Entanglement witnesses arising from Choi type positive linear maps

We construct optimal PPTES witnesses to detect $3\otimes 3$ PPT entangled edge states of type $(6,8)$ constructed recently \cite{kye_osaka}. To do this, we consider positive linear maps which are variants of the Choi type map involving complex numbers, and examine several notions related to optimality for those entanglement witnesses. Through the discussion, we suggest a method to check the optimality of entanglement witnesses without the spanning property.Comment: 18 pages, 4 figures, 1 tabl

Universality classes and crossover behaviors in non-Abelian directed sandpiles

We study universality classes and crossover behaviors in non-Abelian directed sandpile models, in terms of the metastable pattern analysis. The non-Abelian property induces spatially correlated metastable patterns, characterized by the algebraic decay of the grain density along the propagation direction of an avalanche. Crossover scaling behaviors are observed in the grain density due to the interplay between the toppling randomness and the parity of the threshold value. In the presence of such crossovers, we show that the broadness of the grain distribution plays a crucial role in resolving the ambiguity of the universality class. Finally, we claim that the metastable pattern analysis is important as much as the conventional analysis of avalanche dynamics.Comment: 10 pages, 7 figures, 1 table; published in PRE as the full paper of PRL v101, 218001 (2008

Horizon Mass Theorem

A new theorem for black holes is found. It is called the horizon mass theorem. The horizon mass is the mass which cannot escape from the horizon of a black hole. For all black holes: neutral, charged or rotating, the horizon mass is always twice the irreducible mass observed at infinity. Previous theorems on black holes are: 1. the singularity theorem, 2. the area theorem, 3. the uniqueness theorem, 4. the positive energy theorem. The horizon mass theorem is possibly the last general theorem for classical black holes. It is crucial for understanding Hawking radiation and for investigating processes occurring near the horizon.Comment: A new theorem for black holes is establishe

Collective Dynamics of Random Polyampholytes

We consider the Langevin dynamics of a semi-dilute system of chains which are random polyampholytes of average monomer charge $q$ and with a fluctuations in this charge of the size $Q^{-1}$ and with freely floating counter-ions in the surrounding. We cast the dynamics into the functional integral formalism and average over the quenched charge distribution in order to compute the dynamic structure factor and the effective collective potential matrix. The results are given for small charge fluctuations. In the limit of finite $q$ we then find that the scattering approaches the limit of polyelectrolyte solutions.Comment: 13 pages including 6 figures, submitted J. Chem. Phy

Stiff polymer in monomer ensemble

We make use of the previously developed formalism for a monomer ensemble and include angular dependence of the segments of the polymer chains thus described. In particular we show how to deal with stiffness when the polymer chain is confined to certain regions. We investigate the stiffness from the perspectives of a differential equation, integral equations, or recursive relations for both continuum and lattice models. Exact analytical solutions are presented for two cases, whereas numerical results are shown for a third case.Comment: 10 pages, including 6 figure

Large magnetoresistance using hybrid spin filter devices

A magnetic "spin filter" tunnel barrier, sandwiched between a non-magnetic metal and a magnetic metal, is used to create a new magnetoresistive tunnel device, somewhat analogous to an optical polarizer-analyzer configuration. The resistance of these trilayer structures depends on the relative magnetization orientation of the spin filter and the ferromagnetic electrode. The spin filtering in this configuration yields a previously unobserved magnetoresistance effect, exceeding 100%.Comment: 3.5 pages, 3 figures, submitted to Appl. Phys. Let