Non-locality of Foldy-Wouthuysen and related transformations for the Dirac equation

Non-localities of Foldy-Wouthuysen and related transformations, which are used to separate positive and negative energy states in the Dirac equation, are investigated. Second moments of functional kernels generated by the transformations are calculated, the transformed functions and their variances are computed. It is shown that all the transformed quantities are smeared in the coordinate space by the amount comparable to the Compton wavelength $\lambda_c=\hbar/mc$.Comment: 7 pages, two figure

Zitterbewegung of relativistic electrons in a magnetic field and its simulation by trapped ions

One-electron 3+1 and 2+1 Dirac equations are used to calculate the motion of a relativistic electron in a vacuum in the presence of an external magnetic field. First, calculations are carried on an operator level and exact analytical results are obtained for the electron trajectories which contain both intraband frequency components, identified as the cyclotron motion, as well as interband frequency components, identified as the trembling motion (Zitterbewegung, ZB). Next, time-dependent Heisenberg operators are used for the same problem to compute average values of electron position and velocity employing Gaussian wave packets. It is shown that the presence of a magnetic field and the resulting quantization of the energy spectrum has pronounced effects on the electron Zitterbewegung: it introduces intraband frequency components into the motion, influences all the frequencies and makes the motion stationary (not decaying in time) in case of the 2+1 Dirac equation. Finally, simulations of the 2+1 Dirac equation and the resulting electron ZB in the presence of a magnetic field are proposed and described employing trapped ions and laser excitations. Using simulation parameters achieved in recent experiments of Gerritsma and coworkers we show that the effects of the simulated magnetic field on ZB are considerable and can certainly be observed.Comment: 19 pages, 9 figures, published versio

Zitterbewegung (trembling motion) of electrons in narrow gap semiconductors

Theory of trembling motion [Zitterbewegung (ZB)] of charge carriers in various narrow-gap materials is reviewed. Nearly free electrons in a periodic potential, InSb-type semiconductors, bilayer graphene, monolayer graphene and carbon nanotubes are considered. General features of ZB are emphasized. It is shown that, when the charge carriers are prepared in the form of Gaussian wave packets, the ZB has a transient character with the decay time of femtoseconds in graphene and picoseconds in nanotubes. Zitterbewegung of electrons in graphene in the presence of an external magnetic field is mentioned. A similarity of ZB in semiconductors to that of relativistic electrons in a vacuum is stressed. Possible ways of observing the trembling motion in solids are mentioned.Comment: 8 pages, 5 figure

Zitterbewegung of nearly-free and tightly bound electrons in solids

We show theoretically that nonrelativistic nearly-free electrons in solids should experience a trembling motion (Zitterbewegung, ZB) in absence of external fields, similarly to relativistic electrons in vacuum. The Zitterbewegung is directly related to the influence of periodic potential on the free electron motion. The frequency of ZB is $\omega\approx E_g/\hbar$, where $E_g$ is the energy gap. The amplitude of ZB is determined by the strength of periodic potential and the lattice period and it can be of the order of nanometers. We show that the amplitude of ZB does not depend much on the width of the wave packet representing an electron in real space. An analogue of the Foldy-Wouthuysen transformation, known from relativistic quantum mechanics, is introduced in order to decouple electron states in various bands. We demonstrate that, after the bands are decoupled, electrons should be treated as particles of a finite size. In contrast to nearly-free electrons we consider a two-band model of tightly bound electrons. We show that also in this case the electrons should experience the trembling motion. It is concluded that the phenomenon of Zitterbewegung of electrons in crystalline solids is a rule rather than an exception.Comment: 22 pages, 6 figures Published version, minor changes mad

The Sloan Lens ACS Survey. IX. Colors, Lensing and Stellar Masses of Early-type Galaxies

We present the current photometric dataset for the Sloan Lens ACS (SLACS) Survey, including HST photometry from ACS, WFPC2, and NICMOS. These data have enabled the confirmation of an additional 15 grade `A' (certain) lens systems, bringing the number of SLACS grade `A' lenses to 85; including 13 grade `B' (likely) systems, SLACS has identified nearly 100 lenses and lens candidates. Approximately 80% of the grade `A' systems have elliptical morphologies while ~10% show spiral structure; the remaining lenses have lenticular morphologies. Spectroscopic redshifts for the lens and source are available for every system, making SLACS the largest homogeneous dataset of galaxy-scale lenses to date. We have developed a novel Bayesian stellar population analysis code to determine robust stellar masses with accurate error estimates. We apply this code to deep, high-resolution HST imaging and determine stellar masses with typical statistical errors of 0.1 dex; we find that these stellar masses are unbiased compared to estimates obtained using SDSS photometry, provided that informative priors are used. The stellar masses range from 10^10.5 to 10^11.8 M$_\odot$ and the typical stellar mass fraction within the Einstein radius is 0.4, assuming a Chabrier IMF. The ensemble properties of the SLACS lens galaxies, e.g. stellar masses and projected ellipticities, appear to be indistinguishable from other SDSS galaxies with similar stellar velocity dispersions. This further supports that SLACS lenses are representative of the overall population of massive early-type galaxies with M* >~ 10^11 M$_\odot$, and are therefore an ideal dataset to investigate the kpc-scale distribution of luminous and dark matter in galaxies out to z ~ 0.5.Comment: 20 pages, 18 figures, 5 tables, published in Ap

Predictive monitoring for early detection of subacute potentially catastrophic illnesses in critical care

We wish to save lives of patients admitted to ICUs. Their mortality is high enough based simply on the severity of the original injury or illness, but is further raised by events during their stay. We target those events that are subacute but potentially catastrophic, such as infection. Sepsis, for example, is a bacterial infection of the bloodstream, that is common in ICU patients and has a \u3e 25% risk of death. Logically, early detection and treatment with antibiotics should improve outcomes. Our fundamental precepts are (1) some potentially catastrophic medical and surgical illnesses have subclinical phases during which early diagnosis and treatment might have life-saving effects, (2) these phases are characterized by changes in the normal highly complex but highly adaptive regulation and interaction of the nervous system and other organs such as the heart and lungs, (3) teams of clinicians and quantitative scientists can work together to identify clinically important abnormalities of monitoring data, to develop algorithms that match the clinicians\u27 eye in detecting abnormalities, and to undertake the clinical trials to test their impact on outcomes

Redshifts of CLASS Radio Sources

Spectroscopic observations of a sample of 42 flat-spectrum radio sources from the Cosmic Lens All-Sky Survey (CLASS) have yielded a mean redshift of $= 1.27$ with an RMS spread of 0.95, at a completeness level of 64%. The sample consists of sources with a 5-GHz flux density of 25-50 mJy, making it the faintest flat-spectrum radio sample for which the redshift distribution has been studied. The spectra, obtained with the Willam Herschel Telescope (WHT), consist mainly of broad-line quasars at $z>1$ and narrow-line galaxies at $z<0.5$. Though the mean redshift of flat-spectrum radio sources exhibits little variation over more than two orders of magnitude in radio flux density, there is evidence for a decreasing fraction of quasars at weaker flux levels. In this paper we present the results of our spectroscopic observations, and discuss the implications for constraining cosmological parameters with statistical analyses of the CLASS survey.Comment: 10 pages, AJ accepte

Numerical method of characteristics for one-dimensional blood flow

Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant