Weak measurement is a new way to manipulate and control quantum systems. Different from projection measurement, weak measurement only makes a small change in status. Applying weak measurement to quantum discord, Singh and Pati proposed a new kind of quantum correlations called super quantum discord (SQD) [Annals of Physics textbf{343},141(2014)]. Unfortunately, the super quantum discord is also difficult to calculate. There are only few explicit formulae about SQD. We derive an analytical formulae of SQD for general X-type two-qubit states, which surpass the conclusion for Werner states and Bell diagonal states. Furthermore, our results reveal more knowledge about the new insight of quantum correlation and give a new way to compare SQD with normal quantum discord. Finally, we analyze its dynamics under nondissipative channels.
X-ray observations of circumgalactic coronae provide a valuable means by which to test galaxy formation theories. Two primary mechanisms are thought to be responsible for the establishment of such coronae: accretion of intergalactic gas (IGM) and/or galactic feedback. In this paper, we first compare our Chandra sample of galactic coronae of 53 nearby highly-inclined disc galaxies to an analytical model considering only the accretion of IGM. We confirm the existing conclusion that this pure accretion model substantially over-predicts the coronal emission. We then select 30 field galaxies from our original sample, and correct their coronal luminosities to uniformly compare them to deep X-ray measurements of several massive disc galaxies from the literature, as well as to a comparable sample of simulated galaxies drawn from the Galaxies-Intergalactic Medium Interaction Calculation (GIMIC). These simulations explicitly model both accretion and SNe feedback and yield galaxies exhibit X-ray properties in broad agreement with our observational sample. However, notable and potentially instructive discrepancies exist between the slope and scatter of the Lx-M200 and Lx-SFR relations, highlighting some known shortcomings of GIMIC, e.g., the absence of AGN feedback, and possibly the adoption of constant stellar feedback parameters. The simulated galaxies exhibit a tight Lx-M200 correlation with little scatter. Having inferred M200 for our observational sample via the Tully-Fisher relation, we find a weaker and more scattered correlation. In the simulated and observed samples alike, massive non-starburst galaxies above a typical transition mass of M*~2e11Msun or M200~1e13Msun tend to have higher Lx/M* and Lx/M200 than low-mass counterparts, indicating that the accretion of IGM plays an increasingly important role in establishing the observable hot circumgalactic medium with increasing galaxy mass.
X-ray-emitting coronae of nearby galaxies are expected to be produced either by accretion from the intergalactic medium and/or by various galactic feedback. We herein present a systematical analysis of the Chandra observations of 53 nearby edge-on disk galaxies over a range of 3 orders of magnitude in SFR. Various coronal properties, such as the luminosity, vertical/horizontal extent, and other inferred parameters, are characterized for all the sample galaxies. For galaxies with high enough counting statistics, we also examine the thermal and chemical states of the coronal gas. Here we concentrate on the coronal luminosity (Lx), estimated in 0.5-2keV and within 5 times the diffuse X-ray vertical scale height. We find Lx strongly correlates with the SFR for the whole sample. But the inclusion of Ia SNe in the total energy input (E_SN) gives an even tighter correlation, which may be characterized with a linear relation, Lx=0.5%E_SN, and with a dispersion of 0.45dex. Moreover, the coronal radiation efficiency (eta=Lx/E_SN) shows little correlation with either the stellar mass or the gravitational mass (M_TF, inferred from the rotation velocity), but is significantly correlated with their ratio (M_TF/M_*), which may be expressed as a linear scaling relation eta=0.35%M_TF/M_* for the entire ranges of galaxy parameters. This joint scaling relation suggests that the coronae are self-regulated by the combination of gravitational confinement and feedback. But SN appears to be the primary heating source, because about half of our galaxies are not massive enough to allow for the accretion to play a major role. The commonly low eta further suggests that the bulk of the SN energy likely flows out into large-scale galactic halos for essentially all the galaxies. Such ubiquitous outflows could have profound implications for understanding the ecosystem, hence the evolution of galaxies.
Let $M_1$ and $M_2$ be orientable irreducible 3--manifolds with connected boundary and suppose $partial M_1congpartial M_2$. Let $M$ be a closed 3--manifold obtained by gluing $M_1$ to $M_2$ along the boundary. We show that if the gluing homeomorphism is sufficiently complicated, then $M$ is not homeomorphic to $S^3$ and all small-genus Heegaard splittings of $M$ are standard in a certain sense. In particular, $g(M)=g(M_1)+g(M_2)-g(partial M_i)$, where $g(M)$ denotes the Heegaard genus of $M$. This theorem is also true for certain manifolds with multiple boundary components.
In view of the recent experimental facts in the iron-pnictides, we make a proposal that the itinerant electrons and local moments are simultaneously present in such multiband materials. We study a minimal model composed of coupled itinerant electrons and local moments to illustrate how a consistent explanation of the experimental measurements can be obtained in the leading order approximation. In this mean-field approach, the spin-density-wave (SDW) order and superconducting pairing of the itinerant electrons are not directly driven by the Fermi surface nesting, but are mainly induced by their coupling to the local moments. The presence of the local moments as independent degrees of freedom naturally provides strong pairing strength for superconductivity and also explains the normal-state linear-temperature magnetic susceptibility above the SDW transition temperature. We show that this simple model is supported by various anomalous magnetic properties and isotope effect which are in quantitative agreement with experiments.
A bulk left-handed metamaterial with fishnet structure is investigated to show the optical loss compensation via surface plasmon amplification, with the assistance of a Gaussian gain in PbS quantum dots. The optical resonance enhancement around 200 THz is confirmed by the retrieval method. By exploring the dependence of propagation loss on the gain coefficient and metamaterial thickness, we verify numerically that the left-handed response can endure a large propagation thickness with ultralow and stable loss under a certain gain coefficient.
We demonstrate that left-handed resonance transmission from metallic metamaterial, composed of periodically arranged double rings, can be extended to visible spectrum by introducing an active medium layer as the substrate. The severe ohmic loss inside metals at optical frequencies is compensated by stimulated emission of radiation in this active system. Due to the resonance amplification mechanism of recently proposed lasing spaser, the left-handed transmission band can be restored up to 610 nm wavelength, in dependence on the gain coefficient of the active layer. Additionally, threshold gains for different scaling levels of the double-ring unit are investigated to evaluate the gain requirement of left-handed transmission restoration at different frequency ranges.
We show that given a trivalent graph in $S^3$, either the graph complement contains an essential almost meridional planar surface or thin position for the graph is also bridge position. This can be viewed as an extension of a theorem of Thompson to graphs. It follows that any graph complement always contains a useful planar surface.
