Nilpotent invariants in N=4 SYM

It is shown that there are no nilpotent invariants in N=4 analytic superspace for n≤4 points. It is argued that there is (at least) one such invariant for n=5 points which is not invariant under U(1)_Y. The consequences of these results are that the n=2 and 3 point correlation functions of the N=4 gauge-invariant operators which correspond to KK multiplets in AdS supergravity are given exactly by their tree level expressions, the 4 point correlation functions of such operators are invariant under U(1)_Y and correlation functions with n≥4 points have non-trivial dependence on the Yang-Mills coupling constant.     

Real space and configuration space wave function in the intermediate valence problem

This paper analyses the behavior of intermediate valence compounds, from the point of view of wave functions. They are expressed in a linear combination of cellular orbitals (LCCO) basis for SCF plus correlation introduced in the configuration interaction (CI) scheme, suitable to describe the different spatial extension in real space and the correlation between different fⁿ possibilities. This allows the discussion of the large variety of interesting phenomena which arises from the changes of the f electron configuration space wave functions: fⁿ → fⁿ⁺¹ of from the changes of the electronic charge from atomic-like to the different condensed matter-like boundary conditions. In particular an analysis is included of the correspondence between the actual properties in this type of materials and the amount of atomic-like f character n_f^atomic ?n_f^total in some rare earth and actinide compounds, concluding that the experimental evidence is consistent with a large distortion of the actual f-wave functions from their atomic-like forms.     

Lagrangian structure functions in hydrodynamic turbulence

Based on a solution of the Navier-Stokes equations for the inertial range of fully developed turbulence, a statistical theory is developed to determine the Lagrangian structure functions K _n (τ). Over times τ shorter than the large-scale correlation time τ_c, they obey scaling relations of the form K _n (τ) ∞ \(\tau ^{\zeta _n } \). Analytical expressions are derived for ζ _n . A detailed comparison between the theory and the experimental results presented in [1] demonstrates complete quantitative agreement. A new concept is introduced in turbulence theory: the correlation R _n (τ) between tracer-particle positions on a Lagrangian trajectory. It is shown that the position correlation functions R _n exhibit universal scaling behavior for n > 3.     

A mode coupling theory of higher order time correlation functions

Kawasaki's mode coupling theory [Ann. Phys. 61 (1970) 1] is used to compute time correlation functions of the form 〈A_k0(t₀) … A_kn(t_n)〉, where A_k(t) represents some slowly varying quantity. The Gaussian and Bare Vertex approximations are made, thus yielding extremely simple expressions for these higher order correlation functions. These do not contain any bare transport coefficients and suggest relatively simple tests by which the theory could be checked. Examples relating to light scattering in nonequilibrium systems and the hydrodynamics of simple fluids are presented.     

Diffusion-limited annihilation in inhomogeneous environments

We study diffusion-limited (on-site) pair annihilation A + A → 0 and (on-site) fusion A + A → A which we show to be equivalent for arbitrary space-dependent diffusion and reaction rates. For one-dimensional lattices with nearest neighbour hopping we find that in the limit of infinite reaction rate the time-dependent n-point density correlations for many-particle initial states are determined by the correlation functions of a dual diffusion-limited annihilation process with at most 2n particles initially. Furthermore, by reformulating general properties of annihilating random walks in one dimension in terms of fermionic anticommutation relations we derive an exact representation for these correlation functions in terms of conditional probabilities for a single particle performing a random walk with dual hopping rates. This allows for the exact and explicit calculation of a wide range of universal and non-universal types of behaviour for the decay of the density and density correlations.     

Asymptotic correlation functions and FFLO signature for the one-dimensional attractive spin-1/2 Fermi gas

We investigate the long distance asymptotics of various correlation functions for the one-dimensional spin-1/2 Fermi gas with attractive interactions using the dressed charge formalism. In the spin polarized phase, these correlation functions exhibit spatial oscillations with a power-law decay whereby their critical exponents are found through conformal field theory. We show that spatial oscillations of the leading terms in the pair correlation function and the spin correlation function solely depend on ΔkF and 2ΔkF, respectively. Here ΔkF=π(n_↑−n_↓) denotes the mismatch between the Fermi surfaces of spin-up and spin-down fermions. Such spatial modulations are characteristics of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. Our key observation is that backscattering among the Fermi points of bound pairs and unpaired fermions results in a one-dimensional analog of the FFLO state and displays a microscopic origin of the FFLO nature. Furthermore, we show that the pair correlation function in momentum space has a peak at the point of mismatch between both Fermi surfaces k=ΔkF, which has recently been observed in numerous numerical studies.     

Multiplicity distributions in the generalized Feynman gas model

Multiplicity distributions Ψ_n^(k) in the generalized Feynman gas model of order k (defined by saying that all integrated correlation functions f_n except f₁,…,f_k are zero) are derived and expressed in terms of Poisson distributions with different ”average multiplicities”, which are related to the integrated correlation functions. The relations between Ψ_n^(k) and Ψ_n^(j) for arbitrary positive integers k,j are found. An intuitive picture to gain a better feeling for these relations is developed.On the basis of our formulae we show that the experimentally observed multiplicity distributions (between 50 GeV/c and 303 GeV/c incoming momentum) can be well reproduced by those of a Feynman gas model of order two. Other applications of our formulae are suggested.     

Ground state correlation in the two-dimensional polarized electron gas

The ground state energy and radial distribution functions of the polarized two-dimensional electron gas with valley degeneracyn _v =1 and 2 are calculated using the hypernetted-chain approximation with the effective correlation factor method for Fermions. The paramagnetic susceptibility is calculated and compared with experiment in silicon inversion layers.     

