Delayed-choice gedanken experiments and their realizations

The wave-particle duality dates back to Einstein's explanation of the photoelectric effect through quanta of light and de Broglie's hypothesis of matter waves. Quantum mechanics uses an abstract description for the behavior of physical systems such as photons, electrons, or atoms. Whether quantum predictions for single systems in an interferometric experiment allow an intuitive understanding in terms of the particle or wave picture, depends on the specific configuration which is being used. In principle, this leaves open the possibility that quantum systems always either behave definitely as a particle or definitely as a wave in every experimental run by a priori adapting to the specific experimental situation. This is precisely what is tried to be excluded by delayed-choice experiments, in which the observer chooses to reveal the particle or wave character -- or even a continuous transformation between the two -- of a quantum system at a late stage of the experiment. We review the history of delayed-choice gedanken experiments, which can be traced back to the early days of quantum mechanics. Then we discuss their experimental realizations, in particular Wheeler's delayed choice in interferometric setups as well as delayed-choice quantum erasure and entanglement swapping. The latter is particularly interesting, because it elevates the wave-particle duality of a single quantum system to an entanglement-separability duality of multiple systems

On Quadratic g-Evaluations/Expectations and Related Analysis

In this paper we extend the notion of g-evaluation, in particular g-expectation, to the case where the generator g is allowed to have a quadratic growth. We show that some important properties of the g-expectations, including a representation theorem between the generator and the corresponding g-expectation, and consequently the reverse comparison theorem of quadratic BSDEs as well as the Jensen inequality, remain true in the quadratic case. Our main results also include a Doob-Meyer type decomposition, the optional sampling theorem, and the up-crossing inequality. The results of this paper are important in the further development of the general quadratic nonlinear expectations.Comment: 27 page

Globular Clusters in the Outer Halo of M31

In this paper, we present photometry of 53 globular clusters (GCs) in the M31 outer halo, including the {\sl GALEX} FUV and NUV, SDSS $ugriz$, 15 intermediate-band filters of BATC, and 2MASS $JHK_{\rm s}$ bands. By comparing the multicolour photometry with stellar population synthesis models, we determine the metallicities, ages, and masses for these GCs, aiming to probe the merging/accretion history of M31. We find no clear trend of metallicity and mass with the de-projected radius. The halo GCs with age younger than $\approx$ 8 Gyr are mostly located at the de-projected radii around 100 kpc, but this may be due to a selection effect. We also find that the halo GCs have consistent metallicities with their spatially-associated substructures, which provides further evidence of the physical association between them. Both the disk and halo GCs in M31 show a bimodal luminosity distribution. However, we should emphasize that there are more faint halo GCs which are not being seen in the disk. The bimodal luminosity function of the halo GCs may reflect different origin or evolution environment in their original hosts. The M31 halo GCs includes one intermediate metallicity group ($-1.5 <$ [Fe/H] $< -0.4$) and one metal-poor group ([Fe/H] $<-1.5$), while the disk GCs have one metal-rich group more. There are considerable differences between the halo GCs in M31 and the Milky Way (MW). The total number of M31 GCs is approximately three times more numerous than that of the MW, however, M31 has about six times the number of halo GCs in the MW. Compared to M31 halo GCs, the Galactic halo ones are mostly metal-poor. Both the numerous halo GCs and the higher-metallicity component are suggestive of an active merger history of M31.Comment: 14 pages, 16 figures, 6 tables. Accepted for publication in A&

Transition to turbulence in pulsating pipe flow

Fluid flows in nature and applications are frequently subject to periodic velocity modulations. Surprisingly, even for the generic case of flow through a straight pipe, there is little consensus regarding the influence of pulsation on the transition threshold to turbulence: while most studies predict a monotonically increasing threshold with pulsation frequency (i.e. Womersley number, $\alpha$), others observe a decreasing threshold for identical parameters and only observe an increasing threshold at low $\alpha$. In the present study we apply recent advances in the understanding of transition in steady shear flows to pulsating pipe flow. For moderate pulsation amplitudes we find that the first instability encountered is subcritical (i.e. requiring finite amplitude disturbances) and gives rise to localized patches of turbulence ("puffs") analogous to steady pipe flow. By monitoring the impact of pulsation on the lifetime of turbulence we map the onset of turbulence in parameter space. Transition in pulsatile flow can be separated into three regimes. At small Womersley numbers the dynamics are dominated by the decay turbulence suffers during the slower part of the cycle and hence transition is delayed significantly. As shown in this regime thresholds closely agree with estimates based on a quasi steady flow assumption only taking puff decay rates into account. The transition point predicted in the zero $\alpha$ limit equals to the critical point for steady pipe flow offset by the oscillation Reynolds number. In the high frequency limit puff lifetimes are identical to those in steady pipe flow and hence the transition threshold appears to be unaffected by flow pulsation. In the intermediate frequency regime the transition threshold sharply drops (with increasing $\alpha$) from the decay dominated (quasi steady) threshold to the steady pipe flow level