The dynamically induced Fermi arcs and Fermi pockets in two dimensions: a model for underdoped cuprates

We investigate the effects of the dynamic bosonic fluctuations on the Fermi surface reconstruction in two dimensions as a model for the underdoped cuprates. At energies larger than the boson energy $\omega_b$, the dynamic nature of the fluctuations is not important and the quasi-particle dispersion exhibits the shadow feature like that induced by a static long range order. At lower energies, however, the shadow feature is pushed away by the finite $\omega_b$. The detailed low energy features are determined by the bare dispersion and the coupling of quasi-particles to the dynamic fluctuations. We present how these factors reconstruct the Fermi surface to produce the Fermi arcs or the Fermi pockets, or their coexistence. Our principal result is that the dynamic nature of the fluctuations, without invoking a yet-to-be-established translational symmetry breaking hidden order, can produce the Fermi pocket centered away from the $(\pi/2,\pi/2)$ towards the zone center which may coexist with the Fermi arcs. This is discussed in comparison with the experimental observations.Comment: Some comments and references were added and typos were corrected. The published version. 9 page

Effect of radiative transfer on damped Lyman-alpha and Lyman limit systems in cosmological SPH simulations

We study the effect of local stellar radiation and UVB on the physical properties of DLAs and LLSs at z=3 using cosmological SPH simulations. We post-process our simulations with the ART code for radiative transfer of local stellar radiation and UVB. We find that the DLA and LLS cross sections are significantly reduced by the UVB, whereas the local stellar radiation does not affect them very much except in the low-mass halos. This is because clumpy high-density clouds near young star clusters effectively absorb most of the ionizing photons from young stars. We also find that the UVB model with a simple density threshold for self-shielding effect can reproduce the observed column density distribution function of DLAs and LLSs very well, and we validate this model by direct radiative transfer calculations of stellar radiation and UVB with high angular resolution. We show that, with a self-shielding treatment, the DLAs have an extended distribution around star-forming regions typically on ~ 10-30 kpc scales, and LLSs are surrounding DLAs on ~ 30-60 kpc scales. Our simulations suggest that the median properties of DLA host haloes are: Mh = 2.4*10^10 Msun, SFR = 0.3 Msun/yr, M* = 2.4*10^8 Msun, and Z/Zsun = 0.1. About 30 per cent of DLAs are hosted by haloes having SFR = 1 - 20 Msun/yr, which is the typical SFR range for LBGs. More than half of DLAs are hosted by the LBGs that are fainter than the current observational limit. Our results suggest that fractional contribution to LLSs from lower mass haloes is greater than for DLAs. Therefore the median values of LLS host haloes are somewhat lower with Mh = 9.6*10^9 Msun, SFR = 0.06 Msun/yr, M* = 6.5*10^7 Msun and Z/Zsun = 0.08. About 80 per cent of total LLS cross section are hosted by haloes with SFR < 1 Msun/yr, hence most LLSs are associated with low-mass halos with faint LBGs below the current detection limit.Comment: 18 pages, 12 figures, accepted for publication in MNRA

Robust Model Selection in Dynamic Models with an Application to Comparing Predictive Accuracy

A model selection procedure based on a general criterion function, with an example of the Kullback-Leibler Information Criterion (KLIC) using quasi-likelihood functions, is considered for dynamic non-nested models. We propose a robust test which generalizes Lien and Vuong's (1987) test with a Heteroscadasticity/Autocorrelation Consistent (HAC) variance estimator. We use the fixed-b asymptotics developed in Kiefer and Vogelsang (2005) to improve the asymptotic approximation to the sampling distribution of the test statistic. The fixed-b approach is compared with a bootstrap method and the standard normal approximation in Monte Carlo simulations. The fixed-b asymptotics and the bootstrap method are found to be markedly superior to the standard normal approximation. An empirical application for foreign exchange rate forecasting models is presented.

Geometry of the Log-Likelihood Ratio Statistic in Misspecified Models

We show that the asymptotic mean of the log-likelihood ratio in a misspecified model is a differential geometric quantity that is related to the exponential curvature of Efron (1978), Amari (1982), and the preferred point geometry of Critchley et al. (1993, 1994). The mean is invariant with respect to reparametrization, which leads to the differential geometrical approach where coordinate-system invariant quantities like statistical curvatures play an important role. When models are misspecified, the likelihood ratios do not have the chi-squared asymptotic limit, and the asymptotic mean of the likelihood ratio depends on two geometric factors, the departure of models from exponential families (i.e. the exponential curvature) and the departure of embedding spaces from being totally flat in the sense of Critchley et al. (1994). As a special case, the mean becomes the mean of the usual chi-squared limit (i.e. the half of the degrees of freedom) when these two curvatures vanish. The effect of curvatures is shown in the non-nested hypothesis testing approach of Vuong (1989), and we correct the numerator of the test statistic with an estimated asymptotic mean of the log-likelihood ratio to improve the asymptotic approximation to the sampling distribution of the test statistic.

Supermassive Black Hole Formation at High Redshifts via Direct Collapse: Physical Processes in the Early Stage

We use numerical simulations to explore whether direct collapse can lead to the formation of SMBH seeds at high-z. We follow the evolution of gas within DM halos of 2 x 10^8 Mo and 1 kpc. We adopt cosmological density profiles and j-distributions. Our goal is to understand how the collapsing flow overcomes the centrifugal barrier and whether it is subject to fragmentation. We find that the collapse leads either to a central runaway or to off-center fragmentation. A disk-like configuration is formed inside the centrifugal barrier. For more cuspy DM distribution, the gas collapses more and experiences a bar-like perturbation and a central runaway. We have followed this inflow down to ~10^{-4} pc. The flow remains isothermal and the specific angular momentum is efficiently transferred by gravitational torques in a cascade of nested bars. This cascade supports a self-similar, disk-like collapse. In the collapsing phase, virial supersonic turbulence develops and fragmentation is damped. For larger initial DM cores the timescales become longer. In models with more organized initial rotation, a torus forms and appears to be supported by turbulent motions. The evolution depends on the competition between two timescales, corresponding to the onset of the central runaway and off-center fragmentation. For less organized rotation, the torus is greatly weakened, the central accretion timescale is shortened, and off-center fragmentation is suppressed --- triggering the central runaway even in previously `stable' models. The resulting SMBH masses lie in the range 2 x 10^4 Mo - 2 x 10^6 Mo, much higher than for Population III remnants. We argue that the above upper limit appears to be more realistic mass. Corollaries of this model include a possible correlation between SMBH and DM halo masses, and similarity between the SMBH and halo mass functions, at time of formation.Comment: 20 pages, 15 figures, 3 tables. Accepted for publication in the Astrophysical Journa