On the existence of effective potentials in time-dependent density functional theory

We investigate the existence and properties of effective potentials in time-dependent density functional theory. We outline conditions for a general solution of the corresponding Sturm-Liouville boundary value problems. We define the set of potentials and v-representable densities, give a proof of existence of the effective potentials under certain restrictions, and show the set of v-representable densities to be independent of the interaction.Comment: 13 page

An ultraviolet excess in the superluminous supernova Gaia16apd reveals a powerful central engine

Since the discovery of superluminous supernovae (SLSNe) in the last decade, it has been known that these events exhibit bluer spectral energy distributions than other supernova subtypes, with significant output in the ultraviolet. However, the event Gaia16apd seems to outshine even the other SLSNe at rest-frame wavelengths below $\sim 3000$ \AA. Yan et al (2016) have recently presented HST UV spectra and attributed the UV flux to low metallicity and hence reduced line blanketing. Here we present UV and optical light curves over a longer baseline in time, revealing a rapid decline at UV wavelengths despite a typical optical evolution. Combining the published UV spectra with our own optical data, we demonstrate that Gaia16apd has a much hotter continuum than virtually any SLSN at maximum light, but it cools rapidly thereafter and is indistinguishable from the others by $\sim 10$-15 days after peak. Comparing the equivalent widths of UV absorption lines with those of other events, we show that the excess UV continuum is a result of a more powerful central power source, rather than a lack of UV absorption relative to other SLSNe or an additional component from interaction with the surrounding medium. These findings strongly support the central-engine hypothesis for hydrogen-poor SLSNe. An explosion ejecting $M_{\rm ej} = 4 (0.2/\kappa)$ M$_\odot$, where $\kappa$ is the opacity in cm$^2$g$^{-1}$, and forming a magnetar with spin period $P=2$ ms, and $B=2\times10^{14}$ G (lower than other SLSNe with comparable rise-times) can consistently explain the light curve evolution and high temperature at peak. The host metallicity, $Z=0.18$ Z$_\odot$, is comparable to other SLSNe.Comment: Updated to match accepted version (ApJL

A Hydrogen-Poor Superluminous Supernova with Enhanced Iron-Group Absorption: A New Link Between SLSNe and Broad-Lined Type Ic SNe

We present optical observations of the Type I superluminous supernova (SLSN-I) SN2017dwh at $z\!\approx\!0.13$, which reached $M_{i}\!\approx\!-21$ mag at peak. Spectra taken a few days after peak show an unusual and strong absorption line centered near 3200\AA\ that we identify with Co II, suggesting a high fraction of synthesized $^{56}$Ni in the ejecta. By $\sim\!1$ month after peak, SN2017dwh became much redder than other SLSNe-I, instead strongly resembling broad-lined Type Ic supernovae (Ic-BL SNe) with clear suppression of the flux redward of $\sim\!5000$ \AA, providing further evidence for a large mass of Fe-group elements. Late-time upper limits indicate a $^{56}$Ni mass of $\lesssim 0.6$ M$_\odot$, leaving open the possibility that SN2017dwh produced a $^{56}$Ni mass comparable to SN1998bw ($\approx\!0.4$ M$_\odot$). Fitting the light curve with a combined magnetar and $^{56}$Ni model using ${\tt MOSFiT}$, we find that the light curve can easily accommodate such masses without affecting the inferred magnetar parameters. We also find that SN2017dwh occurred in the least-luminous detected host galaxy to date for a SLSN-I, with $M_{B} = -13.5$ mag and an implied metallicity of $Z\!\sim\!0.08$ $Z_\odot$. The spectral properties of SN2017dwh provide new evidence linking SLSNe-I with Type Ic-BL SNe, and in particular the high Fe-group abundance may be due to enhanced $^{56}$Ni production or mixing due to asphericity. Finally, we find that SN2017dwh represents the most extreme end of a correlation between continuum shape and Co II absorption strength in the near-peak spectra of SLSNe-I, indicating that Fe-group abundance likely accounts for some of the variation in their spectral shapes.Comment: 16 pages, 7 figures, Submitted to Ap

PS16dtm: A Tidal Disruption Event in a Narrow-line Seyfert 1 Galaxy

[Abridged] We present observations of PS16dtm, a luminous transient that occurred at the nucleus of a known Narrow-line Seyfert 1 galaxy hosting a 10$^6$ M$_\odot$ black hole. The transient was previously claimed to be a Type IIn SLSN due to its luminosity and hydrogen emission lines. The light curve shows that PS16dtm brightened by about two magnitudes in ~50 days relative to the archival host brightness and then exhibited a plateau phase for about 100 days followed by the onset of fading in the UV. During the plateau PS16dtm showed no color evolution, maintained a blackbody temperature of 1.7 x 10$^4$ K, and radiated at approximately $L_{Edd}$ of the SMBH. The spectra exhibit multi-component hydrogen emission lines and strong FeII emission, show little evolution with time, and closely resemble the spectra of NLS1s while being distinct from those of Type IIn SNe. Moreover, PS16dtm is undetected in the X-rays to a limit an order of magnitude below an archival X-ray detection of its host galaxy. These observations strongly link PS16dtm to activity associated with the SMBH and are difficult to reconcile with a SN origin or any known form of AGN variability, and therefore we argue that it is a TDE in which the accretion of the stellar debris powers the rise in the continuum and excitation of the pre-existing broad line region, while providing material that obscures the X-ray emitting region of the pre-existing AGN accretion disk. A detailed TDE model fit to the light curve indicates that PS16dtm will remain bright for several years; we further predict that the X-ray emission will reappear on a similar timescale as the accretion rate declines. Finally, we place PS16dtm in the context of other TDEs and find that TDEs in AGN galaxies are an order of magnitude more efficient and reach Eddington luminosities, likely due to interaction of the stellar debris with the pre-existing accretion disk.Comment: 19 pages, 17 figures, Submitted to Ap

