RESUMEN

In this paper we establish a connection between density functional theory (DFT) for lattice models and common real-space DFT. We consider the lattice DFT description of a two-level model subject to generic interactions in Mermin's DFT formulation in the grand canonical ensemble at finite temperature. The case of only density-density and Hund's rule interaction studied in earlier work is shown to be equivalent to an exact-exchange description of DFT in the real-space picture. In addition, we also include the so-called pair-hopping interaction which can be treated analytically and, crucially, leads to non-integer occupations of the Kohn-Sham (KS) levels even in the limit of zero temperature. Treating the hydrogen molecule in a minimal basis is shown to be equivalent to our two-level lattice DFT model. By means of the fractional occupations of the KS orbitals (which, in this case, are identical to the many-body ones) we reproduce the results of full configuration interaction, even in the dissociation limit and without breaking the spin symmetry. Beyond the minimal basis, we embed our HOMO-LUMO model into a standard DFT calculation and, again, obtain results in overall good agreement with exact ones without the need of breaking the spin symmetry.

RESUMEN

We present a computationally efficient method to obtain the spectral function of bulk systems in the framework of steady-state density functional theory (i-DFT) using an idealized scanning tunneling microscope (STM) setup. We calculate the current through the STM tip and then extract the spectral function from the finite-bias differential conductance. The fictitious noninteracting system of i-DFT features an exchange-correlation (XC) contribution to the bias which guarantees the same current as in the true interacting system. Exact properties of the XC bias are established using Fermi-liquid theory and subsequently implemented to construct approximations for the Hubbard model. We show for two different lattice structures that the Mott metal-insulator transition is captured by i-DFT.

RESUMEN

We propose a scheme to extract the many-body spectral function of an interacting many-electron system from an equilibrium density functional theory (DFT) calculation. To this end we devise an ideal scanning tunneling microscope (STM) setup and employ the recently proposed steady-state DFT formalism (i-DFT) which allows one to calculate the steady current through a nanoscopic region coupled to two biased electrodes. In our setup, one of the electrodes serves as a probe ("STM tip"), which is weakly coupled to the system we want to measure. In the ideal STM limit of vanishing coupling to the tip, the system is restored to quasi-equilibrium and the normalized differential conductance yields the exact equilibrium many-body spectral function. Calculating this quantity from i-DFT, we derive an exact relation expressing the interacting spectral function in terms of the Kohn-Sham one. As illustrative examples, we apply our scheme to calculate the spectral functions of two nontrivial model systems, namely the single Anderson impurity model and the Constant Interaction Model.

RESUMEN

OBJECTIVES: To prospectively evaluate image quality and organ-specific-radiation dose of spiral cranial CT (cCT) combined with automated tube current modulation (ATCM) and iterative image reconstruction (IR) in comparison to sequential tilted cCT reconstructed with filtered back projection (FBP) without ATCM. METHODS: 31 patients with a previous performed tilted non-contrast enhanced sequential cCT aquisition on a 4-slice CT system with only FBP reconstruction and no ATCM were prospectively enrolled in this study for a clinical indicated cCT scan. All spiral cCT examinations were performed on a 3rd generation dual-source CT system using ATCM in z-axis direction. Images were reconstructed using both, FBP and IR (level 1-5). A Monte-Carlo-simulation-based analysis was used to compare organ-specific-radiation dose. Subjective image quality for various anatomic structures was evaluated using a 4-point Likert-scale and objective image quality was evaluated by comparing signal-to-noise ratios (SNR). RESULTS: Spiral cCT led to a significantly lower (p < 0.05) organ-specific-radiation dose in all targets including eye lense. Subjective image quality of spiral cCT datasets with an IR reconstruction level 5 was rated significantly higher compared to the sequential cCT acquisitions (p < 0.0001). Consecutive mean SNR was significantly higher in all spiral datasets (FBP, IR 1-5) when compared to sequential cCT with a mean SNR improvement of 44.77% (p < 0.0001). CONCLUSIONS: Spiral cCT combined with ATCM and IR allows for significant-radiation dose reduction including a reduce eye lens organ-dose when compared to a tilted sequential cCT while improving subjective and objective image quality.

RESUMEN

BACKGROUND: The brainstem comprises a large variety of fiber tracts and nerve nuclei and is unarguably one of the most crucial parts of the brain. Reliable noninvasive visualization of its anatomy may help relate normal and pathological anatomic variations to neurologic/psychiatric disorders. In this study, we explored the potential of direction-encoded track-density imaging (TDI) for depicting the intricate anatomy of the brainstem. METHODS: A total of 18 healthy volunteers (10 females, 8 males; median age, 34.5 years; interquartile range, 31-44.5 years) were examined on a 3-T MRI system. Diffusion tensor imaging data were processed using MRtrix to generate TDI images. These images were then compared with anatomic atlases to identify nerve nuclei and fiber tracts. The ability of TDI to delineate anatomic structures in the mesencephalon, pons, and medulla oblongata was evaluated using a 6-point Likert scale (5, excellent; 4, good; 3, moderate; 2, poor; 1, no adequate differentiation; 0, evaluation not possible). RESULTS: All generated TDI images were evaluable without limitations. In the mesencephalon, delineation of the substantia nigra, crus cerebri, and red nucleus was rated as excellent, that of the medial lemniscus was rated as good, and that of the inferior colliculus was rated as poor. Delineation of all anatomic structures in the pons was rated as excellent. In the medulla oblongata, delineation of the pyramid was rated as excellent and that of the medial lemniscus as moderate, whereas delineation of the inferior olive was not possible. CONCLUSIONS: TDI images provide optimal delineation of nerve nuclei and fibers in the upper brainstem, but have more difficulty identifying more caudal structures.

Asunto(s)

RESUMEN

OBJECTIVES: To prospectively intra-individually compare image quality of a 3rd generation Dual-Source-CT (DSCT) spiral cranial CT (cCT) to a sequential 4-slice Multi-Slice-CT (MSCT) while maintaining identical intra-individual radiation dose levels. METHODS: 35 patients, who had a non-contrast enhanced sequential cCT examination on a 4-slice MDCT within the past 12 months, underwent a spiral cCT scan on a 3rd generation DSCT. CTDIvol identical to initial 4-slice MDCT was applied. Data was reconstructed using filtered backward projection (FBP) and 3rd-generation iterative reconstruction (IR) algorithm at 5 different IR strength levels. Two neuroradiologists independently evaluated subjective image quality using a 4-point Likert-scale and objective image quality was assessed in white matter and nucleus caudatus with signal-to-noise ratios (SNR) being subsequently calculated. RESULTS: Subjective image quality of all spiral cCT datasets was rated significantly higher compared to the 4-slice MDCT sequential acquisitions (p<0.05). Mean SNR was significantly higher in all spiral compared to sequential cCT datasets with mean SNR improvement of 61.65% (p*Bonferroni0.05<0.0024). Subjective image quality improved with increasing IR levels. CONCLUSION: Combination of 3rd-generation DSCT spiral cCT with an advanced model IR technique significantly improves subjective and objective image quality compared to a standard sequential cCT acquisition acquired at identical dose levels.

Asunto(s)