Abstract: In this article we study excitons and trions in fractional dimensional spaces using the model suggested by C. Palmer [ J. Phys. A: Math. Gen. 37 6987 (2004)] through variational quantum Monte Carlo. We present a direct approach for estimating the exciton binding energy and discuss the von Neumann rejection- and Metropolis sampling methods. A simple variational estimate of trions is presented which shows good agreement with previous calculations done within the fractional dimensional model presented by D. R. Herrick and F. H. Stillinger [ Phys. Rev. A 11 42 (1975) and J. Math. Phys. 18 1224 (1977)]. We explain the spatial physics of the positive and negative trions by investigating angular and inter-atomic distances. We then examine the wave function and explain the differences between the positive and negative trions with heavy holes. As applications of the fractional dimensional model we study three systems: First we apply the model to estimate the energy of the hydrogen molecular ion H2+. Then we estimate trion binding energies in GaAs-based quantum wells and we demonstrate a good agreement with other theoretical work as well as experimentally observed binding energies. Finally, we apply the results to carbon nanotubes. We find good agreement with recently observed binding energies of the positively charged trion.

Abstract: In a standard state-of-the-art measurement the head-related transfer function (HRTF) is obtained in an anechoic room with an elaborate setup involving multiple calibrated loudspeakers. In search for a simplified method that would open up the possibility for an HRTF measurement in a home environment, it has been suggested that this setup could be replaced with one with a single, fixed loudspeaker. In such a setup, the subject samples different directions by moving the head with respect to this loudspeaker, while the head movements are tracked in some way. In this paper, the feasibility of such an approach is studied. To this end, the HRTF is measured in an unmodified (non-anechoic) room by means of a single external speaker and a high resolution head tracking system. The differences between the dynamically obtained HRTF and the standard static HRTF are investigated, and are shown to be mostly due to variable torso reflections.

Abstract: It is standard practice in virtual reality applications to synthesize binaural audio based on a discrete set of directionally-dependent head-related impulse responses (HRIRs). This set of HRIRs is often time-aligned in a pre-processing step, to allow for high-fidelity interpolation between HRIRs corresponding with neighbouring directions. The fidelity of this operation depends on the similarity of neighbouring aligned HRIRs. The pairwise quality of similarity makes it a difficult criterion to optimize globally and consequently one often resorts to alignment methods based on a specific feature that can be extracted for each HRIR separately, e.g., the first-onset of the peak or the group delay. However, such proxies for similarity are very sensitive to noise and therefore require a high signal-to-noise ratio, which makes them less suitable for processing HRIRs acquired outside an anechoic room. In this paper, we advance a novel alignment method, which maximizes the similarity – defined as the correlation between the full-length HRIRs – between neighbouring aligned HRIRs for all directions at once. We show that this correlation-based alignment procedure outperforms the first-onset alignment with regards to the fidelity of the spherical harmonics representation of both the spectral and interaural time difference (ITD) information, when tested on the KEMAR HRIR and six human HRIRs. Finally, we show that the correlation-based alignment is more robust to noise.

Abstract: Chrome yellow refers to a group of synthetic inorganic pigments that became popular as an artists material from the second quarter of the 19th century. The color of the pigment, in which the chromate ion acts as a chromophore, is related to its chemical composition (PbCr1-xSxO4, with 0≤x≤0.8) and crystalline structure (monoclinic/orthorhombic). Their shades range from the yellow-orange to the paler yellow tones with increasing sulfate amount. These pigments show remarkable signs of degradation after limited time periods. Pure PbCrO4 (crocoite in its natural form) has a deep yellow color and is relatively stable, while the co-precipitate with lead sulfate (PbCr1-xSxO4) has a paler shade and seems to degrade faster. This degradation is assumed to be related to the reduction of Cr(VI) to Cr(III). We show that on increasing the sulfur(S)-content in chrome yellow, the band gap increases. Typically, when increasing the band gap, one might assume that a decrease in photo activity is the result. However, the photo activity relative to the Cr content, and thus Cr reduction, of sulfur-rich PbCr1-xSxO4 is found to be much higher compared to the sulfur-poor or non-doped lead chromates. This discrepancy can be explained by the evolution of the crystal and electronic structure as function of the sulfur content: first-principles density functional theory calculations show that both the absorption coefficient and reflection coefficients of the lead chromates change as a result of the sulfate doping in such a way that the generation of electron-hole pairs under illumination relative to the total Cr content increases. These changes in the material properties explain why paler shade yellow colors of this pigment are more prone to discoloration. The electronic structure calculations also demonstrate that lead chromate and its co-precipitates are p-type semiconductors, which explains the observed reduction reaction. As understanding this phenomenon is valuable in the field of cultural heritage, this study is the first joint action of photo-electrochemical measurements and first-principles calculations to approve the higher tendency of sulfur-rich lead chromates to darken.

