory is equivalent to a string theory, and reproduces the known meson spectrum.     

Auditory space expansion via linear filtering

A signal-processing algorithm that modifies the interaural time delays associated with directional sources is described. Signals received at two microphones are processed by four linear filters arranged in a lattice configuration to produce two outputs, one for each ear. Since the processing is linear, the method is equally applicable to single or multiple directional sources. The filters are designed to minimize the average squared error between a user specified desired space warping function and the actual warping function that they implement. Two classes of filters are considered: filters whose frequency response is unconstrained and filters constrained to be causal with finite impulse response. In both cases the solution of the least-squares problem is given and properties of the actual space warping function are examined. Perceptual experiments and analysis of acoustic waveforms are utilized to demonstrate the effectiveness of the algorithm. Extension of this method for utilizing more than two microphones is described.     

Magnetic field-aligned plasma expansion in critical ionizationvelocity space experiments

The temporal evolution of a plasma cloud released in an ambient plasma is studied. Time-dependent Vlasov equations for both electrons and ions, as well as the self-consistent electric field parallel to the ambient magnetic field, are solved. The initial cloud is considered to consist of cold, warm, and hot electrons with temperatures of approximately 0.2 eV, 2 eV, and 10 eV, respectively. It is found that the minor hot electrons escape the cloud; their velocity distribution function shows the typical time-of-flight dispersion feature, i.e. the average drift velocity of the escaping electrons is proportional to the distance from the cloud. The major warm electrons expand along the magnetic field lines with the corresponding ion-acoustic speed. The combined effect of the escaping hot electrons and the expanding warm ones sets up an electric potential structure that accelerates the ambient electrons into the cloud. Thus, the energy loss due to the electron escape is partly replenished. The electric field distribution in the potential structure depends on the stage of the evolution; before the rarefaction waves propagating from the edges of the cloud reach its center, the electric fields point into the cloud. After this stage the cloud divides into two subclouds, each having its own bipolar electric field. The effects of collisions on the evolution of plasma clouds are also discussed. The relevance of the results seen from the calculations are discussed in the context of space experiments on critical ionization velocity     

Emergence and expansion of cosmic space in an accelerating BIon

The European Physical Journal C - In this paper, we calculate the $$B\rightarrow D$$ transition form factors (TFFs) within the light-cone sum rules (LCSRs) and predict the ratio $$\mathcal {R}(D)$$...     

Renormalons as dilatation modes in the functional space

There are two possible sources of the factorial large-order behavior of a typical perturbative series. First, the number of different Feynman diagrams may be large; second, there may be abnormally large diagrams known as renormalons. It is well known that the large combinatorial number of diagrams is described by instanton-type solutions of the classical equations. We demonstrate that, from the functional-integral viewpoint, the renormalons do not correspond to a particular configuration but manifest themselves as dilatation modes in the functional space.     

Non-commutative chaotic expansion of Hilbert-Schmidt operators on Fock space

It is known, from a simple algebraic computation, that every Hilbert-Schmidt operator on the Fock space admits a Maassen-Meyer kernel. Maassen-Meyer kernels are a non-commutative extension of the usual notion of chaotic expansion of random variables. Using an extension of the non-commutative stochastic integrals which allows to define these integrals on the whole Fock space, we prove that a Hilbert-Schmidt operator on Fock space is the sum of a series of iterated non-commutative stochastic integrals with respect to the basic theree quantum noises. In this way we recover its Maassen-Meyer kernel which can be completely described from the operator itself.     

任意维欧氏空间的长程势多极展开

给出了在任意维欧氏空间中一个一般的长程相互作用势的多极展开结果,并推导得到了单极子和偶极子两两之间的相互作用力公式.     

