The Measure for the Multiverse and the Probability for Inflation

We investigate the measure problem in the framework of inflationary cosmology. The measure of the history space is constructed and applied to inflation models. Using this measure, it is shown that the probability for the generalized single field slow roll inflation to last for $N$ e-folds is suppressed by a factor $\exp(-3N)$, and the probability for the generalized $n$-field slow roll inflation is suppressed by a much larger factor $\exp(-3nN)$. Some non-inflationary models such as the cyclic model do not suffer from this difficulty.Comment: 16 page

A Novel Large Moment Antiferromagnetic Order in K0.8Fe1.6Se2 Superconductor

The discovery of cuprate high Tc superconductors has inspired searching for unconventional su- perconductors in magnetic materials. A successful recipe has been to suppress long-range order in a magnetic parent compound by doping or high pressure to drive the material towards a quantum critical point, which is replicated in recent discovery of iron-based high TC superconductors. The long-range magnetic order coexisting with superconductivity has either a small magnetic moment or low ordering temperature in all previously established examples. Here we report an exception to this rule in the recently discovered potassium iron selenide. The superconducting composition is identified as the iron vacancy ordered K0.8Fe1.6Se2 with Tc above 30 K. A novel large moment 3.31 {\mu}B/Fe antiferromagnetic order which conforms to the tetragonal crystal symmetry has the unprecedentedly high an ordering temperature TN = 559 K for a bulk superconductor. Staggeredly polarized electronic density of states thus is suspected, which would stimulate further investigation into superconductivity in a strong spin-exchange field under new circumstance.Comment: 5 figures, 5 pages, and 2 tables in pdf which arXiv.com cannot tak

Crystal growth and magnetic structure of MnBi2Te4

Millimeter-sized MnBi$_2$Te$_4$ single crystals are grown out of Bi-Te flux and characterized by measuring magnetic and transport properties, scanning tunneling microscope (STM) and spectroscopy (STS). The magnetic structure of MnBi$_2$Te$_4$ below T$_N$ is determined by powder and single crystal neutron diffraction measurements. Below T$_N$=24\,K, Mn$^{2+}$ moments order ferromagnetically in the \textit{ab} plane but antiferromagnetically along the crystallographic \textit{c} axis. The ordered moment is 4.04(13) $\mu_{B}$/Mn at 10\,K and aligned along the crystallographic \textit{c}-axis. The electrical resistivity drops upon cooling across T$_N$ or when going across the metamagnetic transition in increasing fields below T$_N$. A critical scattering effect was observed in the vicinity of T$_N$ in the temperature dependence of thermal conductivity. However, A linear temperature dependence was observed for thermopower in the temperature range 2K-300K without any anomaly around T$_N$. These indicate that the magnetic order in Mn-Te layer has negligible effect on the electronic band structure, which makes possible the realization of proposed topological properties in MnBi$_2$Te$_4$ after fine tuning of the electronic band structure

Quadra-Spectrum and Quint-Spectrum from Inflation and Curvaton Models

We calculate the quadra-spectrum and quint-spectrum, corresponding to five and six point correlation functions of the curvature perturbation. For single field inflation with standard kinetic term, the quadra-spectrum and quint-spectrum are small, which are suppressed by slow roll parameters. The calculation can be generalized to multiple fields. When there is no entropy perturbation, the quadra-spectrum and quint-spectrum are suppressed as well. With the presence of entropy perturbation, the quadra-spectrum and quint-spectrum can get boosted. We illustrate this boost in the multi-brid inflation model. For the curvaton scenario, the quadra-spectrum and quint-spectrum are also large in the small r limit. We also calculate representative terms of quadra-spectrum and quint-spectrum for inflation with generalized kinetic terms, and estimate their order of magnitude for quasi-single field inflation.Comment: 16 pages; v2: references added

A geometric description of the non-Gaussianity generated at the end of multi-field inflation

In this paper we mainly focus on the curvature perturbation generated at the end of multi-field inflation, such as the multi-brid inflation. Since the curvature perturbation is produced on the super-horizon scale, the bispectrum and trispectrum have a local shape. The size of bispectrum is measured by $f_{NL}$ and the trispectrum is characterized by two parameters $\tau_{NL}$ and $g_{NL}$. For simplicity, the trajectory of inflaton is assumed to be a straight line in the field space and then the entropic perturbations do not contribute to the curvature perturbation during inflation. As long as the background inflaton path is not orthogonal to the hyper-surface for inflation to end, the entropic perturbation can make a contribution to the curvature perturbation at the end of inflation and a large local-type non-Gaussiantiy is expected. An interesting thing is that the non-Gaussianity parameters are completely determined by the geometric properties of the hyper-surface of the end of inflation. For example, $f_{NL}$ is proportional to the curvature of the curve on this hyper-surface along the adiabatic direction and $g_{NL}$ is related to the change of the curvature radius per unit arc-length of this curve. Both $f_{NL}$ and $g_{NL}$ can be positive or negative respectively, but $\tau_{NL}$ must be positive and not less than $({6\over 5}f_{NL})^2$.Comment: 19 pages, 4 figures; refs added; a correction to \tau_{NL} for n-field inflation added, version accepted for publication in JCA

Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure