Spin-orbit coupled Bose-Einstein condensate in a tilted optical lattice

Bloch oscillations appear for a particle in a weakly tilted periodic potential. The intrinsic spin Hall effect is an outcome of a spin-orbit coupling. We demonstrate that both these phenomena can be realized simultaneously in a gas of weakly interacting ultracold atoms exposed to a tilted optical lattice and to a set of spatially dependent light fields inducing an effective spin-orbit coupling. It is found that both the spin Hall as well as the Bloch oscillation effects may coexist, showing, however, a strong correlation between the two. These correlations are manifested as a transverse spin current oscillating in-phase with the Bloch oscillations.Comment: 12 pages, 7 figure

First quantized approaches to neutrino oscillations and second quantization

Neutrino oscillations are treated from the point of view of relativistic first quantized theories and compared to second quantized treatments. Within first quantized theories, general oscillation probabilities can be found for Dirac fermions and charged spin 0 bosons. A clear modification in the oscillation formulas can be obtained and its origin is elucidated and confirmed to be inevitable from completeness and causality requirements. The left-handed nature of created and detected neutrinos can also be implemented in the first quantized Dirac theory in presence of mixing; the probability loss due to the changing of initially left-handed neutrinos to the undetected right-handed neutrinos can be obtained in analytic form. Concerning second quantized approaches, it is shown in a calculation using virtual neutrino propagation that both neutrinos and antineutrinos may also contribute as intermediate particles. The sign of the contributing neutrino energy may have to be chosen explicitly without being automatic in the formalism. At last, a simple second quantized description of the flavor oscillation phenomenon is devised. In this description there is no interference terms between positive and negative components, but it still gives simple normalized oscillation probabilities. A new effect appearing in this context is an inevitable but tiny violation of the initial flavor of neutrinos. The probability loss due to the conversion of left-handed neutrinos to right-handed neutrinos is also presented.Comment: version accepted for publicatio

Spin dynamics in the Kapitza-Dirac effect

Electron spin dynamics in Kapitza-Dirac scattering from a standing laser wave of high frequency and high intensity is studied. We develop a fully relativistic quantum theory of the electron motion based on the time-dependent Dirac equation. Distinct spin dynamics, with Rabi oscillations and complete spin-flip transitions, is demonstrated for Kapitza-Dirac scattering involving three photons in a parameter regime accessible to future high-power X-ray laser sources. The Rabi frequency and, thus, the diffraction pattern is shown to depend crucially on the spin degree of freedom

Exact solution of the Schrodinger equation with the spin-boson Hamiltonian

We address the problem of obtaining the exact reduced dynamics of the spin-half (qubit) immersed within the bosonic bath (enviroment). An exact solution of the Schrodinger equation with the paradigmatic spin-boson Hamiltonian is obtained. We believe that this result is a major step ahead and may ultimately contribute to the complete resolution of the problem in question. We also construct the constant of motion for the spin-boson system. In contrast to the standard techniques available within the framework of the open quantum systems theory, our analysis is based on the theory of block operator matrices.Comment: 9 pages, LaTeX, to appear in Journal of Physics A: Mathematical and Theoretica

A structure-based proposal for the catalytic mechanism of the bacterial acid phosphatase AphA belonging to the DDDD superfamily of phosphohydrolases

The Escherichia coli gene aphA codes for a periplasmic acid phosphatase called AphA, belonging to class B bacterial phosphatases, which is part of the DDDD superfamily of phosphohydrolases. After our first report about its crystal structure, we have started a series of crystallographic studies aimed at understanding of the catalytic mechanism of the enzyme. Here, we report three crystal structures of the AphA enzyme in complex with the hydrolysis products of nucleoside monophosphate substrates and a fourth with a proposed intermediate analogue that appears to be covalently bound to the enzyme. Comparison with the native enzyme structure and with the available X-ray structures of different phosphatases provides clues about the enzyme chemistry and allows us to propose a catalytic mechanism for AphA, and to discuss it with respect to the mechanism of other bacterial and human phosphatases. (c) 2005 Elsevier Ltd. All rights reserved