Study of magnetic field expansion using a plasma generator for space radiation active protection

There are many active protecting methods including Electrostatic Fields, Confined Magnetic Field, Unconfined Magnetic Field and Plasma Shielding etc. for defending the high-energy solar particle events (SPE) and Galactic Cosmic Rays (GCR) in deep space exploration. The concept of using cold plasma to expand a magnetic field is the best one of all possible methods so far. The magnetic field expansion caused by plasma can improve its protective efficiency of space particles. One kind of plasma generator has been developed and installed into the cylindrical permanent magnet in the eccentric. A plasma stream is produced using a helical-shaped antenna driven by a radio-frequency (RF) power supply of 13.56 MHz, which exits from both sides of the magnet and makes the magnetic field expand on one side. The discharging belts phenomenon is similar to the Earth's radiation belt, but the mechanism has yet to be understood. A magnetic probe is used to measure the magnetic field expansion distributions, and the results indicate that the magnetic field intensity increases under higher increments of the discharge power.     

Convergence properties of Monte Carlo functional expansion tallies

The functional expansion tally (FET) is a method for constructing functional estimates of unknown tally distributions via Monte Carlo simulation. This technique uses a Monte Carlo calculation to estimate expansion coefficients of the tally distribution with respect to a set of orthogonal basis functions. The rate at which the FET approximation converges to the true distribution as the expansion order is increased is developed. For sufficiently smooth distributions the FET is shown to converge faster, and achieve a lower residual error, than a histogram approximation.     

Analysis of free energy functional density expansion theories

Density expansion theories are often used, within the density functional formalism, to approximate the Helmholtz free-energy functional of simple classical fluids. An overview of the theoretical framework of density expansion theories is presented. Several density functional theories that employ truncated density expansions are then analysed with attention focused on their thermodynamic properties. It is found that, of these theories, only the commonly used mean-field theory satisfies the Gibbs adsorption equation; the inconsistencies within the other theories arise from truncation of the density expansion without appropriate modification of the expansion coefficients. Other repercussions of truncating the density expansion are discussed.     

Operator product expansion and quark condensate from lattice QCD in coordinate space

We present a lattice QCD determination of the chiral quark condensate based on a new method. We extract the quark condensate from the operator product expansion of the quark propagator at short euclidean distances, where it represents the leading contribution in the chiral limit. From this study we obtain , in good agreement with determinations of this quantity based on different approaches. The simulation is performed by using the -improved Wilson action at on a volume 32³ × 70 in the quenched approximation.Received: 8 March 2005, Revised: 15 April 2005, Published online: 18 May 2005PACS: 11.15.Ha, 11.30.Rd, 12.38.-t, 12.38.Gc     

Laurent series expansion of sunrise-type diagrams using configuration space techniques

We show that configuration space techniques can be used to efficiently calculate the complete Laurent series -expansion of sunrise-type diagrams to any loop order in D-dimensional space-time for any external momentum and for arbitrary mass configurations. For negative powers of the results are obtained in analytical form. For positive powers of including the finite contribution the result is obtained numerically in terms of low-dimensional integrals. We present general features of the calculation and provide exemplary results up to five-loop order which are compared to available results in the literature.Received: 9 April 2004, Revised: 28 June 2004, Published online: 23 July 2004Partially supported by RFBR grants # 02-01-601, 03-02-17177.     

Improving the resolution of functional brain imaging: analyzing functional data in anatomical space

The accurate mapping of functional magnetic resonance imaging (fMRI) activations to anatomical structures is critical for fMRI studies of brain organization. In the commonly used functional space analysis method, functional images are realigned to a functional reference image and processed in low-resolution functional space. The average functional activations are then projected into high-resolution anatomical space for visualization. Here, we describe a new technique, anatomical space analysis (ASA), whereby low-resolution functional images are first coregistered and resampled directly into high-resolution anatomical space with all subsequent data processing performed in high-resolution space. A major advantage of ASA is that minor scanner sampling instabilities and small head movements can increase spatial resolution by providing multiple samples of the relationship between functional and anatomical space. Both simulations and analyses of real fMRI data show that ASA improves the precision, objectivity and reproducibility of functional brain mapping.     

Loop space Hamiltonians and numerical methods for large-N gauge theories

We consider large-N gauge theories in the hamiltonian, collective field approach. We derive an alternative collective representation which leads to significant reduction when translation invariance is invoked. It allows for a simplified computer simulation of loop rearrangements and the development of numerical techniques in the hamiltonian, loop space formalism. We proceed to give numerical evidence for validity of our representation and outline a general numerical approach for solving large-N QCD in terms of gauge-invariant Wilson loop variables.