Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives

We consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain C_c^\infty(\Omega) where the self-adjointness is defined relative to L^2(\Omega), and \Omega is a given open subset of R^d. The measure on \Omega is Lebesgue measure on R^d restricted to \Omega. The problem originates with I.E. Segal and B. Fuglede, and is difficult in general. In this paper, we provide a representation-theoretic answer in the special case when \Omega=I\times\Omega_2 and I is an open interval. We then apply the results to the case when \Omega is a d-cube, I^d, and we describe possible subsets \Lambda of R^d such that {e^(i2\pi\lambda \dot x) restricted to I^d:\lambda\in\Lambda} is an orthonormal basis in L^2(I^d).Comment: LaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km, 02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt, 61.44.B

A combined experimental and theoretical study on realizing and using laser controlled torsion of molecules

It is demonstrated that strong laser pulses can introduce torsional motion in the axially chiral molecule 3,5-diflouro-3',5'-dibromo-biphenyl (DFDBrBPh). A nanosecond laser pulse spatially aligns the stereogenic carbon-carbon (C-C) bond axis allowing a perpendicularly polarized, intense femtosecond pulse to initiate torsional motion accompanied by a rotation about the fixed axis. We monitor the induced motion by femtosecond time-resolved Coulomb explosion imaging. Our theoretical analysis corroborates the experimental findings and on the basis of these results we discuss future applications of laser induced torsion, viz., time-resolved studies of de-racemization and laser controlled molecular junctions based on molecules with torsion.Comment: 10 pages, 9 figures, 2 tables; submitted to J. Chem. Phys.

The Star Formation Epoch of the Most Massive Early-Type Galaxies

We present new Keck spectroscopy of early-type galaxies in three galaxy clusters at z~0.5. We focus on the fundamental plane (FP) relation, and combine the kinematics with structural parameters determined from HST images. The galaxies obey clear FP relations, which are offset from the FP of the nearby Coma cluster due to passive evolution of the stellar populations. The z~0.5 data are combined with published data for 11 additional clusters at 0.18<z<1.28, to determine the evolution of the mean M/L(B) ratio of cluster galaxies with masses M>10^11 M_sun, as implied by the FP. We find dlog(M/L(B))/dz = -0.555+-0.042, stronger evolution than was previously inferred from smaller samples. The observed evolution depends on the luminosity-weighted mean age of the stars in the galaxies, the initial mass function (IMF), selection effects due to progenitor bias, and other parameters. Assuming a normal IMF but allowing for various other sources of uncertainty we find z* = 2.01+-0.20 for the luminosity-weighted mean star formation epoch. The main uncertainty is the slope of the IMF in the range 1-2 Solar masses: we find z* = 4.0 for a top-heavy IMF with slope x=0. The M/L(B) ratios of the cluster galaxies are compared to those of recently published samples of field early-type galaxies at 0.32<z<1.14. Assuming that progenitor bias and the IMF do not depend on environment we find that the present-day age of stars in massive field galaxies is 4.1 +- 2.0 % (~0.4 Gyr) less than that of stars in massive cluster galaxies, consistent with most, but not all, previous studies of local and distant early-type galaxies. This relatively small age difference is surprising in the context of expectations from ``standard'' hierarchical galaxy formation models. [ABRIDGED]Comment: Accepted for publication in ApJ. Minor corrections to match published versio

The Fundamental Plane at z=1.27: First Calibration of the Mass Scale of Red Galaxies at Redshifts z>1

We present results on the Fundamental Plane (FP) of early-type galaxies in the cluster RDCS J0848+4453 at z=1.27. Internal velocity dispersions of three K-selected early-type galaxies are determined from deep Keck spectra. Structural parameters are determined from HST NICMOS images. The galaxies show substantial offsets from the FP of the nearby Coma cluster, as expected from passive evolution of their stellar populations. The offsets from the FP can be expressed as offsets in M/L ratio. The M/L ratios of the two most massive galaxies are consistent with an extrapolation of results obtained at z=0.02-0.83. The evolution of early-type galaxies with masses >10^11 M_sun is well described by ln M/L(B) = (-1.06 +- 0.09) z, corresponding to passive evolution of -1.50 +- 0.13 mag at z=1.3. Ignoring selection effects, the best fitting stellar formation redshift is z*=2.6, corresponding to a luminosity weighted age at the epoch of observation of ~2 Gyr. The M/L ratios of these two galaxies are also in excellent agreement with predictions from models that include progenitor bias. The third galaxy is a factor ~10 less massive than the other two, shows strong Balmer absorption lines in its spectrum, and is offset from the Coma Fundamental Plane by 2.9 mag in rest-frame B. Despite their large range in M/L ratios, all three galaxies fall in the ``Extremely Red Object'' (ERO) class with I-H>3 and R-K>5, and our results show that it is hazardous to use simple models for converting luminosity to mass for these objects. Measurements of M/L ratios at high redshift can be considered first steps to empirically disentangle luminosity and mass evolution at the high mass end of the galaxy population, lifting an important degeneracy in the interpretation of evolution of the luminosity function. [SHORTENED]Comment: Accepted for publication in the Astrophysical Journa

