Using an operational definition we quantify the entanglement, E(P), between two parties who share an arbitrary pure state of N indistinguishable particles. We show that E(P)< or =E(M), where E(M) is the bipartite entanglement calculated from the mode-occupation representation. Unlike E(M), E(P) is superadditive. For example, E(P)=0 for any single-particle state, but the state |1>|1>, where both...

Abstract. In this paper, the author propose a numerical method to compute the solution of the Cauchy problem: wt − (w m wx)x = w , the initial condition is a nonnegative function with compact support, m > 0, 1 < p < m + 1. The problem is split in two parts: A hyperbolic term solved by using the Hopf and Lax formula and a parabolic term solved by a backward linearized Euler method in time and a ...

We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold M admitting real Killing spinors (resp. parallel spinors), there exist warped product metrics η on M × R such that (M × R, η) admit Einstein spinors (resp. weak Killing spinors). To prove the result we split the Einstein-Dirac equ...

Let F be a perfect field and M(F ) the nonassociative simple Moufang loop consisting of the units in the (unique) split octonion algebra O(F ) modulo the center. Then Aut(M(F )) is equal to G2(F )o Aut(F ). In particular, every automorphism of M(F ) is induced by a semilinear automorphism of O(F ). The proof combines results and methods from geometrical loop theory, groups of Lie type and compo...