Quantum Gauge Equivalence in QED

We discuss gauge transformations in QED coupled to a charged spinor field, and examine whether we can gauge-transform the entire formulation of the theory from one gauge to another, so that not only the gauge and spinor fields, but also the forms of the operator-valued Hamiltonians are transformed. The discussion includes the covariant gauge, in which the gauge condition and Gauss's law are not primary constraints on operator-valued quantities; it also includes the Coulomb gauge, and the spatial axial gauge, in which the constraints are imposed on operator-valued fields by applying the Dirac-Bergmann procedure. We show how to transform the covariant, Coulomb and spatial axial gauges to what we call ``common form,'' in which all particle excitation modes have identical properties. We also show that, once that common form has been reached, QED in different gauges has a common time-evolution operator that defines time-translation for states that represent systems of electrons and photons. By combining gauge transformations with changes of representation from standard to common form, the entire apparatus of a gauge theory can be transformed from one gauge to another.Comment: Contribution for a special issue of Foundations of Physics honoring Fritz Rohrlich; edited by Larry P. Horwitz, Tel-Aviv University, and Alwyn van der Merwe, University of Denver (Plenum Publishing, New York); 40 pages, REVTEX, Preprint UCONN-93-3, 1 figure available upon request from author

Hammerhead, an ultrahigh resolution ePix camera for wavelength-dispersive spectrometers

Wavelength-dispersive spectrometers (WDS) are often used in synchrotron and FEL applications where high energy resolution (in the order of eV) is important. Increasing WDS energy resolution requires increasing spatial resolution of the detectors in the dispersion direction. The common approaches with strip detectors or small pixel detectors are not ideal. We present a novel approach, with a sensor using rectangular pixels with a high aspect ratio (between strips and pixels, further called "strixels"), and strixel redistribution to match the square pixel arrays of typical ASICs while avoiding the considerable effort of redesigning ASICs. This results in a sensor area of 17.4 mm x 77 mm, with a fine pitch of 25 $\mu$m in the horizontal direction resulting in 3072 columns and 176 rows. The sensors use ePix100 readout ASICs, leveraging their low noise (43 e$^-$, or 180 eV rms). We present results obtained with a Hammerhead ePix100 camera, showing that the small pitch (25 $\mu$m) in the dispersion direction maximizes performance for both high and low photon occupancies, resulting in optimal WDS energy resolution. The low noise level at high photon occupancy allows precise photon counting, while at low occupancy, both the energy and the subpixel position can be reconstructed for every photon, allowing an ultrahigh resolution (in the order of 1 $\mu$m) in the dispersion direction and rejection of scattered beam and harmonics. Using strixel sensors with redistribution and flip-chip bonding to standard ePix readout ASICs results in ultrahigh position resolution ($\sim$1 $\mu$m) and low noise in WDS applications, leveraging the advantages of hybrid pixel detectors (high production yield, good availability, relatively inexpensive) while minimizing development complexity through sharing the ASIC, hardware, software and DAQ development with existing versions of ePix cameras.Comment: 8 pages, 6 figure

Precision Measurements of Stretching and Compression in Fluid Mixing

The mixing of an impurity into a flowing fluid is an important process in many areas of science, including geophysical processes, chemical reactors, and microfluidic devices. In some cases, for example periodic flows, the concepts of nonlinear dynamics provide a deep theoretical basis for understanding mixing. Unfortunately, the building blocks of this theory, i.e. the fixed points and invariant manifolds of the associated Poincare map, have remained inaccessible to direct experimental study, thus limiting the insight that could be obtained. Using precision measurements of tracer particle trajectories in a two-dimensional fluid flow producing chaotic mixing, we directly measure the time-dependent stretching and compression fields. These quantities, previously available only numerically, attain local maxima along lines coinciding with the stable and unstable manifolds, thus revealing the dynamical structures that control mixing. Contours or level sets of a passive impurity field are found to be aligned parallel to the lines of large compression (unstable manifolds) at each instant. This connection appears to persist as the onset of turbulence is approached.Comment: 5 pages, 5 figure

