Diffractoid grating configuration for X-ray and ultraviolet focusing

An aspheric grating is described which is operable to image local or distant point sources sharply in a designated wavelength, i.e., produce a perfectly stigmatic image in the given wavelength at grazing angles of incidence. The grating surface comprises a surface of revolution defined by a curve which does not have a constant radius of curvature but is defined by a nonlinear differential equation

Shutters, Boxes, But No Paradoxes: Time Symmetry Puzzles in Quantum Theory

The ``N-Box Experiment'' is a much-discussed thought experiment in quantum mechanics. It is claimed by some authors that a single particle prepared in a superposition of N+1 box locations and which is subject to a final ``post-selection'' measurement corresponding to a different superposition can be said to have occupied ``with certainty'' N boxes during the intervening time. However, others have argued that under closer inspection, this surprising claim fails to hold. Aharonov and Vaidman have continued their advocacy of the claim in question by proposing a variation on the N-box experiment, in which the boxes are replaced by shutters and the pre- and post-selected particle is entangled with a photon. These authors argue that the resulting ``N-shutter experiment'' strengthens their original claim regarding the N-box experiment. It is argued in this paper that the apparently surprising features of this variation are no more robust than those of the N-box experiment and that it is not accurate to say that the particle is ``with certainty'' in all N shutters at any given time.Comment: Presentation improved; to appear in International Studies in Philosophy of Scienc

On Visibility in the Afshar Two-Slit Experiment

A modified version of Young's experiment by Shahriar Afshar indirectly reveals the presence of a fully articulated interference pattern prior to the post-selection of a particle in a "which-slit" basis. While this experiment does not constitute a violation of Bohr's Complementarity Principle as claimed by Afshar, both he and many of his critics incorrectly assume that a commonly used relationship between visibility parameter V and "which-way" parameter K has crucial relevance to his experiment. It is argued here that this relationship does not apply to this experimental situation and that it is wrong to make any use of it in support of claims for or against the bearing of this experiment on Complementarity.Comment: Final version; to appear in Foundations of Physic

On three-dimensional reconstruction of optically thin solar emission sources

Calculations are given for constructing the three dimensional distribution of optically thin EUV emission sources associated with solar active regions, from two dimensional observations (projections) recorded by the spectroheliograph on the OSO 7 satellite. The relation of the method to other image reconstruction methods is briefly discussed as well as the special requirements imposed in the solar case such as a knowledge of the true solar rotation function. A useful correlation criterion for establishing the physical validity of solutions is given

Excitation of the 3.071mm Hyperfine Line in Li-Like 57-Fe in Astrophysical Plasmas

As noted first by Sunyaev & Churazov (1984), the 3.071 mm hyperfine line from $^{57}Fe^{+23}$ might be observable in astrophysical plasmas. We assess the atomic processes which might contribute to the excitation of this line. We determine the intensity of the hyperfine line from an isothermal, coronal plasma in collisional ionization equilibrium and for a coronal plasma cooling isobarically due to its own radiation. Comparisons of the hyperfine line to other lines emitted by the same ion, Fe$^{+23}$, are shown to be useful for deriving the isotopic fraction of $^{57}$Fe. We calculate the ratios of the hyperfine line to the 2s--2p EUV lines at 192 \AA and 255 \AA, and the 2s--3p X-ray doublet at 10.6 \AA.Comment: 28 pages text+figures, Accepted to ApJ in Jan 98, also at http://www.astro.virginia.edu/~nld2n/research.htm

Phase transitions and configuration space topology

Equilibrium phase transitions may be defined as nonanalytic points of thermodynamic functions, e.g., of the canonical free energy. Given a certain physical system, it is of interest to understand which properties of the system account for the presence of a phase transition, and an understanding of these properties may lead to a deeper understanding of the physical phenomenon. One possible approach of this issue, reviewed and discussed in the present paper, is the study of topology changes in configuration space which, remarkably, are found to be related to equilibrium phase transitions in classical statistical mechanical systems. For the study of configuration space topology, one considers the subsets M_v, consisting of all points from configuration space with a potential energy per particle equal to or less than a given v. For finite systems, topology changes of M_v are intimately related to nonanalytic points of the microcanonical entropy (which, as a surprise to many, do exist). In the thermodynamic limit, a more complex relation between nonanalytic points of thermodynamic functions (i.e., phase transitions) and topology changes is observed. For some class of short-range systems, a topology change of the M_v at v=v_t was proved to be necessary for a phase transition to take place at a potential energy v_t. In contrast, phase transitions in systems with long-range interactions or in systems with non-confining potentials need not be accompanied by such a topology change. Instead, for such systems the nonanalytic point in a thermodynamic function is found to have some maximization procedure at its origin. These results may foster insight into the mechanisms which lead to the occurrence of a phase transition, and thus may help to explore the origin of this physical phenomenon.Comment: 22 pages, 6 figure

Equilibration of isolated macroscopic quantum systems

We investigate the equilibration of an isolated macroscopic quantum system in the sense that deviations from a steady state become unmeasurably small for the overwhelming majority of times within any sufficiently large time interval. The main requirements are that the initial state, possibly far from equilibrium, exhibits a macroscopic population of at most one energy level and that degeneracies of energy eigenvalues and of energy gaps (differences of energy eigenvalues) are not of exceedingly large multiplicities. Our approach closely follows and extends recent works by Short and Farrelly [2012 New J. Phys. 14 013063], in particular going beyond the realm of finite-dimensional systems and large effective dimensions.Comment: 19 page

Intercalation and Staging Behavior in Super-Oxygenated La2CuO4+δLa_2CuO_{4 + \delta}

A high temperature electrochemical oxidation process has been used to produce large single crystals of $La_2CuO_{4 + \delta}$ suitable for neutron scattering experiments. Below room temperature the oxygen-rich phases have structural superlattice scattering peaks which indicate new periodicities ranging from 2 to 6.6 layers perpendicular to the copper oxide planes. A model structure originally proposed for $La_2NiO_{4 + \delta}$ can account for the superlattice peaks as a result of anti-phase domain boundaries between different tilt directions of the CuO$_6$ octahedra. Within this model, the changes in CuO$_6$ tilt directions are induced by segregated layers of interstitial oxygen which order in a manner similar to intercalants in graphite. This structural model thus clarifies previous work and establishes $La_2CuO_{4 + \delta}$ as a unique lamellar superconducting system with annealed disorder.Comment: 23 pages, latex, 6 figures (not including Figures 2 & 7 and Table 1 which were not submitted but are available upon request to the Authors at: [email protected]