Hard exclusive meson production and nonforward parton distributions

We present an analysis of twist-2, leading order QCD amplitudes for hard exclusive leptoproduction of mesons in terms of double/nonforward parton distribution functions. After reviewing some general features of nonforward nucleon matrix elements of twist-2 QCD string operators, we propose a phenomenological model for quark and gluon nonforward distribution functions. The corresponding QCD evolution equations are solved in the leading logarithmic approximation for flavor nonsinglet distributions. We derive explicit expressions for hard exclusive , , and neutral vector meson production amplitudes and discuss general features of the corresponding cross sections. Received: 12 November 1997 / Published online: 26 February 1998     

Entanglement of Λ atoms under coherent population trapping

The entanglement of the internal states in ensembles of Λ atoms under coherent population trapping has been considered. The entanglement conditions for the pairs and triples of atoms have been derived in the form of inequalities for the correlation functions of the resonant optical field amplitudes. The fulfillment of these conditions requires the nonclassicality (the absence of positive definiteness) of the probability distribution of the amplitudes.     

Entanglement of Λ atoms under coherent population trapping

The entanglement of the internal states in ensembles of Λ atoms under coherent population trapping has been considered. The entanglement conditions for the pairs and triples of atoms have been derived in the form of inequalities for the correlation functions of the resonant optical field amplitudes. The fulfillment of these conditions requires the nonclassicality (the absence of positive definiteness) of the probability distribution of the amplitudes.

     

Bivariate averaging and the Wigner distribution function

In order to gain insight into the nature of the Wigner and related distribution functions, bivariate averaging functions of real unbounded variables with absolutely continuous marginals that are ordinary probabilities are considered. Accordingly variables are chosen to be phase space variables that are respectively eigenvalues of position and momentum operators. The impact of the condition that the marginals are squared magnitudes of amplitudes that are Fourier transforms of one another is emphasized by the delay of the introduction of this Fourier transform condition until after the form for a bivariate distribution with the given marginals is obtained. When the respective amplitudes are fourier transforms of one another, special cases of the bivariate averaging function correspond to generalized Wigner functions characterized by a parameterα. Such anα-Wigner function can be used as the basis of a consistent averaging procedure if an appropriate corresponding representation for underlying operators to be averaged is specified. Properties of theα-Wigner functions are summarized.     

Modelling the nucleon wave function from soft and hard processes

Current light-cone wave functions for the nucleon are unsatisfactory since they are in conflict with the data of the nucleon’s Dirac form factor at large momentum transfer. Therefore, we attempt a determination of a new wave function respecting theoretical ideas on its parameterization and satisfying the following constraints: It should provide a soft overlap contribution to the proton’s form factor in agreement with data; it should be consistent with current parameterizations of the valence quark distribution functions and lastly it should provide an acceptable value for theJ/ψ → N N decay width. The latter process is calculated within the modified perturbative approach to hard exclusive reactions. A simultaneous fit to the three sets of data leads to a wave function whosex-dependent part, the distribution amplitude, shows the same type of asymmetry as those distribution amplitudes constrained by QCD sum rules. The assymetry is however much more moderate as in those amplitudes. Our distribution amplitude resembles the asymptotic one in shape but the position of the maximum is somewhat shifted.     

Modelling the nucleon wave function from soft and hard processes

Current light-cone wave functions for the nucleon are unsatisfactory since they are in conflict with the data of the nucleon’s Dirac form factor at large momentum transfer. Therefore, we attempt a determination of a new wave function respecting theoretical ideas on its parameterization and satisfying the following constraints: It should provide a soft overlap contribution to the proton’s form factor in agreement with data; it should be consistent with current parameterizations of the valence quark distribution functions and lastly it should provide an acceptable value for the J/ψ → NN decay width. The latter process is calculated within the modified perturbative approach to hard exclusive reactions. A simultaneous fit to the three sets of data leads to a wave function whose x-dependent part, the distribution amplitude, shows the same type of asymmetry as those distribution amplitudes constrained by QCD sum rules. The asymmetry is however much more moderate as in those amplitudes. Our distribution amplitude resembles the asymptotic one in shape but the position of the maximum is somewhat shifted.     