Slow decay of concentration variance due to no-slip walls in chaotic mixing

Chaotic mixing in a closed vessel is studied experimentally and numerically in different 2-D flow configurations. For a purely hyperbolic phase space, it is well-known that concentration fluctuations converge to an eigenmode of the advection-diffusion operator and decay exponentially with time. We illustrate how the unstable manifold of hyperbolic periodic points dominates the resulting persistent pattern. We show for different physical viscous flows that, in the case of a fully chaotic Poincare section, parabolic periodic points at the walls lead to slower (algebraic) decay. A persistent pattern, the backbone of which is the unstable manifold of parabolic points, can be observed. However, slow stretching at the wall forbids the rapid propagation of stretched filaments throughout the whole domain, and hence delays the formation of an eigenmode until it is no longer experimentally observable. Inspired by the baker's map, we introduce a 1-D model with a parabolic point that gives a good account of the slow decay observed in experiments. We derive a universal decay law for such systems parametrized by the rate at which a particle approaches the no-slip wall.Comment: 17 pages, 12 figure

Friction Drag on a Particle Moving in a Nematic Liquid Crystal

The flow of a liquid crystal around a particle does not only depend on its shape and the viscosity coefficients but also on the direction of the molecules. We studied the resulting drag force on a sphere moving in a nematic liquid crystal (MBBA) in a low Reynold's number approach for a fixed director field (low Ericksen number regime) using the computational artificial compressibility method. Taking the necessary disclination loop around the sphere into account, the value of the drag force anisotropy (F_\perp/F_\parallel=1.50) for an exactly computed field is in good agreement with experiments (~1.5) done by conductivity diffusion measurements. We also present data for weak anchoring of the molecules on the particle surface and of trial fields, which show to be sufficiently good for most applications. Furthermore, the behaviour of the friction close to the transition point nematic isotropic and for a rod-like and a disc-like liquid crystal will be given.Comment: 23 pages RevTeX, including 3 PS figures, 1 PS table and 1 PS-LaTeX figure; Accepted for publication in Phys. Rev.

Creating artificial magnetic fields for cold atoms by photon-assisted tunneling

This paper proposes a simple setup for introducing an artificial magnetic field for neutral atoms in 2D optical lattices. This setup is based on the phenomenon of photon-assisted tunneling and involves a low-frequency periodic driving of the optical lattice. This low-frequency driving does not affect the electronic structure of the atom and can be easily realized by the same means which employed to create the lattice. We also address the problem of detecting this effective magnetic field. In particular, we study the center of mass wave-packet dynamics, which is shown to exhibit certain features of cyclotron dynamics of a classical charged particle.Comment: EPL-style, 8 pages, 4 figure

Rain, power laws, and advection

Localized rain events have been found to follow power-law size and duration distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws are generated by treating rain as a passive tracer undergoing advection in a velocity field generated by a two-dimensional system of point vortices.Comment: 7 pages, 4 figure

Performance of ePix10K, a high dynamic range, gain auto-ranging pixel detector for FELs

ePix10K is a hybrid pixel detector developed at SLAC for demanding free-electron laser (FEL) applications, providing an ultrahigh dynamic range (245 eV to 88 MeV) through gain auto-ranging. It has three gain modes (high, medium and low) and two auto-ranging modes (high-to-low and medium-to-low). The first ePix10K cameras are built around modules consisting of a sensor flip-chip bonded to 4 ASICs, resulting in 352x384 pixels of 100 $\mu$m x 100 $\mu$m each. We present results from extensive testing of three ePix10K cameras with FEL beams at LCLS, resulting in a measured noise floor of 245 eV rms, or 67 e$^-$ equivalent noise charge (ENC), and a range of 11000 photons at 8 keV. We demonstrate the linearity of the response in various gain combinations: fixed high, fixed medium, fixed low, auto-ranging high to low, and auto-ranging medium-to-low, while maintaining a low noise (well within the counting statistics), a very low cross-talk, perfect saturation response at fluxes up to 900 times the maximum range, and acquisition rates of up to 480 Hz. Finally, we present examples of high dynamic range x-ray imaging spanning more than 4 orders of magnitude dynamic range (from a single photon to 11000 photons/pixel/pulse at 8 keV). Achieving this high performance with only one auto-ranging switch leads to relatively simple calibration and reconstruction procedures. The low noise levels allow usage with long integration times at non-FEL sources. ePix10K cameras leverage the advantages of hybrid pixel detectors with high production yield and good availability, minimize development complexity through sharing the hardware, software and DAQ development with all other versions of ePix cameras, while providing an upgrade path to 5 kHz, 25 kHz and 100 kHz in three steps over the next few years, matching the LCLS-II requirements.Comment: 9 pages, 5 figure