Double-q\it q Order in a Frustrated Random Spin System

We use the three-dimensional Heisenberg model with site randomness as an effective model of the compound Sr(Fe$_{1-x}$Mn$_x$)O$_2$. The model consists of two types of ions that correspond to Fe and Mn ions. The nearest-neighbor interactions in the ab-plane are antiferromagnetic. The nearest-neighbor interactions along the c-axis between Fe ions are assumed to be antiferromagnetic, whereas other interactions are assumed to be ferromagnetic. From Monte Carlo simulations, we confirm the existence of the double-$\boldsymbol{q}$ ordered phase characterized by two wave numbers, $(\pi\pi\pi)$ and $(\pi\pi0)$. We also identify the spin ordering pattern in the double-$\boldsymbol{q}$ ordered phase.Comment: 5pages, 3figure

Dissipation-induced pure Gaussian state

This paper provides some necessary and sufficient conditions for a generalMarkovian Gaussian master equation to have a unique pure steady state. The conditions are described by simple matrix equations; thus the so-called environment engineering problem for pure-Gaussian-state preparation can be straightforwardly dealt with in the linear algebraic framework. In fact, based on one of those conditions, for an arbitrary given pure Gaussian state,we obtain a complete parametrization of the Gaussian master equation having that state as a unique steady state; this leads to a systematic procedure for engineering a desired dissipative system.We demonstrate some examples including Gaussian cluster states.Comment: 8 page

Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies and correlation functions of the Bose Hubbard model is developed. We illustrate the general formalism, which includes all possible inhomogeneous effects in the formalism, such as disorder, or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third-order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator to superfluid transition along with a generalization of the RPA-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions; the accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling theory results are benchmarked against numerically exact QMC simulations in two and three dimensions and against DMRG calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.Comment: 48 pages 14 figures RevTe

Supernova Explosions in the Early Universe: Evolution of Radiative Remnants and the Halo Destruction Efficiency

We study the evolution of supernova (SN) remnants of the first stars, taking proper account of the radiative feedback of the progenitor stars on the surroundings. We carry out a series of one-dimensional hydrodynamic simulations with radiative cooling, starting from initial configurations that are drawn from the results of our earlier radiation hydrodynamic simulations of the first HII regions. In low-mass (< 10^6 M_sun) halos, the stellar radiation significantly reduces the ambient gas density prior to the SN explosion. The blastwave quickly propagates over the halo's virial radius, leading to complete evacuation of the gas even with the input energy of 10^50 erg. We find that a large fraction of the remnant's thermal energy is lost in 0.1-10 Myr by line cooling, whereas, for larger explosion energies, the remnant expands even more rapidly with decreasing interior density, and cools predominantly via inverse Compton process. In higher mass halos, the gas density near the explosion site remains high and the SN shock is heavily confined; the thermal energy of the remnant is quickly radiated away by free-free emission, even if the total input energy exceeds the binding energy of halos by two orders of magnitude. We show that the efficiency of halo destruction is determined not only by the explosion energy but also by the gas density profile, and thus controlled by radiative feedback prior to the explosion. Several implications of our results for the formation of first quasars and second-generation stars in the universe are also discussed.Comment: 13 pages, 11 embedded figures. Accepted for publication in Ap

Formation of Massive Primordial Stars in a Reionized Gas

We use cosmological hydrodynamic simulations with unprecedented resolution to study the formation of primordial stars in an ionized gas at high redshifts. Our approach includes all the relevant atomic and molecular physics to follow the thermal evolution of a prestellar gas cloud to very high densities of ~10^{18} cm^{-3}. We locate a star-forming gas cloud within a reionized region in our cosmological simulation. The first run-away collapse is triggered when the gas cloud's mass is ~40 Msun. We show that the cloud core remains stable against chemo-thermal instability and also against gravitational deformation throughout its evolution. Consequently, a single proto-stellar seed is formed, which accretes the surrounding hot gas at the rate ~10^{-3} Msun/year. We carry out proto-stellar evolution calculations using the inferred accretion rate. The resulting mass of the star when it reaches the zero-age main sequence is M_ZAMS ~40 Msun. We argue that, since the obtained M_ZAMS is as large as the mass of the collapsing parent cloud, the final stellar mass should be close to this value. Such massive, rather than exceptionally massive, primordial stars are expected to cause early chemical enrichment of the Universe by exploding as black hole-forming super/hypernovae, and may also be progenitors of high redshift gamma-ray bursts. The elemental abundance patterns of recently discovered hyper metal-poor stars suggest that they might have been born from the interstellar medium that was metal-enriched by supernovae of these massive primordial stars.Comment: Revised version. To appear in ApJ

Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks proposed by Caldarelli et al. (2002). Power-law degree distributions, particularly with the dynamically stable scaling exponent 2, realistic clustering, and short path lengths are produced for many types of weight distributions. Thresholding mechanisms can underlie a family of real complex networks that is characterized by cooperativeness and the baseline scaling exponent 2. It contrasts with the class of growth models with preferential attachment, which is marked by competitiveness and baseline scaling exponent 3.Comment: 5 figure

The Era of Massive Population III Stars: Cosmological Implications and Self-Termination

The birth and death of the first generation of stars have important implications for the thermal state and chemical properties of the intergalactic medium (IGM) in the early universe. Sometime after recombination, the neutral, chemically pristine gas was reionized by ultraviolet photons emitted from the first stars, but also enriched with heavy elements when these stars ended their lives as energetic supernovae. Using the results from previous high-resolution cosmological simulations of early structure formation that include radiative transfer, we show that a significant volume fraction of the IGM can be metal-polluted, as well as ionized, by massive Population III stars formed in small-mass (10^6-10^7 Msun) halos early on. If most of the early generation stars die as pair-instability supernovae with energies up to 10^{53} ergs, the volume-averaged mean metallicity will quickly reach Z ~ 10^{-4}Zsun by a redshift of 15-20, possibly causing a prompt transition to the formation of a stellar population that is dominated by low-mass stars. In this scenario, the early chemical enrichment history should closely trace the reionization history of the IGM, and the end of the Population III era is marked by the completion of reionization and pre-enrichment by z=15. We conclude that, while the pre-enrichment may partially account for the ``metallicity-floor'' in high-redshift Lyman-alpha clouds, it does not significantly affect the elemental abundance in the intracluster medium.Comment: Version accepted by ApJ. Minor revisions and a few citations adde

Fast and stable method for simulating quantum electron dynamics

A fast and stable method is formulated to compute the time evolution of a wavefunction by numerically solving the time-dependent Schr{\"o}dinger equation. This method is a real space/real time evolution method implemented by several computational techniques such as Suzuki's exponential product, Cayley's form, the finite differential method and an operator named adhesive operator. This method conserves the norm of the wavefunction, manages periodic conditions and adaptive mesh refinement technique, and is suitable for vector- and parallel-type supercomputers. Applying this method to some simple electron dynamics, we confirmed the efficiency and accuracy of the method for simulating fast time-dependent quantum phenomena.Comment: 10 pages, 35 eps figure

A renormalization procedure for tensor models and scalar-tensor theories of gravity

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian configurations are parameterized by a scalar and a symmetric two-tensor, it is argued that, in general situations, the infrared dynamics of the tensor models should be described by scalar-tensor theories of gravity.Comment: 20 pages, 3 figures, references added, minor correction