Stochastic monotonicity and duality for continuous time Markov chains with general q-Matrix

The key problems in discussing stochastic monotonicity and duality for continuous time Markov chains are to give the criteria for existence and uniqueness and to construct the associated monotone processes in terms of their infinitesimal q -matrices. In their recent paper, Chen and Zhang [6] discussed these problems under the condition that the given q-matrix Q is conservative. The aim of this paper is to generalize their results to a more general case, i.e., the given q-matrix Q is not necessarily conservative. New problems arise 'in removing the conservative assumption. The existence and uniqueness criteria for this general case are given in this paper. Another important problem, the construction of all stochastically monotone Q-processes, is also considered.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Spin asymmetries in spatially resolved processes of ionization of heavy atoms by relativistic electrons

The triple-differential cross section for ionization of a heavy atom is shown to depend on the spin of the incident electron even if this is polarized entirely parallel or antiparallel to its direction of propagation, the atom is unpolarized, and the spins of the ejected electrons are not resolved. Quantitative predictions for the spin asymmetry are presented in a relativistic distorted-wave Born approximation. Simple physical models are introduced to understand both these results and further symmetry properties involving the reversal of a spatial momentum component also.

Entanglement generation in harmonic chains: Tagging by squeezing

We address the problem of springlike coupling between bosons in an open-chain configuration where the counter-rotating terms are explicitly included. We show that fruitful insight can be gained by decomposing the time-evolution operator of this problem into a pattern of linear-optics elements. This allows us to provide a clear picture of the effects of the counter-rotating terms in the important problem of long-haul entanglement distribution. The analytic control over the variance matrix of the state of the bosonic register allows us to track the dynamics of the entanglement. This helps in designing a global addressing scheme, complemented by a proper initialization of the register, which quantitatively improves the entanglement between the extremal oscillators in the chain, thus providing a strategy for feasible long-distance entanglement distribution.

Density functional and Monte Carlo studies of sulfur. I. Structure and bonding in S-n rings and chains (n=2-18) (vol 118, pg 9257, 2003)

Density functional calculations have been performed for ring isomers of sulfur with up to 18 atoms, and for chains with up to ten atoms. There are many isomers of both types, and the calculations predict the existence of new forms. Larger rings and chains are very flexible, with numerous local energy minima. Apart from a small, but consistent overestimate in the bond lengths, the results reproduce experimental structures where known. Calculations are also performed on the energy surfaces of S8 rings, on the interaction between a pair of such rings, and the reaction between one S8 ring and the triplet diradical S8 chain. The results for potential energies, vibrational frequencies, and reaction mechanisms in sulfur rings and chains provide essential ingredients for Monte Carlo simulations of the liquid–liquid phase transition. The results of these simulations will be presented in Part II.

Magnetomechanical interplay in spin-polarized point contacts

We investigate the interplay between magnetic and structural dynamics in ferromagnetic atomic point contacts. In particular, we look at the effect of the atomic relaxation on the energy barrier for magnetic domain wall migration and, reversely, at the effect of the magnetic state on the mechanical forces and structural relaxation. We observe changes of the barrier height due to the atomic relaxation up to 200%, suggesting a very strong coupling between the structural and the magnetic degrees of freedom. The reverse interplay is weak; i.e., the magnetic state has little effect on the structural relaxation at equilibrium or under nonequilibrium, current-carrying conditions.