On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

Numerical method for determination of the NMR frequency of the single-qubit operation in a silicon-based solid-state quantum computer

A numerical method is introduced to determine the nuclear magnetic resonance frequency of a donor (P-31) doped inside a silicon substrate under the influence of an applied electric field. This phosphorus donor has been suggested for operation as a qubit for the realization of a solid-state scalable quantum computer. The operation of the qubit is achieved by a combination of the rotation of the phosphorus nuclear spin through a globally applied magnetic field and the selection of the phosphorus nucleus through a locally applied electric field. To realize the selection function, it is required to know the relationship between the applied electric field and the change of the nuclear magnetic resonance frequency of phosphorus. In this study, based on the wave functions obtained by the effective-mass theory, we introduce an empirical correction factor to the wave functions at the donor nucleus. Using the corrected wave functions, we formulate a first-order perturbation theory for the perturbed system under the influence of an electric field. In order to calculate the potential distributions inside the silicon and the silicon dioxide layers due to the applied electric field, we use the multilayered Green's functions and solve an integral equation by the moment method. This enables us to consider more realistic, arbitrary shape, and three-dimensional qubit structures. With the calculation of the potential distributions, we have investigated the effects of the thicknesses of silicon and silicon dioxide layers, the relative position of the donor, and the applied electric field on the nuclear magnetic resonance frequency of the donor.

Linkage analyses of event-related potential slow wave phenotypes recorded in a working memory task

Working memory is an essential component of wide-ranging cognitive functions. It is a complex genetic trait probably influenced by numerous genes that individually have only a small influence. These genes may have an amplified influence on phenotypes closer to the gene action. In this study, event-related potential (ERP) phenotypes recorded during a working-memory task were collected from 656 adolescents from 299 families for whom genotypes were available. Univariate linkage analyses using the MERLIN variance-components method were conducted on slow wave phenotypes recorded at multiple sites while participants were required to remember the location of a target. Suggestive linkage (LOD > 2.2) was found on chromosomes 4, 5, 6, 10, 17, and 20. After correcting for multiple testing, suggestive linkage remained on chromosome 10. Empirical thresholds were computed for the most promising phenotypes. Those on chromosome 10 remained suggestive. A number of genes reported to regulate neural differentiation and function (i.e. NRP1, ANK3, and CHAT) were found under these linkage peaks and may influence the levels of neural activity occurring in individuals participating in a spatial working-memory task.