电磁迴旋不稳定性的准线性理论

在有弱相对论性电子时,在电子迴旋频率Ω_e附近存在快x模的不稳定性。从这一事实出发,我们用准线性理论分析了具有粒子数倒转的分布函数引起的不稳定性最后达到饱和的物理机制。进行了一些近似的计算,求出了电磁迴旋不稳定性的饱和时间和饱和能量及垂直、平行分布函数随时间的演化过程。发现用此理论算出的饱和能级与观察到的AKR结果是一致的。 关键词：     

Study of quark distribution amplitudes of 1<Emphasis Type="Italic">S</Emphasis> and 2<Emphasis Type="Italic">S</Emphasis> heavy quarkonium states

In this paper, the quark distribution amplitudes of 1S and 2S heavy quarkonium states are studied in terms of Gaussian-type wave functions. The transverse momenta p _⊥ integrals of the formulae for the decay constant are performed analytically. Then the quark distribution amplitudes are obtained. In addition, the ξ-moments are also calculated. After fixing the relevant parameters appearing in the quark distribution amplitude, the curves of the quark distribution amplitude for 1S and 2S heavy quarkonium states are plotted. Finally, the numerical results of this approach are compared with the other theoretical predictions.     

Characteristic functional for one class of non-Gaussian random functions

A generalization of Poissonian random functions is presented. A characteristic functional is derived that includes four arbitrary functions: the generating function of the factorial moments for the number of bursts; the probability density function for the positions of bursts; the characteristic function for the amplitudes of bursts; and the function describing the shape of a burst depending on its position. In the case of the Poisson distribution of the number of bursts, uniform distribution of burst positions, and independence of the burst's shape on its position, this characteristic functional turns out to be known for Poissonian random functions. Many new formulae for the characteristic functional are presented.     

Anomalously localised electronic states in three-dimensional disordered systems

We study the Anderson model of localisation at the metal-insulator transition in the band centre of three-dimensional disordered samples. For the critical disorder we determine a large number of wave functions of the model and study the distribution of the wave function amplitudes. Deviations from scaling of multifractal correlation functions allow us to discriminate anomalously localised states from the usual critical states. The thus identified anomalously localised states lead to deviations of the critical properties and should be eliminated from the ensemble average for a characterisation of criticality.     

Recursion relations and scattering amplitudes in the light-front formalism

The fragmentation functions and scattering amplitudes are investigated in the framework of light-front perturbation theory. It is demonstrated that, the factorization property of the fragmentation functions implies the recursion relations for the off-shell scattering amplitudes which are light-front analogs of the Berends–Giele relations. These recursion relations on the light-front can be solved exactly by induction and it is shown that the expressions for the off-shell light-front amplitudes are represented as a linear combinations of the on-shell amplitudes. By putting external particles on-shell we recover the scattering amplitudes previously derived in the literature.     

Gluon cascades and amplitudes in light-front perturbation theory

We construct the gluon wave functions, fragmentation functions and scattering amplitudes within the light-front perturbation theory. Recursion relations on the light-front are constructed for the wave functions and fragmentation functions, which in the latter case are the light-front analogs of the Berends–Giele recursion relations. Using general relations between wave functions and scattering amplitudes it is demonstrated how to obtain the maximally-helicity violating amplitudes, and explicit verification of the results is based on simple examples.     

Anomalously localised states at the Anderson transition

Non-multifractal critical wave functions at the Anderson transition are numerically investigated for the SU(2) model belonging to the two-dimensional symplectic class. These states can be regarded as anomalously localised states (ALS) at criticality. Giving a quantitative definition of ALS, it has been revealed that the probability to find ALS increases with the system size and remains at a finite value even in the thermodynamic limit. The most probable, namely typical, critical states have the multifractal nature, while its probability measure is zero. In order to understand how ALS affect critical properties in infinite systems, we studied the distribution of the correlation dimension D₂ and the nearest-neighbour level spacing distribution P(s) by paying attention to ALS. Results show that the influence of ALS to these distribution functions is limited. This is because the spatial distribution of amplitudes in tail regions of ALS exhibits multifractality as in the case of typical critical wave functions.     