Tuning of magnetic and electronic states by control of oxygen content in lanthanum strontium cobaltites

We report on the magnetic, resistive, and structural studies of perovskite La$_{1/3}$Sr$_{2/3}$CoO$_{3-\delta}$. By using the relation of synthesis temperature and oxygen partial pressure to oxygen stoichiometry obtained from thermogravimetric analysis, we have synthesized a series of samples with precisely controlled $\delta=0.00-0.49$. These samples show three structural phases at $\delta=0.00-0.15$, $\approx0.25$, $\approx0.5$, and two-phase behavior for other oxygen contents. The stoichiometric material with $\delta=0.00$ is a cubic ferromagnetic metal with the Curie temperature $T_{\rm C}=274$ K. The increase of $\delta$ to 0.15 is followed by a linear decrease of $T_{\rm C}$ to $\approx$ 160 K and a metal-insulator transition near the boundary of the cubic structure range. Further increase of $\delta$ results in formation of a tetragonal $2a_p\times 2a_p \times 4a_p$ phase for $\delta\approx 0.25$ and a brownmillerite phase for $\delta\approx0.5$. At low temperatures, these are weak ferromagnetic insulators (canted antiferromagnets) with magnetic transitions at $T_{\rm m}\approx230$ and 120 K, respectively. At higher temperatures, the $2a_p\times 2a_p \times 4a_p$ phase is $G$-type antiferromagnetic between 230 K and $\approx$360 K. Low temperature magnetic properties of this system for $\delta<1/3$ can be described in terms of a mixture of Co$^{3+}$ ions in the low-spin state and Co$^{4+}$ ions in the intermediate-spin state and a possible spin transition of Co$^{3+}$ to the intermediate-spin state above $T_{\rm C}$. For $\delta>1/3$, there appears to be a combination of Co$^{2+}$ and Co$^{3+}$ ions, both in the high-spin state with dominating antiferromagnetic interactions.Comment: RevTeX, 9 pages, 7 figures, to be published in Physical Review

Photometric Properties of 47 Clusters of Galaxies: I. The Butcher-Oemler Effect

We present gri CCD photometry of 44 Abell clusters and 4 cluster candidates. Twenty one clusters in our sample have spectroscopic redshifts. Fitting a relation between mean g, r and i magnitudes, and redshift for this subsample, we have calculated photometric redshifts for the remainder with an estimated accuracy of 0.03. The resulting redshift range for the sample is 0.03<z<0.38. Color-magnitude diagrams are presented for the complete sample and used to study evolution of the galaxy population in the cluster environment. Our observations show a strong Butcher-Oemler effect (Butcher & Oemler 1978, 1984), with an increase in the fraction of blue galaxies (f_B) with redshift that seems more consistent with the steeper relation estimated by Rakos and Schombert (1995) than with the original one by Butcher & Oemler (1984). However, in the redshift range between ~ 0.08 and 0.2, where most of our clusters lie, there is a wide range of f_B values, consistent with no redshift evolution of the cluster galaxy population. A large range of f_B values is also seen between ~ 0.2 and 0.3, when Smail at al. (1998) x-ray clusters are added to our sample. The discrepancies between samples underscore the need for an unbiased sample to understand how much of the Butcher-Oemler effect is due to evolution, and how much to selection effects. We also tested the idea proposed by Garilli et al. (1996) that there is a population of unusually red galaxies which could be associated either with the field or clusters, but we find that these objects are all near the limiting magnitude of the images (20.5<r<22) and have colors that are consistent with those expected for stars or field galaxies at z ~ 0.7.Comment: 35 pages including 8 figures, submitted to A

