All-optical vector cesium magnetometer

Based on power modulation of a pump laser and precessional projection detection, we present an all-optical vector magnetometer of cesium, which has a demonstrated magnitude sensitivity of 80 fT/Hz 1/2 and an orientation sensitivity of 0.1°/Hz 1/2. In the device, four main factors are measured experimentally, which are the Larmor precession frequency of a polarized magnetic moment that depends on the modulus of the measured magnetic field only, two phase shifts and amplitude ratio of the precession projection in the two probe directions relative to the magnetic field orientation. This kind of magnetometer with high sensitivity in the range of the spatial angle is suitable for solving the inverse problem and geomagnetic navigation

Merger rate of supermassive primordial black hole binaries

The probability that the primordial black hole (PBH) binaries formed in the early Universe can be affected by the Hubble expansion of background, which is non-negligible when the number density of PBHs is very low (it is actually this case for supermassive PBHs). In this paper, taking into account the effect of cosmic expansion on the comoving distance of PBH pairs, we worked out the merger rate of PBHs with any extended mass function. The torques by all PBHs and linear density perturbations are also considered. It is found that the merger rate of PBH, $M\gtrsim 10^6M_\odot$, binaries is significantly lower for $f_\text{pbh}\lesssim 0.01$ than expected.Comment: 16 pages, 5 figure

Efficiency Loss of Mixed Equilibrium Behaviors with Polynomial Cost Functions

This paper investigates the efficiency loss of selfish routing simultaneously with user equilibrium (UE) player and Cournot-Nash (CN) players. The upper bound of the efficiency loss of UE-CN mixed equilibrium with polynomial cost functions is obtained by the scaling method and the nonlinear programming method, respectively. It is shown that the upper bound of efficiency loss obtained by the scaling method only depends on the polynomial degree of the link travel cost function and the upper bound of efficiency loss obtained by the nonlinear programming method depends on the number of the CN players besides the aforementioned factors. The numerical tests validate our analytical results. KEY WORDS: efficiency loss, UE-CN mixed equilibrium, variational inequality, selfish routing gam

Bis[μ-2-(2-naphth­oxy)acetato]bis­{aqua[2-(2-naphth­oxy)acetato]zinc(II)}

The title binuclear ZnII compound, [Zn2(C12H9O3)4(H2O)2], is centrosymmetric. Each Zn atom is coordinated by two bridging 2-naphthoxyacetate anions, one terminal 2-naphth­oxy­acetate anion and one water mol­ecule in a distorted ZnO4 tetra­hedral geometry. The naphthalene system of the bridging ligand is nearly perpendicular to the naphthalene of the terminal ligand, with a dihedral angle of 78.26 (6)°. Within the binuclear mol­ecule the Zn⋯Zn separation is 3.815 (5) Å. In the crystal structure, inter­molecular O—H⋯O hydrogen bonding between the water mol­ecule and carboxyl­ate groups helps to stabilize the crystal structure

Distribution of equilibrium free energies in a thermodynamic system with broken ergodicity

At low temperatures the configurational phase space of a macroscopic complex system (e.g., a spin-glass) of $N\sim 10^{23}$ interacting particles may split into an exponential number $\Omega_s \sim \exp({\rm const} \times N)$ of ergodic sub-spaces (thermodynamic states). Previous theoretical studies assumed that the equilibrium collective behavior of such a system is determined by its ground thermodynamic states of the minimal free-energy density, and that the equilibrium free energies follow the distribution of exponential decay. Here we show that these assumptions are not necessarily valid. For some complex systems, the equilibrium free-energy values may follow a Gaussian distribution within an intermediate temperature range, and consequently their equilibrium properties are contributed by {\em excited} thermodynamic states. This work will help improving our understanding of the equilibrium statistical mechanics of spin-glasses and other complex systems.Comment: 7 pages, 2 figure