We establish an underlying quantum dynamical algebra SU(2) for a one-dimensional Morse potential.

Since there is always an incorrect sign in the mass of the graviton in the so-called perturbation expansion approximation of de Sitter spacetime, the existence of a gravitational wave from the metric perturbation of de Sitter spacetime is doubtful. We try to take another way to start from the assumption that the cosmological gravitation wave equation should be both general covariant and conformal invariant. It is found that the so-called conformal gravitation is no longer part of the metric field and it has an effective mass of m_g =√R/6 =√2Λ/3 with the correct sign in de Sitter spacetime, though its intrinsic mass remains zero.

We study an N-dimensional system based upon a sine map, which is related to the simplified model of an opto-electronic system. The system behavior is analyzed with the tools of nonlinear dynamics (bifurcations in the parameter plane, critical manifolds, basins of attraction, chaotic attractors). Our study relies on a two-dimensional system (N=2). It is interesting that this system shows the existence of bounded chaotic orbits, which can be considered for secure transmissions.

We experimentally study the effect of the air gap on conversion efficiency and the spectrum of generated third-harmonic pulses in the dual-tripler broadband third-harmonic generation scheme. The experimental results are in good agreement with predictions that the 4-cm air gap is equivalent to a full cycle of phase mismatch among the three interacting pulses (i.e. the fundamental, second-harmonic and third-harmonic pulse). The experimental results also show that the spectrum of the third-harmonic pulse is sensitive to the air gap. We also point out that the air gap effect can be ignored when the dual-tripler system is located in 1000 Pa atmosphere. These results will guide the design of the broadband third-harmonic generation system in high power lasers.

The mechanical properties of PbWO₄ (PWO) crystals grown by the vertical Bridgman method are systematically investigated using the microindentation technique. In the present work, the Vickers microhardness H_ν, fracture toughness K_c, yield strength σ_y and friability index B_i of PbWO₄ crystals are measured. The Vickers microhardness H_ν on the (100) wafer is about 140 MPa, which means that PWO is a little ``soft'' scintillator. The anisotropy of mechanical properties is also investigated under a steady load of 0.5 kg. The (100) wafer of the crystal exhibits combined mechanical properties more excellent than those of (111) and (001) wafers, and the values of K_c, σ_y, and B_i are 0.538 MPa・m^1/2, 51.11 kg/mm² and 284.96 νm^-1/2, respectively.