Reply to "Comment on 'Signal correlation between two normal-mode helical antennas for diversity reception in a multipath environment'"

This comment points out an inaccurate formula relating the signal correlation coefficient to the mutual impedance and corrects it. © 2005 IEEE.

Capacity of MIMO Channels: asymptotic evaluation under correlated fading

This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multiple-inputmultiple-output channels with fading correlation at either thetransmitter or the receiver. We consider the asymptotic situation,where the number of inputs and outputs increase without boundat the same rate. A simple uniparametric model for the fadingcorrelation function is proposed and the asymptotic capacity perantenna is derived in closed form. Although the proposed correlationmodel is introduced only for mathematical convenience, itis shown that its shape is very close to an exponentially decayingcorrelation function. The asymptotic expression obtained providesa simple and yet useful way of relating the actual fadingcorrelation to the asymptotic capacity per antenna from a purelyanalytical point of view. For example, the asymptotic expressionsindicate that fading correlation is more harmful when arising atthe side with less antennas. Moreover, fading correlation does notinfluence the rate of growth of the asymptotic capacity per receiveantenna with high Eb /N0.

Pseudofermion dynamical theory for the spin dynamical correlation functions of the half-filled 1D Hubbard model

A modified version of the metallic-phase pseudofermion dynamical theory (PDT) of the 1D Hubbard model is introduced for the spin dynamical correlation functions of the half-filled 1D Hubbard model Mott– Hubbard phase. The Mott–Hubbard insulator phase PDT is applied to the study of the model longitudinal and transverse spin dynamical structure factors at finite magnetic field h, focusing in particular on the sin- gularities at excitation energies in the vicinity of the lower thresholds. The relation of our theoretical results to both condensed-matter and ultra-cold atom systems is discussed.

Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

Evaluation of group electronegativities and hardness (softness) of group 14 elements and containing functional groups through density functional theory and correlation with NMR spectra data

Quantum Chemical calculations for group 14 elements of Periodic Table (C, Si, Ge, Sn, Pb) and their functional groups have been carried out using Density Functional Theory (DFT) based reactivity descriptors such as group electronegativities, hardness and softness. DFT calculations were performed for a large series of tetracoordinated Sn compounds of the CH3SnRR'X type, where X is a halogen and R and R' are alkyl, halogenated alkyl, alkoxy, or alkyl thio groups. The results were interpreted in terms of calculated electronegativity and hardness of the SnRR'X groups, applying a methodology previously developed by Geerlings and coworkers (J. Phys. Chem. 1993, 97, 1826). These calculations allowed to see the regularities concerning the influence of the nature of organic groups RR' and inorganic group X on electronegativities and hardness of the SnRR'X groups; in this case, it was found a very good correlation between the electronegativity of the fragment and experimental 119Sn chemical shifts, a property that sensitively reflects the change in the valence electronic structure of molecules. This work was complemented with the study of some compounds of the EX and ER types, where E= C, Si, Ge, Sn and R= CH3, H, which was performed to study the influence that the central atom has on the electronegativity and hardness of molecules, or whether these properties are mainly affected for the type of ligand bound to the central atom. All these calculations were performed using the B3PW91 functional together with the 6-311++G** basis set level for H, C, Si, Ge, F, Cl and Br atoms and the 3-21G for Sn and I atoms.

Correlation between Fourier series expansion and Hückel orbital theory

The Fourier series can be used to describe periodic phenomena such as the one-dimensional crystal wave function. By the trigonometric treatements in Hückel theory it is shown that Hückel theory is a special case of Fourier series theory. Thus, the conjugated π system is in fact a periodic system. Therefore, it can be explained why such a simple theorem as Hückel theory can be so powerful in organic chemistry. Although it only considers the immediate neighboring interactions, it implicitly takes account of the periodicity in the complete picture where all the interactions are considered. Furthermore, the success of the trigonometric methods in Hückel theory is not accidental, as it based on the fact that Hückel theory is a specific example of the more general method of Fourier series expansion. It is also important for education purposes to expand a specific approach such as Hückel theory into a more general method such as Fourier series expansion.

Correlation functions in super liouville theory

We calculate three- and four-point functions in super Liouville theory coupled to a super Coulomb gas on world sheets with spherical topology. We first integrate over the zero mode and assume that a parameter takes an integer value. We find the amplitudes, give plausibility arguments in favor of the result, and formally continue the parameter to an arbitrary real number. Remarkably the result is completely parallel to the bosonic case.

Total internal reflection fluorescence cross-correlation spectroscopy: theory and application for studying boundary slip phenomenon

