Generalized Entropies

We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation as a semidefinite program, a type of convex optimization. After establishing a few basic properties, we prove upper and lower bounds in terms of the smooth entropies, a family of entropy measures that is used to characterize a wide range of operational quantities. From the formulation as a semidefinite program, we also prove a result on decomposition of hypothesis tests, which leads to a chain rule for the entropy.Comment: 21 page

Metastable Feshbach Molecules in High Rotational States

We experimentally demonstrate Cs2 Feshbach molecules well above the dissociation threshold, which are stable against spontaneous decay on the timescale of one second. An optically trapped sample of ultracold dimers is prepared in an l-wave state and magnetically tuned into a region with negative binding energy. The metastable character of these molecules arises from the large centrifugal barrier in combination with negligible coupling to states with low rotational angular momentum. A sharp onset of dissociation with increasing magnetic field is mediated by a crossing with a g-wave dimer state and facilitates dissociation on demand with a well defined energy.Comment: 4 pages, 5 figure

Elemental Abundances in NGC 3516

We present RGS data from an XMM-Newton observation of the Seyfert 1 galaxy NGC 3516, taken while the continuum source was in an extreme low state. The spectrum shows numerous emission lines including the H-like lines of C, N and O and the He-like lines of N, O and Ne. These data show that the N lines are far stronger than would be expected from gas of solar abundances. Based on our photoionization models, we find that N is overabundant compared to C, O and Ne by at least a factor of 2.5. We suggest this is the result of secondary production of N in intermediate mass stars, and indicative of the history of star formation in NGC 3516.Comment: 19 pages, 3 color figures. ApJ in pres

Vortex nucleation in rotating BEC: the role of the boundary condition for the order parameter

We study the process of vortex nucleation in rotating two-dimensional BEC confined in a harmonic trap. We show that, within the Gross-Pitaevskii theory with the boundary condition of vanishing of the order parameter at infinity, topological defects nucleation occurs via the creation of vortex-antivortex pairs far from the cloud center, where the modulus of the order parameter is small. Then, vortices move towards the center of the cloud and antivortices move in the opposite direction but never disappear. We also discuss the role of surface modes in this process.Comment: 6 pages, 2 figure

Physical Conditions in the Narrow-Line Region of Markarian 3. II. Photoionization Modeling Results

We have examined the physical conditions in the narrow-line region (NLR) of the Seyfert 2 galaxy Markarian 3, using long-slit spectra obtained with the Hubble Space Telescope/Space Telescope Imaging Spectrograph and photoionization models. We find three components of photoionized gas in the NLR. Two of these components, characterized by emission lines such as [NeV] 3426 and [OIII] 5007, lie within the envelope of the bi-conical region described in our previous kinematic study. A component of lower ionization gas, in which lines such as [OII] 3727 arise, is found to lie outside the bi-cone. Each of these components is irradiated by a power-law continuum which is attenuated by intervening gas, presumably closer to the central source. The radiation incident upon the low ionization gas, external to the bi-cone, is much more heavily absorbed. These absorbers are similar to the intrinsic UV and X-ray absorbers detected in many Seyfert 1 galaxies, which suggests that the collimation of the ionizing radiation occurs in a circumnuclear wind, rather than a thick, molecular torus. We estimate the mass for the observed NLR emitting gas to be 2 million solar-masses. It is likely that Markarian 3 acquired this gas through an on-going interaction with the spiral galaxy UGC 3422.Comment: 47 pages, 7 figures; accepted for publication in Ap

Theoretical studies of photoexcitation and ionization in H_2O

Theoretical studies are reported of the complete dipole excitation and ionization spectrum in H_2O employing Franck–Condon and static‐exchange approximations. Large Cartesian Gaussian basis sets are used to represent the required discrete and continuum electronic eigenfunctions at the ground‐state equilibrium geometry, and previously devised moment‐theory techniques are employed in constructing the continuum oscillator‐strength densities from the calculated spectra. Detailed comparisons are made of the calculated excitation and ionization profiles with recent experimental photoabsorption studies and corresponding spectral assignments, electron impact–excitation cross sections, and dipole (e, 2e)/(e, e+ion) and synchrotron‐radiation studies of partial‐channel photoionization cross sections. The various calculated excitation series in the outer‐valence (1b(^−1)_1, 3a(^−1)_1, 1b(^−1)_2) region are found to include contributions from valence‐like 2b_2 (σ*) and 4a_1(γ*) virtual orbitals, as well as appropriate nsa_1, npa_1, nda_1, npb_1, npb_2, ndb_1, ndb_2, and nda_2 Rydberg states. Transition energies and intensities in the ∼7 to 19 eV interval obtained from the present studies are seen to be in excellent agreement with the measured photoabsorption cross section, and to provide a basis for detailed spectral assignments. The calculated (1b(^−1)_1)X(^ 2)B_1, (3a_1(^−1))^2A_1, and (1b_2(^−1))(^2)B_2 partial‐channel cross sections are found to be largely atomic‐like and dominated by 2p→kd components, although the 2b_2(σ*) orbital gives rise to resonance‐like contributions just above threshold in the 3a_1→kb_2 and 1b_2→kb_2 channels. It is suggested that the latter transition couples with the underlying 1b_1→kb_1 channel, accounting for a prominent feature in the recent high‐resolution synchrotron‐radiation measurements. When this feature is taken into account, the calculations of the three outer‐valence channels are in excellent accord with recent synchrotron‐radiation and dipole (e, 2e) photoionization cross‐sectional measurements. The calculated inner‐valence (2a_1(^−1)) cross section is also in excellent agreement with corresponding measured values, although proper account must be taken of the appropriate final‐state configuration‐mixing effects that give rise to a modest failure of the Koopmans approximation, and to the observed broad PES band, in this case. Finally, the origins of the various spectral features present in the measured 1a_1 oxygen K‐edge electron energy‐loss profile in H_2O are seen to be clarified fully by the present calculations