Reduction of the Three Dimensional Schrodinger Equation for Multilayered Films

In this paper, we present a method for reducing the three dimensional Schrodinger equation to study confined metallic states, such as quantum well states, in a multilayer film geometry. While discussing some approximations that are employed when dealing with the three dimensionality of the problem, we derive a one dimensional equation suitable for studying such states using an envelope function approach. Some applications to the Cu/Co multilayer system with regard to spin tunneling/rotations and angle resolved photoemission are discussed.Comment: 14 pages, 1 figur

Computational fluid dynamics as a tool for urban drainage system analysis: a review of applications and best practice

Computational Fluid Dynamics (CFD) can be applied to gain insights into most fluid processes and associated phenomena and so presents potential to add value in the analysis of urban drainage systems. This paper presents a review of CFD studies carried out in this field, with the objective of developing an appreciation of how and where it can be applied. Existing work has tended to focus around the analysis of four types of urban drainage structure, including Combined Sewer Overflows (CSOs), storage and attenuation systems, stormwater sediment interceptors and sewerage conveyance structures. Within the respective studies, the prediction of flowfields, particulate behaviour, water surface profiles and Residence Time Distributions (RTDs) are found to form the main focus, and as such, these are considered in most detail in the paper. It is concluded that CFD presents a number of opportunities in urban drainage system analysis, and that the scope of this opportunity will further develop as both computational hardware and software resources become more advanced

Electronic structures of GaAs/AlxGa1-xAs quantum double rings

In the framework of effective mass envelope function theory, the electronic structures of GaAs/AlxGa1-xAs quantum double rings (QDRs) are studied. Our model can be used to calculate the electronic structures of quantum wells, wires, dots, and the single ring. In calculations, the effects due to the different effective masses of electrons and holes in GaAs and AlxGa1-xAs and the valence band mixing are considered. The energy levels of electrons and holes are calculated for different shapes of QDRs. The calculated results are useful in designing and fabricating the interrelated photoelectric devices. The single electron states presented here are useful for the study of the electron correlations and the effects of magnetic fields in QDRs

Development of an eight-band theory for quantum-dot heterostructures

We derive a nonsymmetrized 8-band effective-mass Hamiltonian for quantum-dot heterostructures (QDHs) in Burt's envelope-function representation. The 8x8 radial Hamiltonian and the boundary conditions for the Schroedinger equation are obtained for spherical QDHs. Boundary conditions for symmetrized and nonsymmetrized radial Hamiltonians are compared with each other and with connection rules that are commonly used to match the wave functions found from the bulk kp Hamiltonians of two adjacent materials. Electron and hole energy spectra in three spherical QDHs: HgS/CdS, InAs/GaAs, and GaAs/AlAs are calculated as a function of the quantum dot radius within the approximate symmetrized and exact nonsymmetrized 8x8 models. The parameters of dissymmetry are shown to influence the energy levels and the wave functions of an electron and a hole and, consequently, the energies of both intraband and interband transitions.Comment: 36 pages, 10 figures, E-mail addresses: [email protected], [email protected]

Electron and hole states in quantum-dot quantum wells within a spherical 8-band model

In order to study heterostructures composed both of materials with strongly different parameters and of materials with narrow band gaps, we have developed an approach, which combines the spherical 8-band effective-mass Hamiltonian and the Burt's envelope function representation. Using this method, electron and hole states are calculated in CdS/HgS/CdS/H_2O and CdTe/HgTe/CdTe/H_2O quantum-dot quantum-well heterostructures. Radial components of the wave functions of the lowest S and P electron and hole states in typical quantum-dot quantum wells (QDQWs) are presented as a function of radius. The 6-band-hole components of the radial wave functions of an electron in the 8-band model have amplitudes comparable with the amplitude of the corresponding 2-band-electron component. This is a consequence of the coupling between the conduction and valence bands, which gives a strong nonparabolicity of the conduction band. At the same time, the 2-band-electron component of the radial wave functions of a hole in the 8-band model is small compared with the amplitudes of the corresponding 6-band-hole components. It is shown that in the CdS/HgS/CdS/H_2O QDQW holes in the lowest states are strongly localized in the well region (HgS). On the contrary, electrons in this QDQW and both electron and holes in the CdTe/HgTe/CdTe/H_2O QDQW are distributed through the entire dot. The importance of the developed theory for QDQWs is proven by the fact that in contrast to our rigorous 8-band model, there appear spurious states within the commonly used symmetrized 8-band model.Comment: 15 pages, 5 figures, E-mail addresses: [email protected], [email protected]

