Many-body diagrammatic expansion in a kohn-sham basis: implications for time-dependent density functional theory of excited states

We formulate diagrammatic rules for many-body perturbation theory which uses Kohn-Sham Green's functions as basic propagators. The diagram technique allows one to study the properties of the dynamic nonlocal exchange-correlation (xc) kernel f(xc). We show that the spatial nonlocality of f(xc) is strongly frequency dependent. In particular, in extended systems the nonlocality range diverges at the excitation energies. This divergency is related to the discontinuity of the xc potential.     

Probability density functions of the enstrophy flux in two dimensional grid turbulence

Probability density functions of the enstrophy flux in two dimensional grid turbulence are found to be strongly non-Gaussian and can be mimicked by stretched exponential functions. Evidence of this behavior is found in experiments using turbulent soap films and numerical simulations. The enstrophy flux itself is found to be constant for a range of scales corresponding to the enstrophy cascade.     

Growth of density inhomogeneities in a flow of wave turbulence

We consider the flow being a superposition of random waves and describe the evolution of the spectrum of the passive scalar in the leading (fourth) order with respect to the wave amplitudes. We find that wave turbulence can produce an exponential growth of the passive scalar fluctuations when either both solenoidal and potential components are present in the flow or there are potential waves with the same frequencies but different wave numbers.     

On the theory of turbulence: A non eulerian renormalized expansion

A non Eulerian framework for a renormalized theory of isotropic homogeneous steady state turbulence at high Reynold's numbers is developed. By construction it is invariant under random Galilei transformations. A direct interaction factorization is free of infrared singularities and yields Kolmogorov scaling for the static as well as for the dynamic correlation and response functions.     

Derivation of the density functional theory from the cluster expansion

The density functional theory is derived from a cluster expansion by truncating the higher-order correlations in one and only one term in the kinetic energy. The formulation allows self-consistent calculation of the exchange correlation effect without imposing additional assumptions to generalize the local density approximation. The pair correlation is described as a two-body collision of bound-state electrons, and modifies the electron- electron interaction energy as well as the kinetic energy. The theory admits excited states, and has no self-interaction energy.     

Steady-state probability density function in wave turbulence under large volume limit

We investigate the possibility for two-mode probability density function(PDF) to have a non-zero flux steady state solution.We take the large volume limit so that the space of modes becomes continuous.It is shown that in this limit all the steady-state two-or higher-mode PDFs are the product of one-mode PDFs.The flux of this steady-state solution turns out to be zero for any finite mode PDF.     

Generalized density expansion in the kinetic theory and the resistivity of liquid metals

For the system of electrons and immovable interacting centers an exact equation for averaged electron Green's function is formulated. The expansion of self-energy part over the one-particle t-matrices and explicit Green's functions is derived. It represents a kind of a generalized density series containing the correlation functions of the centres. In the low approximation over t-matrix, the transition probability (t)²S in the kinetic equation is obtained (S = the structure factor of centers).     

A statistical mechanics model of isotropic turbulence well-defined within the context of the $\mathsf{\epsilon}$ expansion

A statistical mechanics model of isotropic turbulence that renormalizes the effects of turbulent stresses into a velocity-gradient-dependent random force term is introduced. The model is well-defined within the context of the renormalization group expansion, as the effective expansion parameter is . The Kolmogorov constant and N parameter of turbulence are of order unity, in accord with experimental results. Nontrivial intermittency corrections to the single-time structure functions are calculated as a controlled expansion in .Received: 20 December 2002, Published online: 23 July 2003PACS:   47.27.Ak Fundamentals - 47.27.Gs Isotropic turbulence; homogeneous turbulence - 05.10.Cc Renormalization group methods     

Two-parameter expansion in the renormalization-group analysis of turbulence

The renormalization of the solution of the Navier-Stokes equation for randomly stirred fluid with long-range correlations of the driving force is analysed near two dimensions. It is shown that a local term must be added to the correlation function of the random force for the correct renormalization of the model at two dimensions. The interplay of the short-range and long-range terms in the large-scale behaviour of the model is analysed near two dimensions by the field-theoretic renormalization group. A regular expansion in 2ε=d-2 and δ=2-λ is constructed, whered is the space dimension and λ the exponent of the powerlike correlation function of the driving force. It is shown that in spite of the additional divergences, the asymptotic behaviour of the model near two dimensions is the same as in higher dimensions, contrary to recent conjectures based on an incorrect renormalization procedure.     

Two-parameter expansion in the renormalization-group analysis of turbulence

The renormalization of the solution of the Navier-Stokes equation for randomly stirred fluid with long-range correlations of the driving force is analysed near two dimensions. It is shown that a local term must be added to the correlation function of the random force for the correct renormalization of the model at two dimensions. The interplay of the short-range and long-range terms in the large-scale behaviour of the model is analysed near two dimensions by the field-theoretic renormalization group. A regular expansion in 2ε=d-2 and δ=2-λ is constructed, whered is the space dimension and λ the exponent of the powerlike correlation function of the driving force. It is shown that in spite of the additional divergences, the asymptotic behaviour of the model near two dimensions is the same as in higher dimensions, contrary to recent conjectures based on an incorrect renormalization procedure.     

Second-quantization representation and diagrammatic technique for systems of composite particles

A second-quantization formalism for systems of interacting free elementary particles and their bound clusters is presented. A modified version of the Feynman-Goldstone diagrammatic technique is used for the classification and evaluation of individual terms appearing in this formalism. The resulting effective Hamiltonian naturally includes such processes as Coulomb and exchange interactions between bound composite particles, their breakup and recombination reactions, etc. For simplicity, a system of hydrogen atoms, protons, and electrons is studied. The method can easily be generalized to any species of composite particles.Dedicated to Professor Alexander Tká on the occasion of his sixtieth birthday.     

Probability density in the complex plane

The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years, many papers have been published on the extension of both quantum mechanics and classical mechanics into the complex domain. However, the question of whether complex quantum mechanics resembles complex classical mechanics at high energy has not yet been studied. This paper introduces the concept of a local quantum probability density ρ(z) in the complex plane. It is shown that there exist infinitely many complex contours C of infinite length on which ρ(z) dz is real and positive. Furthermore, the probability integral is finite. Demonstrating the existence of such contours is the essential element in establishing the correspondence between complex quantum and classical mechanics. The mathematics needed to analyze these contours is subtle and involves the use of asymptotics beyond all orders.     

Observation of intermittency in wave turbulence

We report the observation of intermittency in gravity-capillary wave turbulence on the surface of mercury. We measure the temporal fluctuations of surface wave amplitude at a given location. We show that the shape of the probability density function of the local slope increments of the surface waves strongly changes across the time scales. The related structure functions and the flatness are found to be power laws of the time scale on more than one decade. The exponents of these power laws increase nonlinearly with the order of the structure function. All these observations show the intermittent nature of the increments of the local slope in wave turbulence. We discuss the possible origin of this intermittency.