Stochastic integration in UMD Banach spaces

In this paper we construct a theory of stochastic integration of processes with values in $\mathcal{L}(H,E)$, where $H$ is a separable Hilbert space and $E$ is a UMD Banach space (i.e., a space in which martingale differences are unconditional). The integrator is an $H$-cylindrical Brownian motion. Our approach is based on a two-sided $L^p$-decoupling inequality for UMD spaces due to Garling, which is combined with the theory of stochastic integration of $\mathcal{L}(H,E)$-valued functions introduced recently by two of the authors. We obtain various characterizations of the stochastic integral and prove versions of the It\^{o} isometry, the Burkholder--Davis--Gundy inequalities, and the representation theorem for Brownian martingales.Comment: Published at http://dx.doi.org/10.1214/009117906000001006 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stochastic evolution equations in UMD Banach spaces

We discuss existence, uniqueness, and space-time H\"older regularity for solutions of the parabolic stochastic evolution equation dU(t) = (AU(t) + F(t,U(t))) dt + B(t,U(t)) dW_H(t), t\in [0,\Tend], U(0) = u_0, where $A$ generates an analytic $C_0$-semigroup on a UMD Banach space $E$ and $W_H$ is a cylindrical Brownian motion with values in a Hilbert space $H$. We prove that if the mappings $F:[0,T]\times E\to E$ and $B:[0,T]\times E\to \mathscr{L}(H,E)$ satisfy suitable Lipschitz conditions and $u_0$ is \F_0-measurable and bounded, then this problem has a unique mild solution, which has trajectories in C^\l([0,T];\D((-A)^\theta) provided $\lambda\ge 0$ and $\theta\ge 0$ satisfy \l+\theta<\frac12. Various extensions of this result are given and the results are applied to parabolic stochastic partial differential equations.Comment: Accepted for publication in Journal of Functional Analysi

Ito's formula in UMD Banach spaces and regularity of solutions of the Zakai equation

Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Ito formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstract results are applied to prove regularity in space and time of the solutions of the Zakai equation.Comment: Accepted for publication in Journal of Differential Equation

Calculations of the Exclusive Processes 2H(e,e'p)n, 3He(e,e'p)2H and 3He(e,e'p)(pn) within a Generalized Glauber Approach

The exclusive processes 2H(e,e'p)n, 3He(e,e'p)2H and 3He(e,e'p)(pn), have been analyzed using realistic few-body wave functions and treating the final state interaction (FSI) within a Generalized Eikonal Approximation (GEA), based upon the direct calculation of the Feynman diagrams describing the rescattering of the struck nucleon with the nucleons of the A-1 system. The approach represents an improvement of the conventional Glauber approach (GA), in that it allows one to take into account the effects of the nuclear excitation of the $A-1$ system on the rescattering of the struck nucleon. Using realistic three-body wave functions corresponding to the AV18 interaction, the results of our parameter free calculations are compared with available experimental data. It is found that in some kinematical conditions FSI effects represent small corrections, whereas in other kinematics conditions they are very large and absolutely necessary to provide a satisfactory agreement between theoretical calculations and experimental data. It is shown that in the kinematics of the experimental data which have been considered, covering the region of missing momentum and energy with p_m < 0.6 GeV/c and E_m < 100 MeV in the perpendicular kinematics, the GA and GEA predictions differ only by less than 3-4 %.Comment: Typos detected and removed while Proof reading. Physical Review C. in Pres

Electrical activation and electron spin resonance measurements of implanted bismuth in isotopically enriched silicon-28

We have performed continuous wave and pulsed electron spin resonance measurements of implanted bismuth donors in isotopically enriched silicon-28. Donors are electrically activated via thermal annealing with minimal diffusion. Damage from bismuth ion implantation is repaired during thermal annealing as evidenced by narrow spin resonance linewidths (B_pp=12uT and long spin coherence times T_2=0.7ms, at temperature T=8K). The results qualify ion implanted bismuth as a promising candidate for spin qubit integration in silicon.Comment: 4 pages, 4 figure

