Gravitational Collapse and Neutrino Emission of Population III Massive Stars

Pop III stars are the first stars in the universe. They do not contain metals and their formation and evolution may be different from that of stars of later generations. In fact, according to the theory of star formation, Pop III stars might have very massive components ($\sim 100 - 10000M_\odot$). In this paper, we compute the spherically symmetric gravitational collapse of these Pop III massive stars. We solve the general relativistic hydrodynamics and neutrino transfer equations simultaneously, treating neutrino reactions in detail. Unlike supermassive stars ($\gtrsim 10^5 M_\odot$), the stars of concern in this paper become opaque to neutrinos. The collapse is simulated until after an apparent horizon is formed. We confirm that the neutrino transfer plays a crucial role in the dynamics of gravitational collapse, and find also that the $\beta$-equilibration leads to a somewhat unfamiliar evolution of electron fraction. Contrary to the naive expectation, the neutrino spectrum does not become harder for more massive stars. This is mainly because the neutrino cooling is more efficient and the outer core is more massive as the stellar mass increases. Here the outer core is the outer part of the iron core falling supersonically. We also evaluate the flux of relic neutrino from Pop III massive stars. As expected, the detection of these neutrinos is difficult for the currently operating detectors. However, if ever observed, the spectrum will enable us to obtain the information on the formation history of Pop III stars. We investigate 18 models covering the mass range of $300 - 10^4 M_\odot$, making this study the most detailed numerical exploration of spherical gravitational collapse of Pop III massive stars. This will also serve as an important foundation for multi-dimensional investigations.Comment: 32 pages, 11 figs, submitted to Ap

Electrochemical kinetics and dimensional considerations at the nanoscale

It is shown that the consideration of the density of states variation in nanoscale electrochemical systems yields modulations in the rate constant and concomitant electrical currents. The proposed models extend the utility of Marcus-Hush-Chidsey (MHC) kinetics to a larger class of materials and could be used as a test of dimensional character. The implications of the study are of much significance to an understanding and modulation of charge transfer nanostructured electrodes.Comment: 15 pages, 6 figure

Primordial Black Holes from Polynomial Potentials in Single Field Inflation

Within canonical single field inflation models, we provide a method to reverse engineer and reconstruct the inflaton potential from a given power spectrum. This is not only a useful tool to find a potential from observational constraints, but also gives insight into how to generate a large amplitude spike in density perturbations, especially those that may lead to primordial black holes (PBHs). In accord with other works, we find that the usual slow-roll conditions need to be violated in order to generate a significant spike in the spectrum. We find that a way to achieve a very large amplitude spike in single field models is for the classical roll of the inflaton to over-shoot a local minimum during inflation. We provide an example of a quintic polynomial potential that implements this idea and leads to the observed spectral index, observed amplitude of fluctuations on large scales, significant PBH formation on small scales, and is compatible with other observational constraints. We quantify how much fine-tuning is required to achieve this in a family of random polynomial potentials, which may be useful to estimate the probability of PBH formation in the string landscape.Comment: 13 pages in double column format, 5 figures. V2: Added references and small clarification

Vacuum Decay in Real Time and Imaginary Time Formalisms

We analyze vacuum tunneling in quantum field theory in a general formalism by using the Wigner representation. In the standard instanton formalism, one usually approximates the initial false vacuum state by an eigenstate of the field operator, imposes Dirichlet boundary conditions on the initial field value, and evolves in imaginary time. This approach does not have an obvious physical interpretation. However, an alternative approach does have a physical interpretation: in quantum field theory, tunneling can happen via classical dynamics, seeded by initial quantum fluctuations in both the field and its momentum conjugate, which was recently implemented in Ref. [1]. We show that the Wigner representation is a useful framework to calculate and understand the relationship between these two approaches. We find there are two, related, saddle point approximations for the path integral of the tunneling process: one corresponds to the instanton solution in imaginary time and the other one corresponds to classical dynamics from initial quantum fluctuations in real time. The classical approximation for the dynamics of the latter process is justified only in a system with many degrees of freedom, as can appear in field theory due to high occupancy of nucleated bubbles, while it is not justified in single particle quantum mechanics, as we explain. We mention possible applications of the real time formalism, including tunneling when the instanton vanishes, or when the imaginary time contour deformation is not possible, which may occur in cosmological settings.Comment: 10 pages in double column format, 2 figures. V2: Further clarifications. Updated to resemble version published in PR

