Massive particles＇ tunnelling radiation from the black hole with a mass-quadruple moment

In this paper, we extend Zhang and Zhao's recent work to the black hole with a mass-quadruple moment. The behaviour of the tunnelling massive particles is investigated, and the emission rate at which massive particles tunnel across the event horizon of the black hole is calculated. The result is consistent with an underlying unitary theory, and takes the same functional form as that of a massless particle.     

Bifurcation of a periodic instanton and quantum－classical transition in the biaxial nano－ferromagnet with a magnetic field along hard axis

Crossover from classical to quantum regimes of the barrier transition rate in a biaxial ferromagnetic magnet with a magnetic field applied along hard anisotropy axis is investigated. We show that the type of action-temperature diagrams can he determined by counting the number of bifurcation points. The model possesses not only the known type I and Ⅱ, hut also the interesting type Ⅲ and Ⅳ of transition which do not occur in general.