Simulation and theory of vibrational phase relaxation in the critical and supercritical nitrogen: Origin of observed anomalies

We present results of extensive computer simulations and theoretical analysis of vibrational phase relaxation of a nitrogen molecule along the critical isochore and also along the gas-liquid coexistence. The simulation includes all the different contributions [atom-atom (AA), vibration-rotation (VR) and resonant transfer] and their cross-correlations. Following Everitt and Skinner, we have included the vibrational coordinate ($q$) dependence of the interatomic potential. It is found that the latter makes an important contribution. The principal important results are: (a) a crossover from a Lorentzian-type to a Gaussian line shape is observed as the critical point is approached along the isochore (from above), (b) the root mean square frequency fluctuation shows nonmonotonic dependence on the temperature along critical isochore, (c) along the coexistence line and the critical isochore the temperature dependent linewidth shows a divergence-like $\lambda$-shape behavior, and (d) the value of the critical exponents along the coexistence and along the isochore are obtained by fitting. The origin of the anomalous temperature dependence of linewidth can be traced to simultaneous occurrence of several factors, (i) the enhancement of negative cross-correlations between AA and VR contributions and (ii) the large density fluctuations as the critical point (CP) is approached. The former makes the decay faster so that local density fluctuations are probed on a femtosecond time scale. A mode coupling theory (MCT) analysis shows the slow decay of the enhanced density fluctuations near critical point. The MCT analysis demonstrates that the large enhancement of VR coupling near CP arises from the non-Gaussian behavior of density fluctuation and this enters through a nonzero value of the triplet direct correlation function.Comment: 35 pages, 15 figures, revtex4 (preprint form

On some strong Poincaré inequalities on Riemannian models and their improvements

We prove second and fourth order improved Poincaré type inequalities on the hyperbolic space involving Hardy-type remainder terms. Since theirs l.h.s. only involve the radial part of the gradient or of the laplacian, they can be seen as stronger versions of the classical Poincaré inequality. We show that such inequalities hold true on model manifolds as well, under suitable curvature assumptions and sharpness of some constants is also discussed

Phase transition and scaling behavior of topological charged black holes in Horava-Lifshitz gravity

Gravity can be thought as an emergent phenomenon and it has a nice "thermodynamic" structure. In this context, it is then possible to study the thermodynamics without knowing the details of the underlying microscopic degrees of freedom. Here, based on the ordinary thermodynamics, we investigate the phase transition of the static, spherically symmetric charged black hole solution with arbitrary scalar curvature $2k$ in Ho\v{r}ava-Lifshitz gravity at the Lifshitz point $z=3$. The analysis is done using the canonical ensemble frame work; i.e. the charge is kept fixed. We find (a) for both $k=0$ and $k=1$, there is no phase transition, (b) while $k=-1$ case exhibits the second order phase transition within the {\it physical region} of the black hole. The critical point of second order phase transition is obtained by the divergence of the heat capacity at constant charge. Near the critical point, we find the various critical exponents. It is also observed that they satisfy the usual thermodynamic scaling laws.Comment: Minor corrections, refs. added, to appear in Class. Quant. Grav. arXiv admin note: text overlap with arXiv:1111.0973 by other author

The Eastwood-Singer gauge in Einstein spaces

Electrodynamics in curved spacetime can be studied in the Eastwood--Singer gauge, which has the advantage of respecting the invariance under conformal rescalings of the Maxwell equations. Such a construction is here studied in Einstein spaces, for which the Ricci tensor is proportional to the metric. The classical field equations for the potential are then equivalent to first solving a scalar wave equation with cosmological constant, and then solving a vector wave equation where the inhomogeneous term is obtained from the gradient of the solution of the scalar wave equation. The Eastwood--Singer condition leads to a field equation on the potential which is preserved under gauge transformations provided that the scalar function therein obeys a fourth-order equation where the highest-order term is the wave operator composed with itself. The second-order scalar equation is here solved in de Sitter spacetime, and also the fourth-order equation in a particular case, and these solutions are found to admit an exponential decay at large time provided that square-integrability for positive time is required. Last, the vector wave equation in the Eastwood-Singer gauge is solved explicitly when the potential is taken to depend only on the time variable.Comment: 13 pages. Section 6, with new original calculations, has been added, and the presentation has been improve

Atomic hydrogen, star formation and feedback in the lowest mass Blue Compact Dwarf galaxies

We present the results from a search for HI emission from a sample of newly discovered dwarf galaxies in the M81 group. HI is detected in three galaxies, all of which are classified as BCDs. The HI masses of these galaxies are ~ 10^6 M_sun, making these some of the lowest mass BCDs known. For these three galaxies FUV images (from GALEX) and H-alpha images (from the Russian 6m BTA telescope) are available.The H-alpha emission is very faint, and, in principle could be produced by a single O star. Further, in all cases we find offsets between the peak of the FUV emission and that of the H-alpha emission. Offsets between the most recent sites of star formation (i.e. those traced by H-alpha) and the older sites (i.e. those traced by FUV) would be natural if the star formation is stochastic. In spite of the expectation that the effects of mechanical feedback from star formation would be most directly seen in the smallest galaxies with low gravitational potentials, we only see tentative evidence of outflowing HI gas associated with the star forming region in one of the galaxies.Comment: 9 pages, 5 figures, 5 tables. Accepted for publication in MNRAS. The definitive version is available at www.blackwell-synergy.co

Small Bites: Star formation recipes in extreme dwarfs

We study the relationship between the gas column density (Sigma_HI) and the star formation rate surface density (Sigma_SFR) for a sample of extremely small (M_B ~ -13, Delta V_50 ~ 30 km/s) dwarf irregular galaxies. We find a clear stochasticity in the relation between the gas column density and star formation. All gas with Sigma_HI >~ 10 M_sun/pc^2 has some ongoing star formation, but the fraction of gas with ongoing star formation decreases as the gas column density decreases, and falls to about 50% at Sigma_HI ~ 3 M_sun/pc^2. Further, even for the most dense gas, the star formation efficiency is at least a factor of ~ 2 smaller than typical of star forming regions in spirals. We also find that the ratio of H-alpha emission to FUV emission increases with increasing gas column density. This is unlikely to be due to increasing dust extinction because the required dust to gas ratios are too high. We suggest instead that this correlation arises because massive (i.e. H-alpha producing) stars are formed preferentially in regions with high gas density.Comment: 5 pages, 5 figures, 1 table. Accepted for publication in MNRAS Letters. The definitive version is available at www.blackwell- synergy.co

Generalized W-Class State and its Monogamy Relation

We generalize the W class of states from $n$ qubits to $n$ qudits and prove that their entanglement is fully characterized by their partial entanglements even for the case of the mixture that consists of a W-class state and a product state $\ket{0}^{\otimes n}$.Comment: 12 pages, 1 figur