Entangled spin clusters: some special features

In this paper, we study three specific aspects of entanglement in small spin clusters. We first study the effect of inhomogeneous exchange coupling strength on the entanglement properties of the S=1/2 antiferromagnetic linear chain tetramer compound NaCuAsO_{4}. The entanglement gap temperature, T_{E}, is found to have a non-monotonic dependence on the value of $\alpha$, the exchange coupling inhomogeneity parameter. We next determine the variation of T_{E} as a function of S for a spin dimer, a trimer and a tetrahedron. The temperature T_{E} is found to increase as a function of S, but the scaled entanglement gap temperature t_{E} goes to zero as S becomes large. Lastly, we study a spin-1 dimer compound to illustrate the quantum complementarity relation. We show that in the experimentally realizable parameter region, magnetization and entanglement plateaus appear simultaneously at low temperatures as a function of the magnetic field. Also, the sharp increase in one quantity as a function of the magnetic field is accompanied by a sharp decrease in the other so that the quantum complementarity relation is not violated.Comment: 17 pages, 6 figures. Accepted in Phys. Rev.

A k-essence Model Of Inflation, Dark Matter and Dark Energy

We investigate the possibility for \textit{k}-essence dynamics to reproduce the primary features of inflation in the early universe, generate dark matter subsequently, and finally account for the presently observed acceleration. We first show that for a purely kinetic \textit{k}-essence model the late time energy density of the universe when expressed simply as a sum of a cosmological constant and a dark matter term leads to a static universe. We then study another \textit{k}-essence model in which the Lagrangian contains a potential for the scalar field as well as a non-canonical kinetic term. We show that such a model generates the basic features of inflation in the early universe, and also gives rise to dark matter and dark energy at appropriate subsequent stages. Observational constraints on the parameters of this model are obtained.Comment: 8 pages, Latex, minor changes to match with published versio

Assessing non-linear models for galaxy clustering III: Theoretical accuracy for Stage IV surveys

We provide in depth MCMC comparisons of two different models for the halo redshift space power spectrum, namely a variant of the commonly applied Taruya-Nishimichi-Saito (TNS) model and an effective field theory of large scale structure (EFTofLSS) inspired model. Using many simulation realisations and Stage IV survey-like specifications for the covariance matrix, we check each model's range of validity by testing for bias in the recovery of the fiducial growth rate of structure formation. The robustness of the determined range of validity is then tested by performing additional MCMC analyses using higher order multipoles, a larger survey volume and a more highly biased tracer catalogue. We find that under all tests, the TNS model's range of validity remains robust and is found to be much higher than previous estimates. The EFTofLSS model fails to capture the spectra for highly biased tracers as well as becoming biased at higher wavenumbers when considering a very large survey volume. Further, we find that the marginalised constraints on $f$ for all analyses are stronger when using the TNS model.Comment: 25 pages, 19 figures. Accepted version for publication in JCA