A simple proof of Birkhoff's theorem for cosmological constant

We provide a simple, unified proof of Birkhoff's theorem for the vacuum and cosmological constant case, emphasizing its local nature. We discuss its implications for the maximal analytic extensions of Schwarzschild, Schwarzschild(-anti)-de Sitter and Nariai spacetimes. In particular, we note that the maximal analytic extensions of extremal and over-extremal Schwarzschild-de Sitter spacetimes exhibit no static region. Hence the common belief that Birkhoff's theorem implies staticity is false for the case of positive cosmological constant. Instead, the correct point of view is that generalized Birkhoff's theorems are local uniqueness theorems whose corollary is that locally spherically symmetric solutions of Einstein's equations exhibit an additional local killing vector field.Comment: 10 pages, 5 figures References added; typo in eqn. 12 fixe

Sympathetic ground state cooling and coherent manipulation with two-ion-crystals

We have cooled a two-ion-crystal to the ground state of its collective modes of motion. Laser cooling, more specific resolved sideband cooling is performed sympathetically by illuminating only one of the two $^{40}$Ca$^+$ ions in the crystal. The heating rates of the motional modes of the crystal in our linear trap have been measured, and we found them considerably smaller than those previously reported by Q. Turchette {\em et. al.} Phys. Rev. A 61, 063418 (2000) in the case of trapped $^9$Be$^+$ ions. After the ground state is prepared, coherent quantum state manipulation of the atomic population can be performed. Within the coherence time, up to 12 Rabi oscillations are observed, showing that many coherent manipulations can be achieved. Coherent excitation of each ion individually and ground state cooling are important tools for the realization of quantum information processing in ion traps

Further results on the cross norm criterion for separability

In the present paper the cross norm criterion for separability of density matrices is studied. In the first part of the paper we determine the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal states. In the second part we show that the greatest cross norm criterion induces a novel computable separability criterion for bipartite systems. This new criterion is a necessary but in general not a sufficient criterion for separability. It is shown, however, that for all pure states, for Bell diagonal states, for Werner states in dimension d=2 and for isotropic states in arbitrary dimensions the new criterion is necessary and sufficient. Moreover, it is shown that for Werner states in higher dimensions (d greater than 2), the new criterion is only necessary.Comment: REVTeX, 19 page

Type II Quasars from the Sloan Digital Sky Survey: V. Imaging host galaxies with the Hubble Space Telescope

Type II quasars are luminous Active Galactic Nuclei whose centers are obscured by large amounts of gas and dust. In this paper we present 3-band HST images of nine type II quasars with redshifts 0.2 < z < 0.4 selected from the Sloan Digital Sky Survey based on their emission line properties. The intrinsic luminosities of these AGN are estimated to be -24 > M_B > -26, but optical obscuration allows their host galaxies to be studied unencumbered by bright nuclei. Each object has been imaged in three continuum filters (`UV', `blue' and `yellow') placed between the strong emission lines. The spectacular, high quality images reveal a wealth of details about the structure of the host galaxies and their environments. Six of the nine galaxies in the sample are ellipticals with de Vaucouleurs light profiles, one object has a well-defined disk component and the remaining two have marginal disks. Stellar populations of type II quasar hosts are more luminous (by a median of 0.3-0.7 mag, depending on the wavelength) and bluer (by about 0.4 mag) than are M* galaxies at the same redshift. When smooth fits to stellar light are subtracted from the images, we find both positive and negative residuals that become more prominent toward shorter wavelengths. We argue that the negative residuals are due to kpc-scale dust obscuration, while most positive residuals are due to the light from the nucleus scattered off interstellar material in the host galaxy. Scattered light makes a significant contribution to the broad band continuum emission and can be the dominant component of the extended emission in the UV in extreme cases.Comment: 51 pages, including 12 grey scale figures, 4 color figures, 5 tables. In press in AJ. Version with higher-resolution images available at http://www.astro.princeton.edu/~nadia/qso2.html. (Minor changes in response to the referee report

