Limit Cycle Bifurcations from Centers of Symmetric Hamiltonian Systems Perturbing by Cubic Polynomials

In this paper, we consider some cubic near-Hamiltonian systems obtained from perturbing the symmetric cubic Hamiltonian system with two symmetric singular points by cubic polynomials. First, following Han [2012] we develop a method to study the analytical property of the Melnikov function near the origin for near-Hamiltonian system having the origin as its elementary center or nilpotent center. Based on the method, a computationally efficient algorithm is established to systematically compute the coefficients of Melnikov function. Then, we consider the symmetric singular points and present the conditions for one of them to be elementary center or nilpotent center. Under the condition for the singular point to be a center, we obtain the normal form of the Hamiltonian systems near the center. Moreover, perturbing the symmetric cubic Hamiltonian systems by cubic polynomials, we consider limit cycles bifurcating from the center using the algorithm to compute the coefficients of Melnikov function. Finally, perturbing the symmetric hamiltonian system by symmetric cubic polynomials, we consider the number of limit cycles near one of the symmetric centers of the symmetric near-Hamiltonian system, which is same to that of another center

Insulator-to-metal phase transition in Yb-based Kondo insulators

The periodic Anderson lattice model for the crystalline electric field (CEF)split 4f quartet states is used to describe the Yb-based Kondo insulators/semiconductors. In the slave-boson mean-field approximation, we derive the hybridized quasiparticle bands, and find that decreasing the hybridization difference of the two CEF quartets may induce an insulator-to-metal phase transition. The resulting metallic phase has a hole and an electron Fermi pockets. Such a phase transition may be realized experimentally by applying pressure, reducing the difference in hybridization of the two CEF quartets.Comment: 5 pages, 3 figure

Quasi-optical SIS mixers with normal metal tuning structures

We recently reported (1996) a quasi-optical SIS mixer which used Nb/Al-oxide/Nb tunnel junctions and a normal-metal (Al) tuning circuit to achieve an uncorrected receiver noise temperature of 840 K (DSB) at 1042 GHz. Here we present results on several different device designs, which together cover the 300-1200 GHz frequency range. The mixers utilize an antireflection-coated silicon hyper-hemispherical lens, a twin-slot antenna, and a two-junction tuning circuit. The broad-band frequency response was measured using Fourier transform spectrometry (FTS), and is in good agreement with model calculations. Heterodyne tests were carried out from 400 GHz up to 1040 GHz, and these measurements agree well with the FTS results and with calculations based on Tucker's theory (1985)

Low-noise 1 THz niobium superconducting tunnel junction mixer with a normal metal tuning circuit

We describe a 1 THz quasioptical SIS mixer which uses a twin-slot antenna, an antireflection-coated silicon hyperhemispherical lens, Nb/Al-oxide/Nb tunnel junctions, and an aluminum normal-metal tuning circuit in a two-junction configuration. Since the mixer operates substantially above the gap frequency of niobium (nu >~ 2 Delta/h ~ 700 GHz), a normal metal is used in the tuning circuit in place of niobium to reduce the Ohmic loss. The frequency response of the device was measured using a Fourier transform spectrometer and agrees reasonably well with the theoretical prediction. At 1042 GHz, the uncorrected double-sideband receiver noise temperature is 840 K when the physical temperature of the mixer is 2.5 K. This is the first SIS mixer which outperforms GaAs Schottky diode mixers by a large margin at 1 THz

Temporal Profiles and Spectral Lags of XRF 060218

The spectral and temporal properties of the non-thermal emission ofthe nearby XRF 060218 in 0.3-150 keV band are studied. We show that both the spectral energy distribution and the light curve properties suggest the same origin of the non-thermal emission detected by {\em Swift} BAT and XRT. This event has the longest pulse duration and spectral lag observed to date among the known GRBs. The pulse structure and its energy dependence are analogous to typical GRBs. By extrapolating the observed spectral lag to the {\em CGRO/BATSE} bands we find that the hypothesis that this event complies with the same luminosity-lag relation with bright GRBs cannot be ruled out at $2\sigma$ significance level. These intriguing facts, along with its compliance with the Amati-relation, indicate that XRF 060218 shares the similar radiation physics as typical GRBs.Comment: 9 pages in emulateapj format, including 4 figures and 1 table, accepted for publication in ApJ Letter