Bell-CHSH function approach to quantum phase transitions in matrix product systems

Recently, nonlocality and Bell inequalities have been used to investigate quantum phase transitions (QPTs) in low-dimensional quantum systems. Nonlocality can be detected by the Bell-CHSH function (BCF). In this work, we extend the study of BCF to the QPTs in matrix product systems (MPSs). In this kind of QPTs, the ground-state energy keeps analytical in the vicinity of the QPT points, and is usually called the MPS-QPTs. For several typical models, our results show that BCF can signal the MPS-QPTs very well. In addition, we find BCF can capture signal of QPTs in unentangled states and classical states, for which other measures of quantum correlation (quantum entanglement and quantum discord) fail. Furthermore, we find that in these MPSs, there exists some kind of quantum correlation which cannot be characterized by entanglement, or by nonlocality.Comment: 12 pages, 4 figure

Blow up solutions to a viscoelastic fluid system and a coupled Navier-Stokes/Phase-Field system in R^2

We find explicit solutions to both the Oldroyd-B model with infinite Weissenberg number and the coupled Navier-Stokes/Phase-Field system. The solutions blow up in finite time.Comment: 5 page

Empirical metallicity-dependent calibrations of effective temperature against colours for dwarfs and giants based on interferometric data

We present empirical metallicity-dependent calibrations of effective temperature against colours for dwarfs of luminosity classes IV and V and for giants of luminosity classes II and III, based on a collection from the literature of about two hundred nearby stars with direct effective temperature measurements of better than 2.5 per cent. The calibrations are valid for an effective temperature range 3,100 - 10,000 K for dwarfs of spectral types M5 to A0 and 3,100 - 5,700 K for giants of spectral types K5 to G5. A total of twenty-one colours for dwarfs and eighteen colours for giants of bands of four photometric systems, i.e. the Johnson ($UBVR_{\rm J}I_{\rm J}JHK$), the Cousins ($R_{\rm C}I_{\rm C}$), the Sloan Digital Sky Survey (SDSS, $gr$) and the Two Micron All Sky Survey (2MASS, $JHK_{\rm s}$), have been calibrated. Restricted by the metallicity range of the current sample, the calibrations are mainly applicable for disk stars ([Fe/H]$\,\gtrsim\,-1.0$). The normalized percentage residuals of the calibrations are typically 2.0 and 1.5 per cent for dwarfs and giants, respectively. Some systematic discrepancies at various levels are found between the current scales and those available in the literature (e.g. those based on the infrared flux method IRFM or spectroscopy). Based on the current calibrations, we have re-determined the colours of the Sun. We have also investigated the systematic errors in effective temperatures yielded by the current on-going large scale low- to intermediate-resolution stellar spectroscopic surveys. We show that the calibration of colour ($g-K_{\rm s}$) presented in the current work provides an invaluable tool for the estimation of stellar effective temperature for those on-going or upcoming surveys.Comment: 28 pages, 19 figures, 8 tables, accepted for publication in MNRA