Time-dependent exchange-correlation hole and potential of the electron gas

The exchange-correlation hole and potential of the homogeneous electron gas have been investigated within the random-phase approximation, employing the plasmon-pole approximation for the linear density response function. The angular dependence as well as the time dependence of the exchange-correlation hole are illustrated for a Wigner-Seitz radius $r_s=4$ (atomic unit). It is found that there is a substantial cancellation between exchange and correlation potentials in space and time, analogous to the cancellation of exchange and correlation self-energies. Analysis of the sum rule explains why it is more advantageous to use a non-interacting Green function than a renormalized one when calculating the response function within the random-phase approximation and consequently the self-energy within the well-established $GW$ approximation. The present study provides a starting point for more accurate and comprehensive calculations of the exchange-correlation hole and potential of the electron gas with the aim of constructing a model based on the local density approximation as in density functional theory.Comment: 19 pages, 15 figure

Calculations of Hubbard U from first-principles

The Hubbard \emph{U} of the \emph{3d} transition metal series as well as SrVO$_{3}$, YTiO$_{3}$, Ce and Gd has been estimated using a recently proposed scheme based on the random-phase approximation. The values obtained are generally in good accord with the values often used in model calculations but for some cases the estimated values are somewhat smaller than those used in the literature. We have also calculated the frequency-dependent \emph{U} for some of the materials. The strong frequency dependence of \emph{U} in some of the cases considered in this paper suggests that the static value of \emph{U} may not be the most appropriate one to use in model calculations. We have also made comparison with the constrained LDA method and found some discrepancies in a number of cases. We emphasize that our scheme and the constrained LDA method theoretically ought to give similar results and the discrepancies may be attributed to technical difficulties in performing calculations based on currently implemented constrained LDA schemes.Comment: 24 pages, 13 figures; Submitted to Phys. Rev.

GW approximation with self-screening correction

The \emph{GW} approximation takes into account electrostatic self-interaction contained in the Hartree potential through the exchange potential. However, it has been known for a long time that the approximation contains self-screening error as evident in the case of the hydrogen atom. When applied to the hydrogen atom, the \emph{GW} approximation does not yield the exact result for the electron removal spectra because of the presence of self-screening: the hole left behind is erroneously screened by the only electron in the system which is no longer present. We present a scheme to take into account self-screening and show that the removal of self-screening is equivalent to including exchange diagrams, as far as self-screening is concerned. The scheme is tested on a model hydrogen dimer and it is shown that the scheme yields the exact result to second order in $(U_{0}-U_{1})/2t$ where $U_{0}$ and $U_{1}$ are respectively the onsite and offsite Hubbard interaction parameters and $t$ the hopping parameter.Comment: 9 pages, 2 figures; Submitted to Phys. Rev.

The Distribution of Redshifts in New Samples of Quasi-stellar Objects

Two new samples of QSOs have been constructed from recent surveys to test the hypothesis that the redshift distribution of bright QSOs is periodic in $\log(1+z)$. The first of these comprises 57 different redshifts among all known close pairs or multiple QSOs, with image separations $\leq$ 10\arcsec, and the second consists of 39 QSOs selected through their X-ray emission and their proximity to bright comparatively nearby active galaxies. The redshift distributions of the samples are found to exhibit distinct peaks with a periodic separation of $\sim 0.089$ in $\log(1+z)$ identical to that claimed in earlier samples but now extended out to higher redshift peaks $z = 2.63, 3.45$ and 4.47, predicted by the formula but never seen before. The periodicity is also seen in a third sample, the 78 QSOs of the 3C and 3CR catalogues. It is present in these three datasets at an overall significance level $10^{-5}$ - $10^{-6}$, and appears not to be explicable by spectroscopic or similar selection effects. Possible interpretations are briefly discussed.Comment: submitted for publication in the Astronomical Journal, 15 figure

Quantum secret sharing between m-party and n-party with six states

We propose a quantum secret sharing scheme between $m$-party and $n$-party using three conjugate bases, i.e. six states. A sequence of single photons, each of which is prepared in one of the six states, is used directly to encode classical information in the quantum secret sharing process. In this scheme, each of all $m$ members in group 1 choose randomly their own secret key individually and independently, and then directly encode their respective secret information on the states of single photons via unitary operations, then the last one (the $m$th member of group 1) sends $1/n$ of the resulting qubits to each of group 2. By measuring their respective qubits, all members in group 2 share the secret information shared by all members in group 1. The secret message shared by group 1 and group 2 in such a way that neither subset of each group nor the union of a subset of group 1 and a subset of group 2 can extract the secret message, but each whole group (all the members of each group) can. The scheme is asymptotically 100% in efficiency. It makes the Trojan horse attack with a multi-photon signal, the fake-signal attack with EPR pairs, the attack with single photons, and the attack with invisible photons to be nullification. We show that it is secure and has an advantage over the one based on two conjugate bases. We also give the upper bounds of the average success probabilities for dishonest agent eavesdropping encryption using the fake-signal attack with any two-particle entangled states. This protocol is feasible with present-day technique.Comment: 7 page

Energy input is primary controller of methane bubbling in subarctic lakes

Emission of methane (CH4) from surface waters is often dominated by ebullition (bubbling), a transport mode with high‐spatiotemporal variability. Based on new and extensive CH4 ebullition data, we demonstrate striking correlations (r2 between 0.92 and 0.997) when comparing seasonal bubble CH4 flux from three shallow subarctic lakes to four readily measurable proxies of incoming energy flux and daily flux magnitudes to surface sediment temperature (r2 between 0.86 and 0.94). Our results after continuous multiyear sampling suggest that CH4 ebullition is a predictable process, and that heat flux into the lakes is the dominant driver of gas production and release. Future changes in the energy received by lakes and ponds due to shorter ice‐covered seasons will predictably alter the ebullitive CH4 flux from freshwater systems across northern landscapes. This finding is critical for our understanding of the dynamics of radiatively important trace gas sources and associated climate feedback