Esmerindo de Sousa Bernardes

Spin-orbit interaction in symmetric wells with two subbands.

We investigate the spin-orbit (SO) interaction in two-dimensional electron gases in quantum wells with two subbands. From the 8x8 Kane model, we derive a new intersubband-induced SO term which resembles the functional form of the Rashba SO but is nonzero even in symmetric structures. This follows from the distinct parity of the confined states (even or odd) which obliterates the need for asymmetric potentials. We self-consistently calculate the new SO coupling strength for realistic wells and find it comparable to the usual Rashba constant. Our new SO term gives rise to a nonzero ballistic spin-Hall conductivity, which changes sign as a function of the Fermi energy (epsilonF) and can induce an unusual Zitterbewegung with cycloidal trajectories without magnetic fields.

Intersubband-induced spin-orbit interaction in quantum wells

Recently, we have found an additional spin-orbit (SO) interaction in quantum wells with two subbands [Bernardes et al., Phys. Rev. Lett. 99, 076603 (2007)]. This new SO term is nonzero even in symmetric geometries, as it arises from the intersubband coupling between confined states of distinct parities, and its strength is comparable to that of the ordinary Rashba. Starting from the

Neuromorphometric characterization with shape functionals

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Characterizing neuromorphologic alterations with additive shape functionals

Kane model, here we present a detailed derivation of this new SO Hamiltonian and the corresponding SO coupling. In addition, within the self-consistent Hartree approximation, we calculate the strength of this new SO coupling for realistic symmetric modulation-doped wells with two subbands. We consider gated structures with either a constant areal electron density or a constant chemical potential. In the parameter range studied, both models give similar results. By considering the effects of an external applied bias, which breaks the structural inversion symmetry of the wells, we also calculate the strength of the resulting induced Rashba couplings within each subband. Interestingly, we find that for double wells the Rashba couplings for the first and second subbands interchange signs abruptly across the zero bias, while the intersubband SO coupling exhibits a resonant behavior near this symmetric configuration. For completeness we also determine the strength of the Dresselhaus couplings and find them essentially constant as function of the applied bias.

Matrix elements for the symplectic sp(4) Lie algebra

This work presents a procedure to extract morphological information from neuronal cells based on the variation of shape functionals as the cell geometry undergoes a dilation through a wide interval of spatial scales. The targeted shapes are alpha and beta cat retinal ganglion cells, which are characterized by different ranges of dendritic field diameter. Image functionals are expected to act as descriptors of the shape, gathering relevant geometric and topological features of the complex cell form. We present a comparative study of classification performance of additive shape descriptors, namely, Minkowski functionals, and the nonadditive multiscale fractal. We found that the proposed measures perform efficiently the task of identifying the two main classes alpha and beta based solely on scale invariant information, while also providing intraclass morphological assessment.

Differential invariants for symplectic Lie algebras realized by boson operators

The complexity of a neuronal cell shape is known to be related to its function. Specifically, among other indicators, a decreased complexity in the dendritic trees of cortical pyramidal neurons has been associated with mental retardation. In this paper we develop a procedure to address the characterization of morphological changes induced in cultured neurons by over-expressing a gene involved in mental retardation. Measures associated with the multiscale connectivity, an additive image functional, are found to give a reasonable separation criterion between two categories of cells. One category consists of a control group and two transfected groups of neurons, and the other, a class of cat ganglionary cells. The reported framework also identified a trend towards lower complexity in one of the transfected groups. Such results establish the suggested measures as an effective descriptors of cell shape.

KILLING - An algebraic computational package for Lie algebras

The closed Gelfand-Tsetlin type formulae are constructed in this paper for the matrix elements of the symplectic sp(4) Lie algebra in an arbitrary irreducible representation using the reduction chain sp(4) sp(2) sp(2). All resulting formulae for the matrix elements were obtained by directly solving the Cartan-Weyl commutation relations of the sp(4) algebra.

Spin Hall effect due to intersubband-induced spin-orbit interaction in symmetric quantum wells

The study of algebraic symplectic models in high energy physics and even in molecular genetics has received much attention in the past decades. In this paper, we first survey one known bosonic realization with N types of bosons operators in a (2j + 1)-dimensional space (with j being the semi-integer). Then, using the general theory of differential invariants, we determine two sets of sp(2j + 1)-differential invariants. In one set, when N ≥ 2j + 1, all independent invariants of any order are obtained in a simple closed form. When N < 2j + 1, we could present only particular matrix forms. In the latter case, the differential invariants up to the second order are explicitly presented for the symplectic algebras sp(2), sp(4) and sp(6) realized by up to three types of bosons. As applications, we present the simplest sp(2)-invariant Lagrangians, null-Lagrangians, new solutions to the Helmholtz inverse problem and evolution equations, which will be of fundamental importance in the construction of dynamical systems invariant under the symplectic group.

Harmonic functions of suq(2) for q ∊ ℝ and q → S1

Abstract The Killing package is a set of algebraic computational procedures to manipulate elements of representation theory for classical, exceptional and deformed Lie algebras. It is divided in two major parts: (1) The Roots & Weights formalism to classify all semisimple Lie algebras and their irreducible representations, and (2) The Gelfand–Tsetlin method to construct explicitly the irreducible representations of classical Lie algebras, including the deformed unitary Lie algebras.

Spin orbit interaction and zitterbewegung in symmetric wells

We investigate the intrinsic spin Hall effect in two-dimensional electron gases in quantum wells with two subbands, where a new intersubband-induced spin-orbit coupling is operative. The bulk spin Hall conductivity sigma(z)(xy) is calculated in the ballistic limit within the standard Kubo formalism in the presence of a magnetic field B and is found to remain finite in the B=0 limit, as long as only the lowest subband is occupied. Our calculated sigma(z)(xy) exhibits a nonmonotonic behavior and can change its sign as the Fermi energy (the carrier areal density n(2D)) is varied between the subband edges. We determine the magnitude of sigma(z)(xy) for realistic InSb quantum wells by performing a self-consistent calculation of the intersubband-induced spin-orbit coupling.