Monopole Excitation to Cluster States

We discuss strength of monopole excitation of the ground state to cluster states in light nuclei. We clarify that the monopole excitation to cluster states is in general strong as to be comparable with the single particle strength and shares an appreciable portion of the sum rule value in spite of large difference of the structure between the cluster state and the shell-model-like ground state. We argue that the essential reasons of the large strength are twofold. One is the fact that the clustering degree of freedom is possessed even by simple shell model wave functions. The detailed feature of this fact is described by the so-called Bayman-Bohr theorem which tells us that SU(3) shell model wave function is equivalent to cluster model wave function. The other is the ground state correlation induced by the activation of the cluster degrees of freedom described by the Bayman-Bohr theorem. We demonstrate, by deriving analytical expressions of monopole matrix elements, that the order of magnitude of the monopole strength is governed by the first reason, while the second reason plays a sufficient role in reproducing the data up to the factor of magnitude of the monopole strength. Our explanation is made by analysing three examples which are the monopole excitations to the $0^+_2$ and $0^+_3$ states in $^{16}$O and the one to the $0^+_2$ state in $^{12}$C. The present results imply that the measurement of strong monopole transitions or excitations is in general very useful for the study of cluster states.Comment: 11 pages, 1 figure: revised versio

Reflection equation for the N=3 Cremmer-Gervais R-matrix

We consider the reflection equation of the N=3 Cremmer-Gervais R-matrix. The reflection equation is shown to be equivalent to 38 equations which do not depend on the parameter of the R-matrix, q. Solving those 38 equations. the solution space is found to be the union of two types of spaces, each of which is parametrized by the algebraic variety $\mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^2(\mathbb{C})$ and $\mathbb{C} \times \mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^2(\mathbb{C})$.Comment: 28 pages, revised versio

Reflectivity measurements in uniaxial superconductors: a methodological discussion applied to the case of La(2-x)Sr(x)CuO(4)

Most of the novel superconductors are uniaxial crystals, with metallic planes ($ab$) orthogonal to an insulating axis ($c$). Far-infrared measurements of the reflectivity $R_{ab} (\omega)$ provide valuable information on their low-energy electrodynamics, but involve delicate experimental issues. Two of them are a possible contamination of $R_{ab} (\omega)$ from the c axis and the extrapolation of the $R_{ab}$ data to $\omega$ =0, both above and below $T_c$. Here we discuss quantitatively these issues with particular regard to La$_{2-x}$Sr$_x$CuO$_{4+y}$, one of the most studied high-$T_c$ materials.Comment: 13 pages with 3 Fig

The Grounds For Time Dependent Market Potentials From Dealers' Dynamics

We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers' feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market's potential force. When markets are dominated by dealers with positive feedback the resulting potential force is repulsive, while the effect of negative feedback enhances the attractive potential force.Comment: 9 pages, 3 figures, proceedings of APFA

Search for effective models of stripes in the cuprates

We argue that effective 1D models of stripes in the cuprate superconductors can be constructed by studying ground states and elementary excitations of domain walls in 2D model antiferromagnets. This method, applied to the t-J model with Ising anisotropy, yields two such limiting cases: an ordinary 1D electron gas and a 1D gas of holons strongly coupled to transversal fluctuations of the stripe.Comment: LaTeX2e, 2 pages, 2 EPS figures, a style file include

Synthetic Observations of Carbon Lines of Turbulent Flows in Diffuse Multiphase Interstellar Medium

We examine observational characteristics of multi-phase turbulent flows in the diffuse interstellar medium (ISM) using a synthetic radiation field of atomic and molecular lines. We consider the multi-phase ISM which is formed by thermal instability under the irradiation of UV photons with moderate visual extinction $A_V\sim 1$. Radiation field maps of C$^{+}$, C$^0$, and CO line emissions were generated by calculating the non-local thermodynamic equilibrium (nonLTE) level populations from the results of high resolution hydrodynamic simulations of diffuse ISM models. By analyzing synthetic radiation field of carbon lines of [\ion{C}{2}] 158 $\mu$m, [\ion{C}{1}] $^3P_2-^3P_1$ (809 GHz), $^3P_1-^3P_0$ (492 GHz), and CO rotational transitions, we found a high ratio between the lines of high- and low-excitation energies in the diffuse multi-phase interstellar medium. This shows that simultaneous observations of the lines of warm- and cold-gas tracers will be useful in examining the thermal structure, and hence the origin of diffuse interstellar clouds.Comment: 16 pages, 10 figures : accepted for publication in ApJ. PDF version with high resolution figures is available (http://yso.mtk.nao.ac.jp/~ymasako/paper/ms_hires.pdf