Theory of strongly correlated electron systems. I. Intersite coulomb interaction and the approximation of renormalized fermions in total energy calculations

The diagrammatic strong-coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many - electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one-to-one correspondence is found between the subset of such graphs for the many - electron GFs and the complete set of Feynman graphs of weak-coupling perturbation theory (WCPT) for single-electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many-electron quasi-particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self-energy and the exchange- correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LIDA (RF LDA), is obtained by introducing the spectral weights of the many electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self-interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LIDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part 11 of this study (this issue). (c) 2005 Wiley Periodicals, Inc.

Self-consistent theory of atomic Fermi gases with a Feshbach resonance at the superfluid transition

A self-consistent theory is derived to describe the BCS-Bose-Einstein-condensate crossover for a strongly interacting Fermi gas with a Feshbach resonance. In the theory the fluctuation of the dressed molecules, consisting of both preformed Cooper pairs and bare Feshbach molecules, has been included within a self-consistent T-matrix approximation, beyond the Nozieres and Schmitt-Rink strategy considered by Ohashi and Griffin. The resulting self-consistent equations are solved numerically to investigate the normal-state properties of the crossover at various resonance widths. It is found that the superfluid transition temperature T-c increases monotonically at all widths as the effective interaction between atoms becomes more attractive. Furthermore, a residue factor Z(m) of the molecule's Green function and a complex effective mass have been determined to characterize the fraction and lifetime of Feshbach molecules at T-c. Our many-body calculations of Z(m) agree qualitatively well with recent measurments of the gas of Li-6 atoms near the broad resonance at 834 G. The crossover from narrow to broad resonances has also been studied.

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.

Steps in theory-of-mind development for children with deafness or autism

Prior research demonstrates that understanding theory of mind (ToM) is seriously and similarly delayed in late-signing deaf children and children with autism. Are these children simply delayed in timing relative to typical children, or do they demonstrate different patterns of development? The current research addressed this question by testing 145 children (ranging from 3 to 13 years) with deafness, autism, or typical development using a ToM scale. Results indicate that all groups followed the same sequence of steps, up to a point, but that children with autism showed an importantly different sequence of understandings (in the later steps of the progression) relative to all other groups.

Adsorption in slit pores and pore-size distribution: A molecular layer structure theory

A new approach is developed to analyze the thermodynamic properties of a sub-critical fluid adsorbed in a slit pore of activated carbon. The approach is based on a representation that an adsorbed fluid forms an ordered structure close to a smoothed solid surface. This ordered structure is modelled as a collection of parallel molecular layers. Such a structure allows us to express the Helmholtz free energy of a molecular layer as the sum of the intrinsic Helmholtz free energy specific to that layer and the potential energy of interaction of that layer with all other layers and the solid surface. The intrinsic Helmholtz free energy of a molecular layer is a function (at given temperature) of its two-dimensional density and it can be readily obtained from bulk-phase properties, while the interlayer potential energy interaction is determined by using the 10-4 Lennard-Jones potential. The positions of all layers close to the graphite surface or in a slit pore are considered to correspond to the minimum of the potential energy of the system. This model has led to accurate predictions of nitrogen and argon adsorption on carbon black at their normal boiling points. In the case of adsorption in slit pores, local isotherms are determined from the minimization of the grand potential. The model provides a reasonable description of the 0-1 monolayer transition, phase transition and packing effect. The adsorption of nitrogen at 77.35 K and argon at 87.29 K on activated carbons is analyzed to illustrate the potential of this theory, and the derived pore-size distribution is compared favourably with that obtained by the Density Functional Theory (DFT). The model is less time-consuming than methods such as the DFT and Monte-Carlo simulation, and most importantly it can be readily extended to the adsorption of mixtures and capillary condensation phenomena.

Validation of the Action Research Arm Test using item response theory in patients after stroke

Objective: To validate the unidimensionality of the Action Research Arm Test (ARAT) using Mokken analysis and to examine whether scores of the ARAT can be transformed into interval scores using Rasch analysis. Subjects and methods: A total of 351 patients with stroke were recruited from 5 rehabilitation departments located in 4 regions of Taiwan. The 19-item ARAT was administered to all the subjects by a physical therapist. The data were analysed using item response theory by non-parametric Mokken analysis followed by Rasch analysis. Results: The results supported a unidimensional scale of the 19-item ARAT by Mokken analysis, with the scalability coefficient H = 0.95. Except for the item pinch ball bearing 3rd finger and thumb'', the remaining 18 items have a consistently hierarchical order along the upper extremity function's continuum. In contrast, the Rasch analysis, with a stepwise deletion of misfit items, showed that only 4 items (grasp ball'', grasp block 5 cm(3)'', grasp block 2.5 cm(3)'', and grip tube 1 cm(3)'') fit the Rasch rating scale model's expectations. Conclusion: Our findings indicated that the 19-item ARAT constituted a unidimensional construct measuring upper extremity function in stroke patients. However, the results did not support the premise that the raw sum scores of the ARAT can be transformed into interval Rasch scores. Thus, the raw sum scores of the ARAT can provide information only about order of patients on their upper extremity functional abilities, but not represent each patient's exact functioning.