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator

We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and $\gamma^5$ chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry related problems have the same spectrum, but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.Comment: 33 pages, 10 figures, uses revtex macro

Dynamics of chiral oscillations - A comparative analysis with spin-flipping

Chiral oscillation as well as spin flipping effects correspond to quantum phenomena of fundamental importance in the context of particle physics and, in particular, of neutrino physics. From the point of view of first quantized theories, we are specifically interested in appointing the differences between chirality and helicity by obtaining their dynamic equations for a fermionic Dirac-type particle (neutrino). We also identify both effects when the non-minimal coupling with an external (electro)magnetic field in the neutrino interacting Lagrangian is taken into account. We demonstrate that, however, there is no constraint between chiral oscillations, when it takes place in vacuum, and the process of spin flipping related to the helicity quantum number, which does not take place in vacuum. To conclude, we show that the origin of chiral oscillations (in vacuum) can be interpreted as position very rapid oscillation projections onto the longitudinal direction of momentum.Comment: 14 pages, no figure

Exact results for `bouncing' Gaussian wave packets

We consider time-dependent Gaussian wave packet solutions of the Schrodinger equation (with arbitrary initial central position, x_0, and momentum, p_0, for an otherwise free-particle, but with an infinite wall at x=0, so-called bouncing wave packets. We show how difference or mirror solutions of the form psi(x,t)-psi(-x,t) can, in this case, be normalized exactly, allowing for the evaluation of a number of time-dependent expectation values and other quantities in closed form. For example, we calculate _t explicitly which illustrates how the free-particle kinetic (and hence total) energy is affected by the presence of the distant boundary. We also discuss the time dependence of the expectation values of position, _t, and momentum, _t, and their relation to the impulsive force during the `collision' with the wall. Finally, the x_0,p_0 --> 0 limit is shown to reduce to a special case of a non-standard free-particle Gaussian solution. The addition of this example to the literature then expands on the relatively small number of Gaussian solutions to quantum mechanical problems with familiar classical analogs (free particle, uniform acceleration, harmonic oscillator, unstable oscillator, and uniform magnetic field) available in closed form.Comment: 14 pages, 1 embedded .eps figur

Relativistic Spin-Flavor States in Light Front Dynamics

Orthonormal spin-flavor wave functions of Lorentz covariant quark models of the Bakamjian-Thomas type are constructed for nucleon resonances. Three different bases are presented. The manifestly Lorentz covariant Dirac-Melosh basis is related to the Pauli-Melosh basis and the symmetrized Bargmann-Wigner basis that are manifestly orthogonal.Comment: 30 pages, 8 tables, no figs; submitted to Ann.Phys.(NY

Complementary Domains of Retinoic Acid Production and Degradation in the Early Chick Embryo

AbstractExcess retinoids as well as retinoid deprivation cause abnormal development, suggesting that retinoid homeostasis is critical for proper morphogenesis. RALDH-2 and CYP26, two key enzymes that carry out retinoic acid (RA) synthesis and degradation, respectively, were cloned from the chick and show significant homology with their orthologs in other vertebrates. Expression patterns of RALDH-2 and CYP26 genes were determined in the early chick embryo by in situ hybridization. During gastrulation and neurulation RALDH-2 and CYP26 were expressed in nonoverlapping regions, with RALDH-2 transcripts localized to the presumptive presomitic and lateral plate mesoderm and CYP26 mRNA to the presumptive mid- and forebrain. The two domains of expression were separated by an approximately 300-μm-wide gap, encompassing the presumptive hindbrain. In the limb region, a similar spatial segregation of RALDH-2 and CYP26 expression was found at stages 14 and 15. Limb region mesoderm expressed RALDH-2, whereas the overlying limb ectoderm expressed CYP26. RA-synthesizing and -degrading enzymatic activities were measured biochemically in regions expressing RALDH-2 or CYP26. Regions expressing RALDH-2 generated RA efficiently from precursor retinal but degraded RA only inefficiently. Conversely, tissue expressing CYP26 efficiently degraded but did not synthesize RA. Localized regions of RA synthesis and degradation mediated by these two enzymes may therefore provide a mechanism to regulate RA homeostasis spatially in vertebrate embryos