Perfect Simulation of a Coupling Achieving the (d)over-bar-distance Between Ordered Pairs of Binary Chains of Infinite Order

We explicitly construct a stationary coupling attaining Ornstein`s (d) over bar -distance between ordered pairs of binary chains of infinite order. Our main tool is a representation of the transition probabilities of the coupled bivariate chain of infinite order as a countable mixture of Markov transition probabilities of increasing order. Under suitable conditions on the loss of memory of the chains, this representation implies that the coupled chain can be represented as a concatenation of i.i.d. sequences of bivariate finite random strings of symbols. The perfect simulation algorithm is based on the fact that we can identify the first regeneration point to the left of the origin almost surely.

On slowdown and speedup of transient random walks in random environment

We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(n (kappa) ) from the origin, kappa is an element of (0, 1). We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order O (n (nu 0)) from the origin, nu(0) is an element of (0, kappa)), and speedup (at time n, the particle is at a distance of order n (nu 1) from the origin , nu(1) is an element of (kappa, 1)), for the current location of the particle and for the hitting times. Also, we study probabilities of backtracking: at time n, the particle is located around (-n (nu) ), thus making an unusual excursion to the left. For the slowdown, our results are valid in the ballistic case as well.

The low-lying electronic states of BeP: a reliable and accurate quantum mechanical prediction

A very high level of theoretical treatment (complete active space self-consistent field CASSCF/MRCI/aug-cc-pV5Z) was used to characterize the spectroscopic properties of a manifold of quartet and doublet states of the species BeP, as yet experimentally unknown. Potential energy curves for 11 electronic states were obtained, as well as the associated vibrational energy levels, and a whole set of spectroscopic constants. Dipole moment functions and vibrationally averaged dipole moments were also evaluated. Similarities and differences between BeN and BeP were analysed along with the isovalent SiB species. The molecule BeP has a X (4)Sigma(-) ground state, with an equilibrium bond distance of 2.073 angstrom, and a harmonic frequency of 516.2 cm(-1); it is followed closely by the states (2)Pi (R(e) = 2.081 angstrom, omega(e) = 639.6 cm(-1)) and (2)Sigma(-) (R(e) = 2.074 angstrom, omega(e) = 536.5 cm(-1)), at 502 and 1976 cm(-1), respectively. The other quartets investigated, A (4)Pi (R(e) = 1.991 angstrom, omega(e) = 555.3 cm(-1)) and B (4)Sigma(-) (R(e) = 2.758 angstrom, omega(e) = 292.2 cm(-1)) lie at 13 291 and 24 394 cm(-1), respectively. The remaining doublets ((2)Delta, (2)Sigma(+)(2) and (2)Pi(3)) all fall below 28 000 cm(-1). Avoided crossings between the (2)Sigma(+) states and between the (2)Pi states add an extra complexity to this manifold of states.

Excited states of the CaAl molecule: An MRCI study

Accurate potential energy curves, dissociation energies and spectroscopic constants for several low-lying doublet and quartet electronic states of CaAl were investigated using the CASSCF/MRCI methodology, and the cc-pVQZ basis set. Our results represent an improvement over a previous theoretical description, and also characterizes new higher excited states not previously investigated, thus confirming the assignment of four excited states investigated experimentally. With the theoretical transition moment functions, transition probabilities and radiative lifetimes were estimated via Einstein spontaneous emission coefficients. (c) 2008 Elsevier B. V. All rights reserved.