Non-interacting dimer kinetics in hypercubic lattices

The exact formulation of the kinetic of dimer in hypercubic lattices is developed in the framework of the kinetic lattice gas model. The so-called local evolution rules are used to obtain the hierarchy of equation of motion for the correlation functions where processes like adsorption and desorption are included. The hierarchy of equations are truncated using a mean field (m, n) closures which allows the analytical treatment of the system. A general expression for non-interacting dimer isotherm and two particle correlation functions are obtained in hypercubic lattices.     

Exact solution of the impure one-dimensional n-vector model with bilinear and biquadratic exchange interactions

We demonstrate explicitly that the impure one-dimensional n-vector model with bilinear and biquadratic exchange interactions can be solved exactly. Results are provided for the free energy, equal-time spin-spin correlation functions and the initial susceptibility of the corresponding bond and site model in the annealed and quenched limit. A numerical analysis of the thermodynamic response functions in the n = 3 case is performed, and therein some interesting consequences of the simultaneous influence of the biquadratic interactions and impurities are established. The presence of the biquadratic interaction is interpreted as an effect of the lattice compressibility.     

Entanglement of three qubits

For the formulation of Bell inequalities, it is important to include not just N-site correlation functions, but also (N-n)-site correlation functions. In this article, we focus on a three-qubit Bell inequality, which has been shown to be a good candidate for generalizing Gisin’s theorem to three qubits. The three-qubit Bell inequality can be used to detect the W-type entanglement in a proposed experiment.     

Transition energy and dipole oscillator strength of 1s23d-1s2 nf transitions for Sc18+ ion

The transition energies of the 1s²3d-1s² nf (4?n?9) transitions and fine structure splittings of 1s² nf (n?9) states for Sc¹⁸⁺ ion are calculated with the full-core plus correlation method. The quantum defect of 1s² nf series is determined by the single-channel quantum defect theory. The energies of any highly excited states with n?10 for this series can be reliably predicted using the quantum defect as function of energy. Three alternative forms of the dipole oscillator strengths for the 1s²3d-1s² nf (n?9) transitions of Sc¹⁸⁺ ion are calculated with the transition energies and wave functions obtained above. Combining the quantum defect theory with the discrete oscillator strengths, the discrete oscillator strengths for 1s²3d-1s² nf (n > 9) transitions and the oscillator strengths densities corresponding to the bound-free transitions are obtained.     

Spectra of random contractions and scattering theory for discrete-time systems

Random contractions (subunitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex eigenvalues of generic N × N random matrices  of such a type, corresponding to systems with broken time reversal invariance. Deviations from unitarity are characterized by rank M≤N and a set of eigenvalues 0<T _i≤1, i=1,..., M of the matrix $\hat T = \hat 1 - \hat A^\dag \hat A$ . We solve the problem completely by deriving the joint probability density of N complex eigenvalues and calculating all n-point correlation functions. In the limit N?M, n, the correlation functions acquire the universal form found earlier for weakly non-Hermitian random matrices.     

Photon states and Wigner functions in parametric generation

The problem of preparation of photon states from two correlated modes of subharmonics generated in pulsed regime of optical parametric oscillator is investigated. Because of quantum correlation, detecting of n-photon Fock states in one mode transfers the other mode into also an n-photon state. Conditional Wigner functions are calculated whose negative parts describe the prepared photon states in cases of one-, two-, and three-photon schemes of measurements.     

On the approach to kinetic theory due to Gross

A classical kinetic theory introduced by Gross is explored in further detail. The theory consists of a sequence of approximations to the Liouville distribution function, with each approximation leading to a truncation of the BBGKY hierarchy at successively higher order. We formulate the truncation scheme at general order in terms of a set of time-dependent equilibrium correlation functions. It has the correct symmetries and, as is implied by the work of Gross with the first two approximations, is such that the interparticle potential appears only implicitly via static equilibrium correlation functions. We arrange the theory as a sequence of linear kinetic equations for the phase-space density correlation function, and solve for the collision kernels which result in each order. The collision kernel of the second approximation, which involves only binary dynamics, is shown to be a mean-field generalization of the known low-density kernel. The third approximation gives a similar generalization of the triple-collision kernel. The nth approximation also reproduces the frequency moments of S(kω) through order ω²ⁿ. More generally, the approximations are shown to give a continued-fraction expansion of the collision kernel, with the levels governed by the dynamics of successively larger numbers of particles. This is a renormalized kinetic theory in the sense that the potential is eliminated and clusters of particles are never isolated.     

Numerical simulation of coherent effects under conditions of multiple scattering

The time correlation function and the interference component of the coherent backscattering from a multiple-scattering medium are calculated in the framework of the Monte Carlo technique. By comparing the stochastic Monte Carlo technique with the iteration procedure of solving the Bethe-Salpeter equation, it is shown that the simulation of the optical path of photon packets that have experienced n scattering events is exactly equivalent to calculating the nth-order ladder diagram. Using this equivalence, the Monte Carlo technique is generalized for simulation of the time correlation functions and coherent backscattering.     

Distributions of products of the quasifree knocking-out reaction (p,p′n) on halo nuclei in the intermediate-energy region

Expressions for the distribution functions of products of the reaction (p, p′n) of valence neutron knocking-out from halo nuclei were derived using space-time correlation functions. The possibility of using this reaction to study the neutron halo structure was analyzed.