High transport currents in mechanically reinforced MgB2 wires

We prepared and characterized monofilamentary MgB2 wires with a mechanically reinforced composite sheath of Ta(Nb)/Cu/steel, which leads to dense filaments and correspondingly high transport currents up to Jc = 10^5 A/cm^2 at 4.2 K, self field. The reproducibility of the measured transport currents was excellent and not depending on the wire diameter. Using different precursors, commercial reacted powder or an unreacted Mg/B powder mixture, a strong influence on the pinning behaviour and the irreversibility field was observed. The critical transport current density showed a nearly linear temperature dependency for all wires being still 52 kA/cm^2 at 20 K and 23 kA/cm^2 at 30 K. Detailed data for Jc(B,T) and Tc(B) were measured.Comment: 21 pages, 13 figures, revised version, to be published in Supercond. Sci. Techno

The history of mass assembly of faint red galaxies in 28 galaxy clusters since z=1.3

We measure the relative evolution of the number of bright and faint (as faint as 0.05 L*) red galaxies in a sample of 28 clusters, of which 16 are at 0.50<= z<=1.27, all observed through a pair of filters bracketing the 4000 Angstrom break rest-frame. The abundance of red galaxies, relative to bright ones, is constant over all the studied redshift range, 0<z<1.3, and rules out a differential evolution between bright and faint red galaxies as large as claimed in some past works. Faint red galaxies are largely assembled and in place at z=1.3 and their deficit does not depend on cluster mass, parametrized by velocity dispersion or X-ray luminosity. Our analysis, with respect to previous one, samples a wider redshift range, minimizes systematics and put a more attention to statistical issues, keeping at the same time a large number of clusters.Comment: MNRAS, 386, 1045. Half a single sentence (in sec 4.4) change

Entanglement and Timing-Based Mechanisms in the Coherent Control of Scattering Processes

The coherent control of scattering processes is considered, with electron impact dissociation of H$_2^+$ used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a control scenario that relies on previously established entanglement requirements between the scattering partners. Specifically, initial state entanglement assures that all collisions in the scattering volume yield the desirable scattering configuration. Scattering is controlled by preparing the particular internal state wave function that leads to the favored collisional configuration in the collision volume. This insight allows coherent control to be extended to the case of time-dependent scattering. Specifically, we identify reactive scattering scenarios using incident wave packets of translational motion where coherent control is operational and initial state entanglement is unnecessary. Both the stationary and time-dependent scenarios incorporate extended coherence features, making them physically distinct. From a theoretical point of view, this work represents a large step forward in the qualitative understanding of coherently controlled reactive scattering. From an experimental viewpoint, it offers an alternative to entanglement-based control schemes. However, both methods present significant challenges to existing experimental technologies

Toward Equations of Galactic Structure

We find that all classes of galaxies, ranging from disks to spheroids and from dwarf spheroidals to brightest cluster galaxies, lie on a two dimensional surface within the space defined by the logarithms of the half-light radius, r_e, mean surface brightness within r_e, I_e, and internal velocity, V^2 = (1/2)v_c^2 + sigma^2, where v_c is the rotational velocity and sigma is the velocity dispersion. If these quantities are expressed in terms of kpc, L_solar/pc^2, and km/s, then log r_e - log V^2 + log I_e + log Upsilon_e + 0.8 = 0, where we provide a fitting function for Upsilon_e, the mass-to-light ratio within r_e in units of M_solar/L_solar, that depends only on V and I_e. The scatter about this surface for our heterogeneous sample of 1925 galaxies is small (< 0.1 dex) and could be as low as ~ 0.05 dex, or 10%. This small scatter has three possible implications for how gross galactic structure is affected by internal factors, such as stellar orbital structure, and by external factors, such as environment. These factors either 1) play no role beyond generating some of the observed scatter, 2) move galaxies along the surface, or 3) balance each other to maintain this surface as the locus of galactic structure equilibria. We cast the behavior of Upsilon_e in terms of the fraction of baryons converted to stars, eta, and the concentration of those stars within the dark matter halo, xi = R_{200}/r_e. We derive eta = 1.9 x 10^{-5} (L/L^*) Upsilon_* V^{-3} and xi = 1.4 V/r_e. Finally, we present and discuss the distributions of eta and xi for the full range of galaxies. For systems with internal velocities comparable to that of the Milky Way (149 < V < 163 km/s), eta = 0.14 +- 0.05, and xi is, on average, ~ 5 times greater for spheroids than for disks. (Abridged)Comment: submitted to Ap