Geometric Allocation Approaches in Markov Chain Monte Carlo

The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the selection of candidate states, the optimization of transition kernel, algorithm for choosing a configuration according to the transition probabilities. We show that the unconventional approaches based on the geometric allocation of probabilities or weights can improve the dynamics and scaling of the Monte Carlo simulation in several aspects. Particularly, the approach using the irreversible kernel can reduce or sometimes completely eliminate the rejection of trial move in the Markov chain. We also discuss how the space-time interchange technique together with Walker's method of aliases can reduce the computational time especially for the case where the number of candidates is large, such as models with long-range interactions.Comment: 10pages, 4 figure

Can Gamma-Ray Burst Jets Break Out the First Stars?

We show that a relativistic gamma-ray burst (GRB) jet can potentially pierce the envelope of very massive first generation star (Population III; Pop III) by using the stellar density profile to estimate both the jet luminosity (via accretion) and its penetrability. The jet breakout is possible even if the Pop III star has a supergiant hydrogen envelope without mass loss, thanks to the long-lived powerful accretion of the envelope itself. While the Pop III GRB is estimated to be energetic, E_{gamma,iso} ~ 10^{55} erg, the supergiant envelope hides the initial bright phase into the cocoon component, leading to a GRB with a long duration ~ 1000(1+z) sec and an ordinary isotropic luminosity ~ 10^{52} erg s^{-1} (~ 10^{-9} erg cm^{-2} s^{-1} at redshift z ~ 20). The neutrino-annihilation is not effective for Pop III GRBs because of a low central temperature, while the magnetic mechanism is viable. We also derive analytic estimates of the breakout conditions, which are applicable to various progenitor models. The GRB luminosity and duration are found to be very sensitive to the core and envelope mass, providing possible probes of the first luminous objects at the end of the high redshift dark ages.Comment: 7 pages, 2 figures; accepted for publication in Ap

Intrinsic optical gain of ultrathin silicon quantum wells from first-principles calculations

Optical gains of ultrathin Si(001) quantum wells are calculated from first principles, and found to be positive because of an intrinsic quantum confinement effect. The gain of the ultrathin silicon film is comparable to that of the bulk GaAs if the carrier density is large enough. The impact of surface structure of the silicon film on the efficiency of light emission is also investigated and we found that SiO2 crystal that forms a strainless connection with a Si(001) surface such as quartz enhances optical gain