Abstract: A classical two-dimensional (2D) model for an artificial atom is used to make a numerical exact study of elastic and nonelastic scattering. Interesting differences in the scattering angle distribution between this model and the well-known Rutherford scattering are found in the small energy and/or small impact parameter scattering regime. For scattering off a classical 2D hydrogen atom different phenomena such as ionization, exchange of particles, and inelastic scattering can occur. A scattering regime diagram is constructed as function of the impact parameter (b) and the initial velocity (v) of the incoming particle. In a small regime of the (b,v) space the system exhibits chaos, which is studied in more detail. Analytic expressions for the scattering angle are given in the high impact parameter asymptotic limit.

Abstract: The properties of free-standing silicon and germanium nanowires oriented along the [110] direction are studied using different first principles methods. We show the corrections due to quasi-particles to the band structures obtained using the local-density approximation. The formation energies of B and P doped nanowires are calculated, both in the absence and presence of dangling bond defects and we link these to experimental results. Furthermore, we report on the phonon properties of pure Si and Ge nanowires, as well as Ge/Si core-shell nanowires, and discuss the differences between them.

Abstract: We present full ab initio calculations of the phonon band structure of thin Si nanowires oriented along the [110] direction. Using these phonon dispersion relations we investigate the structural stability of these wires. We found that all studied wires were stable also when doped with either B or P, if the unit cell was taken sufficiently large along the wire axis. The evolution of the phonon dispersion relations and of the sound velocities with respect to the wire diameters is discussed. Softening is observed for acoustic modes and hardening for optical phonon modes with increasing wire diameters.

Abstract: The vibrational properties of graphene fluoride and graphane are studied using ab initio calculations. We find that both sp(3) bonded derivatives of graphene have different phonon dispersion relations and phonon densities of states as expected from the different masses associated with the attached atoms of fluorine and hydrogen, respectively. These differences manifest themselves in the predicted temperature behavior of the constant-volume specific heat of both compounds. (C) 2011 American Institute of Physics. [doi:10.1063/1.3551712]

Abstract: We observe magnetic-field-induced level mixing and quantum superposition phenomena between three approaching single-particle states in a quantum dot probed via the ground state of an adjacent quantum dot by single-electron resonant tunneling. The mixing is attributed to anisotropy and anharmonicity in realistic dot confining potentials. The pronounced anticrossing and transfer of strengths (both enhancement and suppression) between resonances can be understood with a simple coherent level mixing model. Superposition can lead to the formation of a dark state by complete cancellation of an otherwise strong resonance, an effect resembling coherent population trapping in a three-level-system of quantum and atom optics.

Abstract: We study single-electron-elastic-resonant-tunneling through two weakly coupled vertical quantum dots and investigate the branch current behavior at anti-crossings between two single-particle energy levels in the constituent dot spectra that are induced to approach each other by application of an out-of-dot-plane magnetic field. We observe both the familiar case of monotonic transfer of the resonant current strengths between the two branches as well as the less familiar case of concurrent enhancement and suppression (ideally complete cancellation) of the resonant current in the two branches. These two situations can be explained in terms of a simple coherent tunneling model. ©2009 American Institute of Physics