Symmetry restoration and quantumness reestablishment

A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a powerful tool, but unfortunately often violate the symmetry of the Hamiltonian. The conventional BCS theory, as an excellent mean field approach, violates the particle number conservation and completely erases quantumness characterized by concurrence and quantum discord between different modes. We restore the symmetry by using the projected BCS theory and the exact numerical solution and find that the lost quantumness is synchronously reestablished. We show that while entanglement remains unchanged with the particle numbers, quantum discord behaves as an extensive quantity with respect to the system size. Surprisingly, discord is hardly dependent on the interaction strengths. The new feature of discord offers promising applications in modern quantum technologies.Comment: 17 pages and 3 figure

The puzzle of anomalously large isospin violations in η(1405/1475)→3π\eta(1405/1475)\to 3\pi

The BES-III Collaboration recently report the observation of anomalously large isospin violations in $J/\psi\to \gamma\eta(1405/1475) \to \gamma \pi^0 f_0(980)\to \gamma +3\pi$, where the $f_0(980)$ in the $\pi\pi$ invariant mass spectrum appears to be much narrower ($\sim$ 10 MeV) than the peak width ($\sim$50 MeV) measured in other processes. We show that a mechanism, named as triangle singularity (TS), can produce a narrow enhancement between the charged and neutral $K\bar{K}$ thresholds, i.e., $2m_{K^\pm}\sim 2m_{K^0}$. It can also lead to different invariant mass spectra for $\eta(1405/1475)\to a_0(980)\pi$ and $K\bar{K}^*+c.c.$, which can possibly explain the long-standing puzzle about the need for two close states $\eta(1405)$ and $\eta(1475)$ in $\eta\pi\pi$ and $K\bar{K}\pi$, respectively. The TS could be a key to our understanding of the nature of $\eta(1405/1475)$ and advance our knowledge about the mixing between $a_0(980)$ and $f_0(980)$.Comment: 4 pages and 7 eps figures; Journal-matched versio

The Age-Redshift Relationship of Old Passive Galaxies

We use 32 age measurements of passively evolving galaxies as a function of redshift to test and compare the standard model ($\Lambda$CDM) with the $R_{\rm h}=ct$ Universe. We show that the latter fits the data with a reduced $\chi^2_{\rm dof}=0.435$ for a Hubble constant $H_{0}= 67.2_{-4.0}^{+4.5}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$. By comparison, the optimal flat $\Lambda$CDM model, with two free parameters (including $\Omega_{\rm m}=0.12_{-0.11}^{+0.54}$ and $H_{0}=94.3_{-35.8}^{+32.7}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$), fits the age-\emph{z} data with a reduced $\chi^2_{\rm dof}=0.428$. Based solely on their $\chi^2_{\rm dof}$ values, both models appear to account for the data very well, though the optimized $\Lambda$CDM parameters are only marginally consistent with those of the concordance model ($\Omega_{\rm m}=0.27$ and $H_{0}= 70$ km $\rm s^{-1}$ $\rm Mpc^{-1}$). Fitting the age-$z$ data with the latter results in a reduced $\chi^2_{\rm dof}=0.523$. However, because of the different number of free parameters in these models, selection tools, such as the Akaike, Kullback and Bayes Information Criteria, favour $R_{\rm h}=ct$ over $\Lambda$CDM with a likelihood of $\sim 66.5\%-80.5\%$ versus $\sim 19.5\%-33.5\%$. These results are suggestive, though not yet compelling, given the current limited galaxy age-$z$ sample. We carry out Monte Carlo simulations based on these current age measurements to estimate how large the sample would have to be in order to rule out either model at a $\sim 99.7\%$ confidence level. We find that if the real cosmology is $\Lambda$CDM, a sample of $\sim 45$ galaxy ages would be sufficient to rule out $R_{\rm h}=ct$ at this level of accuracy, while $\sim 350$ galaxy ages would be required to rule out $\Lambda$CDM if the real Universe were instead $R_{\rm h}=ct$.Comment: 36 pages, 13 figures, 1 table; accepted for publication in The Astronomical Journal. arXiv admin note: text overlap with arXiv:1405.238