Phase diagram and phase transitions in ferroelectric tris-sarcosine calcium chloride and its brominated isomorphs

Tris-sarcosine calcium chloride [(TSCC), (CH3NHCH2COOH)3CaCl2] is a uniaxial ferroelectric (FE) with a displacive second-order phase transition near Tc=130 K. A continuous range of solid solutions can be made by substituting Br for Cl, which lowers Tc to 0 K at ∼72% Br. Such a quantum critical point differs from that in pseudocubic FEs, such as O-18 SrTiO3 or doped KTaO3. For many years, this system was thought to have only two phases, paraelectric and FE, at ambient pressure. However, we find from dielectric and resonant ultrasound spectroscopy that there are four phase transitions in TSCC and in TSCC:Br (for 0 < Br < 40%): Order-disorder of the sarcosine methyl group at 185 K; displacive FE transition at 130 K (in pure TSCC); a second FE transition [previously hypothesized to be antiferroelectric (AFE) but probably not] at 64 K; and a new anomaly at ∼45 K which might be due to a phase transition or to Debye-like freezing of orientational disorder of some part of the sarcosine molecule. The probable sequence of structures is (upon cooling): Pnma with Z=4(D2h16) ambient 500 K > T > 185 K, disordered; Pnma with Z=4(D2h16)185 K>T>130 K (ordered); Pn21a with Z=4(C2v9)130 K>T>64 K (FE); P21a (C2h5) with Z =4, 64 K > T > 45 K (not AFE); T < 45 K, unknown structure. A sixth hexagonal structure at high temperatures (>500 K) is hypothesized to be D6h3(P63/mcm) with Z =2, but the samples decompose first at 503 K (230 °C)

Entanglement measures and purification procedures

Published versio

Unique thermodynamic relationships for ΔfHo and ΔfGo for crystalline inorganic salts. I, Predicting the possible existence and synthesis of Na2SO2 and Na2SeO2

The concept that equates oxidation and pressure has been successfully utilized in explaining the structural changes observed in the M2S subnets of M2SOx (x = 3, 4) compounds (M = Na, K) when compared with the structures (room- and high-pressure phases) of their parent M2S 'alloy' [Martinez-Cruz et al. (1994), J. Solid State Chem. 110, 397-398; Vegas (2000), Crystallogr. Rev. 7, 189-286; Vegas et al. (2002), Solid State Sci. 4, 1077-1081]. These structural changes suggest that if M2SO2 would exist, its cation array might well have an anti-CaF2 structure. On the other hand, in an analysis of the existing thermodynamic data for M2S, M2SO3 and M2SO4 we have identified, and report, a series of unique linear relationships between the known Delta H-f(o) and Delta(f)G(o) values of the alkali metal (M) sulfide (x = 0) and their oxyanion salts M2SOx (x = 3 and 4), and the similarly between M2S2 disulfide (x = 0) and disulfur oxyanion salts M2S2Ox (x = 3, 4, 5, 6 and 7) and the number of O atoms in their anions x. These linear relationships appear to be unique to sulfur compounds and their inherent simplicity permits us to interpolate thermochemical data (Delta H-f(o)) for as yet unprepared compounds, M2SO (x = 1) and M2SO2 (x = 2). The excellent linearity indicates the reliability of the interpolated data. Making use of the volume-based thermodynamics, VBT [Jenkins et al. (1999), Inorg. Chem. 38, 3609-3620], the values of the absolute entropies were estimated and from them, the standard Delta S-f(o) values, and then the Delta(f)G(o) values of the salts. A tentative proposal is made for the synthesis of Na2SO2 which involves bubbling SO2 through a solution of sodium in liquid ammonia. For this attractive thermodynamic route, we estimate Delta G(o) to be approximately -500 kJ mol(-1). However, examination of the stability of Na2SO2 raises doubts and Na2SeO2 emerges as a more attractive target material. Its synthesis is likely to be easier and it is stable to disproportionation into Na2S and Na2SeO4. Like Na2SO2, this compound is predicted to have an anti-CaF2 Na2Se subnet