Corrugated structure insertion for extending the SASE bandwidth up to 3% at the European XFEL

The usage of x-ray free electron laser (XFEL) in femtosecond nanocrystallography involves sequential illumination of many small crystals of arbitrary orientation. Hence a wide radiation bandwidth will be useful in order to obtain and to index a larger number of Bragg peaks used for determination of the crystal orientation. Considering the baseline configuration of the European XFEL in Hamburg, and based on beam dynamics simulations, we demonstrate here that the usage of corrugated structures allows for a considerable increase in radiation bandwidth. Data collection with a 3% bandwidth, a few microjoule radiation pulse energy, a few femtosecond pulse duration, and a photon energy of 5.4 keV is possible. For this study we have developed an analytical modal representation of the short-range wake function of the flat corrugated structures for arbitrary offsets of the source and the witness particles.Comment: 29 pages, 17 figure

Improved minimax predictive densities under Kullback--Leibler loss

Let $X| \mu \sim N_p(\mu,v_xI)$ and $Y| \mu \sim N_p(\mu,v_yI)$ be independent p-dimensional multivariate normal vectors with common unknown mean $\mu$. Based on only observing $X=x$, we consider the problem of obtaining a predictive density $\hat{p}(y| x)$ for $Y$ that is close to $p(y| \mu)$ as measured by expected Kullback--Leibler loss. A natural procedure for this problem is the (formal) Bayes predictive density $\hat{p}_{\mathrm{U}}(y| x)$ under the uniform prior $\pi_{\mathrm{U}}(\mu)\equiv 1$, which is best invariant and minimax. We show that any Bayes predictive density will be minimax if it is obtained by a prior yielding a marginal that is superharmonic or whose square root is superharmonic. This yields wide classes of minimax procedures that dominate $\hat{p}_{\mathrm{U}}(y| x)$, including Bayes predictive densities under superharmonic priors. Fundamental similarities and differences with the parallel theory of estimating a multivariate normal mean under quadratic loss are described.Comment: Published at http://dx.doi.org/10.1214/009053606000000155 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the Structure of the Bose-Einstein Condensate Ground State

We construct a macroscopic wave function that describes the Bose-Einstein condensate and weakly excited states, using the su(1,1) structure of the mean-field hamiltonian, and compare this state with the experimental values of second and third order correlation functions.Comment: 10 pages, 2 figure

Persistent spin current in spin-orbit coupling systems in the absence of an external magnetic field

The spin-orbit coupling systems with a zero magnetic field is studied under the equilibrium situation, {\it i.e.}, without a voltage bias. A persistent spin current is predicted to exist under most circumstances, although the persistent charge current and the spin accumulation are identically zero. In particular, a two-dimensional quantum wire is investigated in detail. Surprisingly, a persistent spin current is found to flow along the confined direction, due to the spin precession in accompany with the particle motion. This provides an interesting example of constant spin flowing without inducing a spin accumulation, contrary to common intuition.Comment: 4 pages, 5 figure

Nature of Spin Hall Effect in a finite Ballistic Two-Dimensional System with Rashba and Dresselhaus spin-orbit interaction

The spin Hall effect in a finite ballistic two-dimensional system with Rashba and Dresselhaus spin-orbit interaction is studied numerically. We find that the spin Hall conductance is very sensitive to the transverse measuring location, the shape and size of the device, and the strength of the spin-orbit interaction. Not only the amplitude of spin Hall conductance but also its sign can change. This non-universal behavior of the spin Hall effect is essentially different from that of the charge Hall effect, in which the Hall voltage is almost invariant with the transverse measuring site and is a monotonic function of the strength of the magnetic field. These surprise behavior of the spin Hall conductance are attributed to the fact that the eigenstates of the spin Hall system is extended in the transverse direction and do not form the edge states.Comment: 5 pages, 5 figure

Bias-controllable intrinsic spin polarization in a quantum dot

We propose a novel scheme to efficiently polarize and manipulate the electron spin in a quantum dot. This scheme is based on the spin-orbit interaction and it possesses following advantages: (1) The direction and the strength of the spin polarization is well controllable and manipulatable by simply varying the bias or the gate voltage. (2) The spin polarization is quite large even with a weak spin-orbit interaction. (3) Both electron-electron interaction and multi-energy levels do not weaken but strengthen the spin polarization. (4) It has the short spin flip time. (5) The device is free of a magnetic field or a ferromagnetic material. (6) It can be easily realized with present technology.Comment: 9 pages, 5 figure