Two-dimensional Bloch electrons in perpendicular magnetic fields: an exact calculation of the Hofstadter butterfly spectrum

The problem of two-dimensional, independent electrons subject to a periodic potential and a uniform perpendicular magnetic field unveils surprisingly rich physics, as epitomized by the fractal energy spectrum known as Hofstadter's Butterfly. It has hitherto been addressed using various approximations rooted in either the strong potential or the strong field limiting cases. Here we report calculations of the full spectrum of the single-particle Schr\"{o}dinger equation without further approximations. Our method is exact, up to numerical precision, for any combination of potential and uniform field strength. We first study a situation that corresponds to the strong potential limit, and compare the exact results to the predictions of a Hofstadter-like model. We then go on to analyze the evolution of the fractal spectrum from a Landau-like nearly-free electron system to the Hofstadter tight-binding limit by tuning the amplitude of the modulation potential

Stability of the shell structure in 2D quantum dots

We study the effects of external impurities on the shell structure in semiconductor quantum dots by using a fast response-function method for solving the Kohn-Sham equations. We perform statistics of the addition energies up to 20 interacting electrons. The results show that the shell structure is generally preserved even if effects of high disorder are clear. The Coulomb interaction and the variation in ground-state spins have a strong effect on the addition-energy distributions, which in the noninteracting single-electron picture correspond to level statistics showing mixtures of Poisson and Wigner forms.Comment: 7 pages, 8 figures, submitted to Phys. Rev.

Geometric and impurity effects on quantum rings in magnetic fields

We investigate the effects of impurities and changing ring geometry on the energetics of quantum rings under different magnetic field strengths. We show that as the magnetic field and/or the electron number are/is increased, both the quasiperiodic Aharonov-Bohm oscillations and various magnetic phases become insensitive to whether the ring is circular or square in shape. This is in qualitative agreement with experiments. However, we also find that the Aharonov-Bohm oscillation can be greatly phase-shifted by only a few impurities and can be completely obliterated by a high level of impurity density. In the many-electron calculations we use a recently developed fourth-order imaginary time projection algorithm that can exactly compute the density matrix of a free-electron in a uniform magnetic field.Comment: 8 pages, 7 figures, to appear in PR

Any order imaginary time propagation method for solving the Schrodinger equation

The eigenvalue-function pair of the 3D Schr\"odinger equation can be efficiently computed by use of high order, imaginary time propagators. Due to the diffusion character of the kinetic energy operator in imaginary time, algorithms developed so far are at most fourth-order. In this work, we show that for a grid based algorithm, imaginary time propagation of any even order can be devised on the basis of multi-product splitting. The effectiveness of these algorithms, up to the 12$^{\rm th}$ order, is demonstrated by computing all 120 eigenstates of a model C$_{60}$ molecule to very high precisions. The algorithms are particularly useful when implemented on parallel computer architectures.Comment: 8 pages, 3 figure

In vitro interactions of Alternaria mycotoxins, an emerging class of food contaminants, with the gut microbiota: a bidirectional relationship

The human gut microbiota plays an important role in the maintenance of human health. Factors able to modify its composition might predispose the host to the development of pathologies. Among the various xenobiotics introduced through the diet, Alternaria mycotoxins are speculated to represent a threat for human health. However, limited data are currently available about the bidirectional relation between gut microbiota and Alternaria mycotoxins. In the present work, we investigated the in vitro effects of different concentrations of a complex extract of Alternaria mycotoxins (CE; containing eleven mycotoxins; e.g. 0.153 µM alternariol and 2.3 µM altersetin, at the maximum CE concentration tested) on human gut bacterial strains, as well as the ability of the latter to metabolize or adsorb these compounds. Results from the minimum inhibitory concentration assay showed the scarce ability of CE to inhibit the growth of the tested strains. However, the growth kinetics of most of the strains were negatively affected by exposure to the various CE concentrations, mainly at the highest dose (50 µg/mL). The CE was also found to antagonize the formation of biofilms, already at concentrations of 0.5 µg/mL. LC–MS/MS data analysis of the mycotoxin concentrations found in bacterial pellets and supernatants after 24 h incubation showed the ability of bacterial strains to adsorb some Alternaria mycotoxins, especially the key toxins alternariol, alternariol monomethyl ether, and altersetin. The tendency of these mycotoxins to accumulate within bacterial pellets, especially in those of Gram-negative strains, was found to be directly related to their lipophilicity

Value of tissue harmonic imaging (THI) and contrast harmonic imaging (CHI) in detection and characterisation of breast tumours

The purpose of this study was to investigate the extent to which tissue harmonic imaging (THI), speckle reduction imaging (SRI), spatial compounding (SC) and contrast can improve detection and differentiation of breast tumours. We examined 38 patients (14 benign, 24 malignant tumours) with different combinations of THI, SRI and SC. The effect on delineation, margin, tissue differentiation and posttumoral phenomena was evaluated with a three-point score. Additionally, 1oo not palpable tumours (diameters: 4–15 mm) were examined by contrast harmonic imaging (CHI) with power Doppler. After bolus injection (0.5 ml Optison), vascularisation and enhancement were observed for 20 min. The best combination for detection of margin, infiltration, echo pattern and posterior lesion boundary was the combination of SRI level 2 with SC low. THI was helpful for lesions OF more than 1 cm depth. In native Power Doppler, vessels were found in 54 of 100 lesions. Within 5 min after contrast medium (CM) injection, marginal and penetrating vessels increased in benign and malignant tumours and central vessels mostly in carcinomas (p<0.05). A diffuse CM accumulation was observed up to 20 min after injection in malignant tumours only (p<0.05). THI, SRI and SC improved delineation and tissue differentiation. Second-generation contrast agent allowed detection of tumour vascularisation with prolonged enhancement