N-representability and stationarity in time-dependent density functional theory

To construct an N-representable time-dependent density-functional theory, a generalization to the time domain of the Levy-Lieb (LL) constrained search algorithm is required. That the action is only stationary in the Dirac-Frenkel variational principle eliminates the possibility of basing the search on the action itself. Instead, we use the norm of the partial functional derivative of the action in the Hilbert space of the wave functions in place of the energy of the LL search. The electron densities entering the formalism are $N$-representable, and the resulting universal action functional has a unique stationary point in the density at that corresponding to the solution of the Schr\"{o}dinger equation. The original Runge-Gross (RG) formulation is subsumed within the new formalism. Concerns in the literature about the meaning of the functional derivatives and the internal consistency of the RG formulation are allayed by clarifying the nature of the functional derivatives entering the formalism.Comment: 9 pages, 0 figures, Phys. Rev. A accepted. Introduction was expanded, subsections reorganized, appendix and new references adde

Negative Differential Resistance, Memory and Reconfigurable Logic Functions based on Monolayer Devices derived from Gold Nanoparticles Functionalized with Electro-polymerizable Thiophene-EDOT Units

We report on hybrid memristive devices made of a network of gold nanoparticles (10 nm diameter) functionalized by tailored 3,4(ethylenedioxy)thiophene (TEDOT) molecules, deposited between two planar electrodes with nanometer and micrometer gaps (100 nm to 10 um apart), and electropolymerized in situ to form a monolayer film of conjugated polymer with embedded gold nanoparticles (AuNPs). Electrical properties of these films exhibit two interesting behaviors: (i) a NDR (negative differential resistance) behavior with a peak/valley ratio up to 17, and (ii) a memory behavior with an ON/OFF current ratio of about 1E3 to 1E4. A careful study of the switching dynamics and programming voltage window is conducted demonstrating a non-volatile memory. The data retention of the ON and OFF states is stable (tested up to 24h), well controlled by the voltage and preserved when repeating the switching cycles (800 in this study). We demonstrate reconfigurable Boolean functions in multiterminal connected NP molecule devices.Comment: Full manuscript, figures and supporting information, J. Phys. Chem. C, on line, asap (2017

Spitzer Space Telescope Infrared Observations of the Binary Neutron Star Merger GW170817

We present Spitzer Space Telescope 3.6 and 4.5 micron observations of the binary neutron star merger GW170817 at 43, 74, and 264 days post-merger. Using the final observation as a template, we uncover a source at the position of GW170817 at 4.5 micron with a brightness of 22.9+/-0.3 AB mag at 43 days and 23.8+/-0.3 AB mag at 74 days (the uncertainty is dominated by systematics from the image subtraction); no obvious source is detected at 3.6 micron to a 3-sigma limit of >23.3 AB mag in both epochs. The measured brightness is dimmer by a factor of about 2-3 times compared to our previously published kilonova model, which is based on UV, optical, and near-IR data at <30 days. However, the observed fading rate and color (m_{3.6}-m_{4.5}> 0 AB mag) are consistent with our model. We suggest that the discrepancy is likely due to a transition to the nebular phase, or a reduced thermalization efficiency at such late time. Using the Spitzer data as a guide, we briefly discuss the prospects of observing future binary neutron star mergers with Spitzer (in LIGO/Virgo Observing Run 3) and the James Webb Space Telescope (in LIGO/Virgo Observing Run 4 and beyond).Comment: 6 pages, 2 figures, submitted to ApJ

Completeness in Photometric and Spectroscopic Searches for Clusters

We investigate, using simulated galaxy catalogues, the completeness of searches for massive clusters of galaxies in redshift surveys or imaging surveys with photometric redshift estimates, i.e. what fraction of clusters (M>10^14/h Msun) are found in such surveys. We demonstrate that the matched filter method provides an efficient and reliable means of identifying massive clusters even when the redshift estimates are crude. In true redshift surveys the method works extremely well. We demonstrate that it is possible to construct catalogues with high completeness, low contamination and both varying little with redshift.Comment: ApJ in press, 15 pages, 10 figure

Cellular automata and Lyapunov exponents

In this article we give a new definition of some analog of Lyapunov exponents for cellular automata . Then for a shift ergodic and cellular automaton invariant probability measure we establish an inequality between the entropy of the automaton, the entropy of the shift and the Lyapunov exponent