Statistical properties of dark matter mini-haloes at z >= 15

Understanding the formation of the first objects in the universe critically depends on knowing whether the properties of small dark matter structures at high-redshift (z > 15) are different from their more massive lower-redshift counterparts. To clarify this point, we performed a high-resolution N-body simulation of a cosmological volume 1 Mpc/h comoving on a side, reaching the highest mass resolution to date in this regime. We make precision measurements of various physical properties that characterize dark matter haloes (such as the virial ratio, spin parameter, shape, and formation times, etc.) for the high-redshift (z > 15) dark matter mini-haloes we find in our simulation, and compare them to literature results and a moderate-resolution comparison run within a cube of side-length 100 Mpc/h. We find that dark matter haloes at high-redshift have a log-normal distribution of the dimensionless spin parameter centered around {\lambda} $\sim$ 0.03, similar to their more massive counterparts. They tend to have a small ratio of the length of the shortest axis to the longest axis (sphericity), and are highly prolate. In fact, haloes of given mass that formed recently are the least spherical, have the highest virial ratios, and have the highest spins. Interestingly, the formation times of our mini-halos depend only very weakly on mass, in contrast to more massive objects. This is expected from the slope of the linear power spectrum of density perturbations at this scale, but despite this difference, dark matter structures at high-redshift share many properties with their much more massive counterparts observed at later times.Comment: 17 pages. Accepted for publication in MNRA

A cluster expansion approach to exponential random graph models

The exponential family of random graphs is among the most widely-studied network models. We show that any exponential random graph model may alternatively be viewed as a lattice gas model with a finite Banach space norm. The system may then be treated by cluster expansion methods from statistical mechanics. In particular, we derive a convergent power series expansion for the limiting free energy in the case of small parameters. Since the free energy is the generating function for the expectations of other random variables, this characterizes the structure and behavior of the limiting network in this parameter region.Comment: 15 pages, 1 figur

Hybrid exciton-polaritons in a bad microcavity containing the organic and inorganic quantum wells

We study the hybrid exciton-polaritons in a bad microcavity containing the organic and inorganic quantum wells. The corresponding polariton states are given. The analytical solution and the numerical result of the stationary spectrum for the cavity field are finishedComment: 3 pages, 1 figure. appear in Communications in Theoretical Physic

Do Linear Dispersions of Classical Waves Mean Dirac Cones?

By using the \vec{k}\cdot\vec{p} method, we propose a first-principles theory to study the linear dispersions in phononic and photonic crystals. The theory reveals that only those linear dispersions created by doubly-degenerate states can be described by a reduced Hamiltonian that can be mapped into the Dirac Hamiltonian and possess a Berry phase of -\pi. Triply-degenerate states can also generate Dirac-like cone dispersions, but the wavefunctions transform like a spin-1 particle and the Berry phase is zero. Our theory is capable of predicting accurately the linear slopes of Dirac/Dirac-like cones at various symmetry points in a Brilliouin zone, independent of frequency and lattice structure

Broadband spin-controlled focusing via logarithmic-spiral nanoslits of varying width

This work presents analytical, numerical and experimental demonstrations of light diffracted through a logarithmic spiral (LS) nanoslit, which forms a type of switchable and focus-tunable structure. Owing to a strong dependence on the incident photon spin, the proposed LS-nanoslit converges incoming light of opposite handedness (to that of the LS-nanoslit) into a confined subwavelength spot, while it shapes light with similar chirality into a donut-like intensity profile. Benefitting from the varying width of the LS-nanoslit, different incident wavelengths interfere constructively at different positions, i.e., the focal length shifts from 7.5 μm (at λ = 632.8 nm) to 10 μm (at λ = 488 nm), which opens up new opportunities for tuning and spatially separating broadband light at the micrometer scale

Cosmogenic activation of materials used in rare event search experiments

We evaluate the cosmogenic production rates in some materials that are commonly used as targets and shielding/supporting components for detecting rare events. The results from Geant4 simulations and the calculations of ACTIVIA are compared with the available experimental data. We demonstrate that the production rates from the Geant4-based simulations agree with the available data reasonably well. As a result, we report that the cosmogenic production of several isotopes in various materials can generate potential backgrounds for direct detection of dark matter and neutrinoless double-beta decay