The Q2 evolution of flavour singlet wave functions in QCD

We calculate the Q² evolution of the quark-antiquark and gluon-gluon components of helicity-zero, flavour and colour singlet wave functions by summing diagrams to all orders in axial gauge QCD perturbation theory in the leading logarithm approximation. We find that Gegenbauer moments of these components have exactly the same scale-breaking behaviour as moments of singlet quark and gluon distribution functions in leptoproduction. The resulting singlet wave function is used to calculate the amplitudes for quark-antiquark and gluon-gluon jet production in off-shell photon-photon collisions.     

The statistical wave function

Statistical considerations are applied to quantum mechanical amplitudes. The physical motivation is the progress in the spectroscopy of highly excited states, The corresponding wave functions are strongly mixed. In terms of a basis set of eigenfunctions of a zeroth-order Hamiltonian with good quantum numbers, such wave functions have contributions from many basis states. The vector x is considered whose components are the expansion coefficients in that basis. Any amplitude can be written as a·x. It is argued that the components of x and hence other amplitudes can be regarded as random variables. The maximum entropy formalism is applied to determine the corresponding distribution function. Two amplitudes a·x and b·x are independently distributed if b·a=0. It is suggested that the theory of quantal measurements implies that, in general, one can one determine the distribution of amplitudes and not the amplitudes themselves.This paper is dedicated to Prof. Howard Reiss on the occasion of his 66th birthday.     

Angular momentum and temperature dependence of fission barriers with a realistic force

Angular distributions and excitation functions were measured for 30 2⁺ resonances in the³⁹K(p,p₀) and₃₉K(p, α⁰) reactions. Partial reduced widths have been extracted for three proton channels; the relative signs of the reduced width amplitudes for two of these channels were also determined. Reduced widths are generally consistent with a Gaussian distribution for the reduced width amplitudes, but the amplitudes themselves are not. These data represent the first measurement of correlation coefficients in an entrance channel and suggest that the large correlations previously observed in exit channels are generic features of this mass region.     

Development of ultrahigh-precision coherent control and its applications

Coherent control is based on optical manipulation of the amplitudes and phases of wave functions. It is expected to be a key technique to develop novel quantum technologies such as bond-selective chemistry and quantum computing, and to better understand the quantum worldview founded on wave-particle duality. We have developed high-precision coherent control by imprinting optical amplitudes and phases of ultrashort laser pulses on the quantum amplitudes and phases of molecular wave functions. The history and perspective of coherent control and our recent achievements are described.     

Current Algebra on the Torus

We derive the N-point one-loop correlation functions for the currents of an arbitrary affine Kac-Moody algebra. The one-loop amplitudes, which are elliptic functions defined on the torus Riemann surface, are specified by group invariant tensors and certain constant tau-dependent functions. We compute the elliptic functions via a generating function, and explicitly construct the invariant tensor functions recursively in terms of Young tableaux. The lowest tensors are related to the character formula of the representation of the affine algebra. These general current algebra loop amplitudes provide a building block for open twistor string theory, among other applications.     

Siebenmann-type cobordisms with borders and topology changes by quantum tunneling

Siebenmann-type cobordisms are constructed to describe topology changes with the Seifert fibered homology spheres in in- and out-states. We study the problem of determining of topology-changing amplitudes for these quantum tunneling processes. The calculations are performed in the stationary phase approximation for Kodama wave functions. In this approximation the amplitudes are expressed in terms of Chern-Simons invariants of flatSU(2)-connections over the cobordism boundary components. The topology-change amplitudes found are factorized into the Kodama wave functions for the lens spaces. The results are compared with those for Fintushel-Stern-type cobordisms which have been previously investigated.