Reaching the quantum limit of sensitivity in electron spin resonance

We report pulsed electron-spin resonance (ESR) measurements on an ensemble of Bismuth donors in Silicon cooled at 10mK in a dilution refrigerator. Using a Josephson parametric microwave amplifier combined with high-quality factor superconducting micro-resonators cooled at millikelvin temperatures, we improve the state-of-the-art sensitivity of inductive ESR detection by nearly 4 orders of magnitude. We demonstrate the detection of 1700 bismuth donor spins in silicon within a single Hahn echo with unit signal-to-noise (SNR) ratio, reduced to just 150 spins by averaging a single Carr-Purcell-Meiboom-Gill sequence. This unprecedented sensitivity reaches the limit set by quantum fluctuations of the electromagnetic field instead of thermal or technical noise, which constitutes a novel regime for magnetic resonance.Comment: Main text : 10 pages, 4 figures. Supplementary text : 16 pages, 8 figure

Spin relaxation in semiconductor quantum dots

We have studied the physical processes responsible for the spin -flip in GaAs quantum dots. We have calculated the rates for different mechanisms which are related to spin-orbit coupling and cause a spin-flip during the inelastic relaxation of the electron in the dot both with and without a magnetic field. We have shown that the zero-dimensional character of the problem when electron wave functions are localized in all directions leads to freezing out of the most effective spin-flip mechanisms related to the absence of the inversion centers in the elementary crystal cell and at the heterointerface and, as a result, to unusually low spin-flip rates.Comment: 6 pages, RevTe

Stark shift and field ionization of arsenic donors in 28^{28}Si-SOI structures

We develop an efficient back gate for silicon-on-insulator (SOI) devices operating at cryogenic temperatures, and measure the quadratic hyperfine Stark shift parameter of arsenic donors in isotopically purified $^{28}$Si-SOI layers using such structures. The back gate is implemented using MeV ion implantation through the SOI layer forming a metallic electrode in the handle wafer, enabling large and uniform electric fields up to $\sim$ 2 V/$\mu$m to be applied across the SOI layer. Utilizing this structure we measure the Stark shift parameters of arsenic donors embedded in the $^{28}$Si SOI layer and find a contact hyperfine Stark parameter of $\eta_a=-1.9\pm0.2\times10^{-3} \mu$m$^2$/V$^2$. We also demonstrate electric-field driven dopant ionization in the SOI device layer, measured by electron spin resonance.Comment: 5 pages, 3 figure

Physical Structure of Small Wolf-Rayet Ring Nebulae

We have selected the seven most well-defined WR ring nebulae in the LMC (Br 2, Br 10, Br 13, Br 40a, Br 48, Br 52, and Br 100) to study their physical nature and evolutionary stages. New CCD imaging and echelle observations have been obtained for five of these nebulae; previous photographic imaging and echelle observations are available for the remaining two nebulae. Using the nebular dynamics and abundances, we find that the Br 13 nebula is a circumstellar bubble, and that the Br 2 nebula may represent a circumstellar bubble merging with a fossil main-sequence interstellar bubble. The nebulae around Br 10, Br 52, and Br 100 all show influence of the ambient interstellar medium. Their regular expansion patterns suggest that they still contain significant amounts of circumstellar material. Their nebular abundances would be extremely interesting, as their central stars are WC5 and WN3-4 stars whose nebular abundances have not been derived previously. Intriguing and tantalizing implications are obtained from comparisons of the LMC WR ring nebulae with ring nebulae around Galactic WR stars, Galactic LBVs, LMC LBVs, and LMC BSGs; however, these implications may be limited by small-number statistics. A SNR candidate close to Br 2 is diagnosed by its large expansion velocity and nonthermal radio emission. There is no indication that Br 2's ring nebula interacts dynamically with this SNR candidate.Comment: 20 pages, Latex (aaspp4.sty), 2 figures, accepted by the Astronomical Journal (March 99 issue