We calculate exactly the time-dependent reduced density matrix for the central spin in the central-spin model with homogeneous Heisenberg couplings. Therefrom, the dynamics and the entanglement entropy of the central spin are obtained. A rich variety of behaviors is found, depending on the initial state of the bath spins. For an initially unpolarized unentangled bath, the polarization of the ce...

We attach the degenerate signature (n,0,1) to the dual Grassmann algebra of projective space to obtain a real Clifford algebra which provides a powerful, efficient model for euclidean geometry. We avoid problems with the degenerate metric by constructing an algebra isomorphism between the Grassmann algebra and its dual that yields non-metric meet and join operators. We focus on the cases of n=2...

For a flat family of Du Val singularities, we can take a simultaneous resolution after finite base change. It is an interesting problem to consider this analogy for a flat family of higher dimensional canonical singularities. In this note, we consider an existence of simultaneous terminalization for K. Altmann’s homogeneous toric deformation whose central fibre is an affine Gorenstein toric sin...

one of the most valid and efficient models of long rod projectile penetration in homogeneous targets is tate and alekseevskii’s (a&t;) model. based on tate’s model, the present research tries to calculate the optimum speeds to achieve the maximum penetration depth in the homogeneous targets. the proposed collision speed-penetration depth diagrams are developed using tate’s model. in this way, v...