We experimentally realize spin-tensor momentum coupling (STMC) using three ground Zeeman states coupled by three Raman laser beams in an ultracold atomic system of ${}^{40}\mathrm{K}$ Fermi atoms. This type of STMC consists of two bright-state bands as a spin-orbit coupled spin-1/2 system and one dark-state middle band. Using radio-frequency spin-injection spectroscopy, we investigate the energy band of STMC. It is demonstrated that the middle state is a dark state in the STMC system. The experimental realization of STMC open the door for further exploring exotic quantum matter.

The initial-boundary value problem for a wave equation with nonlinear averaged damping and nonlocal nonlinear source term is considered. We provide the sufficient conditions of finite time blow-up fo...

In this paper, we consider a nonlinear viscoelastic equation with nonlocal nonlinear boundary damping and two nonlinear source terms (boundary and interior). We obtain the global existence of solution via the potential well method. By introducing suitable Lyapunov functionals, using the multiplier method, and constructing convex differential inequality, we establish an explicit and general decay rate result. This improves previous decay results concerning the problem. We also get a finite time blow-up result of solution with positive initial energy under suitable conditions on the initial data and positive memory function. This is the first result for blow-up of the problem with nonlocal nonlinear boundary damping.

The viscoelastic wave equation with nonlinear nonlocal weak damping is considered. The local existence of solutions is established. Under arbitrary positive initial energy, a finite-time blow-up result is proved by a new modified concavity method.

In this paper, the wave equation with logarithmic damping is considered. The global existence of solutions is proved by means of Faedo-Galerkin combined with the stable set method. By using multiplier method, integral inequalities, and special algebraic inequalities, the exponential decay of energy is obtained. Finally, the blow-up in finite time under some conditions on initial data is given. These contributions complement existing literature on logarithmic damping, which is an area that remains relatively unexplored.