Input-output theory for fermions in an atom cavity

We generalize the quantum optical input-output theory developed for optical cavities to ultracold fermionic atoms confined in a trapping potential, which forms an "atom cavity". In order to account for the Pauli exclusion principle, quantum Langevin equations for all cavity modes are derived. The dissipative part of these multi-mode Langevin equations includes a coupling between cavity modes. We also derive a set of boundary conditions for the Fermi field that relate the output fields to the input fields and the field radiated by the cavity. Starting from a constant uniform current of fermions incident on one side of the cavity, we use the boundary conditions to calculate the occupation numbers and current density for the fermions that are reflected and transmitted by the cavity

Interface electronic states and boundary conditions for envelope functions

The envelope-function method with generalized boundary conditions is applied to the description of localized and resonant interface states. A complete set of phenomenological conditions which restrict the form of connection rules for envelope functions is derived using the Hermiticity and symmetry requirements. Empirical coefficients in the connection rules play role of material parameters which characterize an internal structure of every particular heterointerface. As an illustration we present the derivation of the most general connection rules for the one-band effective mass and 4-band Kane models. The conditions for the existence of Tamm-like localized interface states are established. It is shown that a nontrivial form of the connection rules can also result in the formation of resonant states. The most transparent manifestation of such states is the resonant tunneling through a single-barrier heterostructure.Comment: RevTeX4, 11 pages, 5 eps figures, submitted to Phys.Rev.

Angle dependence of Andreev scattering at semiconductor-superconductor interfaces

We study the angle dependence of the Andreev scattering at a semiconductor-superconductor interface, generalizing the one-dimensional theory of Blonder, Tinkham and Klapwijk. An increase of the momentum parallel to the interface leads to suppression of the probability of Andreev reflection and increase of the probability of normal reflection. We show that in the presence of a Fermi velocity mismatch between the semiconductor and the superconductor the angles of incidence and transmission are related according to the well-known Snell's law in optics. As a consequence there is a critical angle of incidence above which only normal reflection exists. For two and three-dimensional interfaces a lower excess current compared to ballistic transport with perpendicular incidence is found. Thus, the one-dimensional BTK model overestimates the barrier strength for two and three-dimensional interfaces.Comment: 8 pages including 3 figures (revised, 6 references added

General boundary conditions for the envelope function in multiband k.p model

We have derived general boundary conditions (BC) for the multiband envelope functions (which do not contain spurious solutions) in semiconductor heterostructures with abrupt heterointerfaces. These BC require the conservation of the probability flux density normal to the interface and guarantee that the multiband Hamiltonian be self--adjoint. The BC are energy independent and are characteristic properties of the interface. Calculations have been performed of the effect of the general BC on the electron energy levels in a potential well with infinite potential barriers using a coupled two band model. The connection with other approaches to determining BC for the envelope function and to the spurious solution problem in the multiband k.p model are discussed.Comment: 15 pages, 2 figures; to be published in Phys. Rev. B 65, March 15 issue 200

Analysis of talpid3 and wild-type chicken embryos reveals roles for Hedgehog signalling in development of the limb bud vasculature

Chicken talpid mutant embryos have a wide range of Hedgehog-signalling related defects and it is now known that the talpid gene product encodes a novel protein essential for Hedgehog signalling which is required for both activator and repressor functions of Gli transcription factors (Davey, M.G., Paton, I.R., Yin, Y., Schmidt, M., Bangs, F.K., Morrice, D.R., Gordon-Smith, T., Buxton, P., Stamataki, D., Tanaka, M., Münsterberg, A.E., Briscoe, J., Tickle, C., Burt, D.W. (2006). The chicken talpid gene encodes a novel protein essential for Hedgehog signalling. Genes Dev 20 1365-77). Haemorrhaging, oedema and other severe vascular defects are a central aspect of the talpid phenotype (Ede, D.A. and Kelly, W.A (1964a). Developmental abnormalities in the head region of the talpid mutant fowl. J. Embryol. exp. Morp. 12:161-182) and, as Hedgehog (Hh) signalling has been implicated in every stage of development of the vascular system, the vascular defects seen in talpid are also likely to be attributable to abnormal Hedgehog signalling. Gene expression of members of the VEGF and Angiopoietin families of angiogenic growth factors has been linked to haemorrhaging and oedema and we find widespread expression of VEGF-D, rigf and Ang2a in the talpid limb. Furthermore, ectopic expression of these genes in talpid limbs points to regulation via Gli repression rather than activation. We monitored specification of vessel identity in talpid limb vasculature by examining expression of artery-specific genes, Np1 and EphrinB2, and the vein-specific genes, Np2a and Tie2. We show that there are supernumerary subclavian arteries in talpid limb buds and abnormal expression of an artery-specific gene in the venous submarginal sinus, despite the direction of blood flow being normal. Furthermore, we show that Shh can induce Np1 expression but has no effect on Np2a. Finally, we demonstrate that induction of VEGF and Ang2a expression by Shh in normal limb buds is accompanied by vascular remodelling. Thus Hedgehog signalling has a pivotal role in the cascade of angiogenic events in a growing embryonic organ which is similar to that proposed in tumours