I present a new experimental method called Total Internal Reflection Fluorescence Cross-Correlation Spectroscopy (TIR-FCCS). It is a method that can probe hydrodynamic flows near solid surfaces, on length scales of tens of nanometres. Fluorescent tracers flowing with the liquid are excited by evanescent light, produced by epi-illumination through the periphery of a high NA oil-immersion objective. Due to the fast decay of the evanescent wave, fluorescence only occurs for tracers in the ~100 nm proximity of the surface, thus resulting in very high normal resolution. The time-resolved fluorescence intensity signals from two laterally shifted (in flow direction) observation volumes, created by two confocal pinholes are independently measured and recorded. The cross-correlation of these signals provides important information for the tracers’ motion and thus their flow velocity. Due to the high sensitivity of the method, fluorescent species with different size, down to single dye molecules can be used as tracers. The aim of my work was to build an experimental setup for TIR-FCCS and use it to experimentally measure the shear rate and slip length of water flowing on hydrophilic and hydrophobic surfaces. However, in order to extract these parameters from the measured correlation curves a quantitative data analysis is needed. This is not straightforward task due to the complexity of the problem, which makes the derivation of analytical expressions for the correlation functions needed to fit the experimental data, impossible. Therefore in order to process and interpret the experimental results I also describe a new numerical method of data analysis of the acquired auto- and cross-correlation curves – Brownian Dynamics techniques are used to produce simulated auto- and cross-correlation functions and to fit the corresponding experimental data. I show how to combine detailed and fairly realistic theoretical modelling of the phenomena with accurate measurements of the correlation functions, in order to establish a fully quantitative method to retrieve the flow properties from the experiments. An importance-sampling Monte Carlo procedure is employed in order to fit the experiments. This provides the optimum parameter values together with their statistical error bars. The approach is well suited for both modern desktop PC machines and massively parallel computers. The latter allows making the data analysis within short computing times. I applied this method to study flow of aqueous electrolyte solution near smooth hydrophilic and hydrophobic surfaces. Generally on hydrophilic surface slip is not expected, while on hydrophobic surface some slippage may exists. Our results show that on both hydrophilic and moderately hydrophobic (contact angle ~85°) surfaces the slip length is ~10-15nm or lower, and within the limitations of the experiments and the model, indistinguishable from zero.

Some theorems in the theory of probability, with special reference to their importance in the theory of homograde correlation ...

Mode of access: Internet.

Theory of strongly correlated electron systems. II. Including correlation effects into electronic structure calculations

We have previously shown that a division of the f-shell into two subsystems gives a better understanding of the cohesive properties as well the general behavior of lanthanide systems. In this article, we present numerical computations, using the suggested method. We show that the picture is consistent with most experimental data, e.g., the equilibrium volume and electronic structure in general. Compared with standard energy band calculations and calculations based on the self-interaction correction and LIDA + U, the f-(non-f)-mixing interaction is decreased by spectral weights of the many-body states of the f-ion. (c) 2005 Wiley Periodicals, Inc.

Quantum statistical correlations in thermal field theories: Boundary effective theory

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field phi(c), and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schrodinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field phi(c), a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example.

Approximation to density functional theory for the calculation of band gaps of semiconductors

The local-density approximation (LDA) together with the half occupation (transitionstate) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite system, it has been very difficult to find a way to half ionize because the hole tends to be infinitely extended (a Bloch wave). The answer to this problem lies in the LDA formalism itself. One proves that the half occupation is equivalent to introducing the hole self-energy (electrostatic and exchange correlation) into the Schrodinger equation. The argument then becomes simple: The eigenvalue minus the self-energy has to be minimized because the atom has a minimal energy. Then one simply proves that the hole is localized, not infinitely extended, because it must have maximal self-energy. Then one also arrives at an equation similar to the self- interaction correction equation, but corrected for the removal of just 1/2 electron. Applied to the calculation of band gaps and effective masses, we use the self- energy calculated in atoms and attain a precision similar to that of GW, but with the great advantage that it requires no more computational effort than standard LDA.

Spin gaps and spin-flip energies in density-functional theory

Energy gaps are crucial aspects of the electronic structure of finite and extended systems. Whereas much is known about how to define and calculate charge gaps in density-functional theory (DFT), and about the relation between these gaps and derivative discontinuities of the exchange-correlation functional, much less is known about spin gaps. In this paper we give density-functional definitions of spin-conserving gaps, spin-flip gaps and the spin stiffness in terms of many-body energies and in terms of single-particle (Kohn-Sham) energies. Our definitions are as analogous as possible to those commonly made in the charge case, but important differences between spin and charge gaps emerge already on the single-particle level because unlike the fundamental charge gap spin gaps involve excited-state energies. Kohn-Sham and many-body spin gaps are predicted to differ, and the difference is related to derivative discontinuities that are similar to, but distinct from, those usually considered in the case of charge gaps. Both ensemble DFT and time-dependent DFT (TDDFT) can be used to calculate these spin discontinuities from a suitable functional. We illustrate our findings by evaluating our definitions for the Lithium atom, for which we calculate spin gaps and spin discontinuities by making use of near-exact Kohn-Sham eigenvalues and, independently, from the single-pole approximation to TDDFT. The many-body corrections to the Kohn-Sham spin gaps are found to be negative, i.e., single-particle calculations tend to overestimate spin gaps while they underestimate charge gaps.

Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions

Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasione dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained and give evidence of an interesting dimensional crossover between two and one dimensions.

Physical signatures of discontinuities of the time-dependent exchange-correlation potential

The exact exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT) is known to develop steps and discontinuities upon change of the particle number in spatially confined regions or isolated subsystems. We demonstrate that the self-interaction corrected adiabatic local-density approximation for the XC potential has this property, using the example of electron loss of a model quantum well system. We then study the influence of the XC potential discontinuity in a real-time simulation of a dissociation process of an asymmetric double quantum well system, and show that it dramatically affects the population of the resulting isolated single quantum wells. This indicates the importance of a proper account of the discontinuities in TDDFT descriptions of ionization, dissociation or charge transfer processes.