Efficiency analysis of reaction rate calculation methods using analytical models I: The 2D sharp barrier

We analyze the efficiency of different methods for the calculation of reaction rates in the case of two simple analytical benchmark systems. Two classes of methods are considered: the first are based on the free energy calculation along a reaction coordinate and the calculation of the transmission coefficient, the second on the sampling of dynamical pathways. We give scaling rules for how this efficiency depends on barrier height and width, and we hand out simple optimization rules for the method-specific parameters. We show that the path sampling methods, using the transition interface sampling technique, become exceedingly more efficient than the others when the reaction coordinate is not the optimal one.Comment: 22 pages, 5 figure

Projective construction of the Zk\mathbb{Z}_k Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry

Multilayer fractional quantum Hall wave functions can be used to construct the non-Abelian states of the $\mathbb{Z}_k$ Read-Rezayi series upon symmetrization over the layer index. Unfortunately, this construction does not yield the complete set of $\mathbb{Z}_k$ ground states on the torus. We develop an alternative projective construction of $\mathbb{Z}_k$ Read-Rezayi states that complements the existing one. On the multi-layer torus geometry, our construction consists of introducing twisted boundary conditions connecting the layers before performing the symmetrization. We give a comprehensive account of this construction for bosonic states, and numerically show that the full ground state and quasihole manifolds are recovered for all computationally accessible system sizes. Furthermore, we analyze the neutral excitation modes above the Moore-Read on the torus through an extensive exact diagonalization study. We show numerically that our construction can be used to obtain excellent approximations to these modes. Finally, we extend the new symmetrization scheme to the plane and sphere geometries.Comment: 19 pages, 9 figure

ICT: Vehicle for Educational Development and Social Transformation

The world has become a global village as a result of the information tsunami and knowledge explosion being experienced as a result of Information Communication and Technology (ICT). The industrialized nations are miles ahead of the developing countries as a result of the information revolution. Education is a process by which society transmits its values, norms, mores, and ethos to generation yet unborn across time and space. The medium of transmission cuts across formal, non-formal and informal settings. This paper examines the impact/roles of ICT on education as an agent of social transformation and the hindrances of developing countries such as Nigeria in adopting ICT to aid their educational development and transformation of the society. The interconnection between information, ICT and social transformations is succinctly discussed in this paper. Furthermore, the paper examines the relationship between ICT and education and suggests measures that can be taken in adopting the use of ICT in Nigeria as well as the crucial role of government and the educational sector in this regard. The paper concludes that ICT make a significant contribution to the educational development and the social transformation of the Nigerian society

Dynamics of a two-level system coupled with a quantum oscillator in the very strong coupling limit

The time-dependent behavior of a two-level system interacting with a quantum oscillator system is analyzed in the case of a coupling larger than both the energy separation between the two levels and the energy of quantum oscillator ($\Omega < \omega < \lambda$, where $\Omega$ is the frequency of the transition between the two levels, $\omega$ is the frequency of the oscillator, and $\lambda$ is the coupling between the two-level system and the oscillator). Our calculations show that the amplitude of the expectation value of the oscillator coordinate decreases as the two-level system undergoes the transition from one level to the other, while the transfer probability between the levels is staircase-like. This behavior is explained by the interplay between the adiabatic and the non-adiabatic regimes encountered during the dynamics with the system acting as a quantum counterpart of the Landau-Zener model. The transition between the two levels occurs as long as the expectation value of the oscillator coordinate is driven close to zero. On the contrary, if the initial conditions are set such that the expectation values of the oscillator coordinate are far from zero, the system will remain locked on one level.Comment: 4 pages, 4 figures, to be published in Physical Review

The crystal and molecular structure of Hydridotetrakis(diethyl phenylphosphonite)cobalt(I)

An X-ray structure determination of the title compound shows that the co-ordination about the cobalt atom is approximately trigonal bipyramidal; n.m.r. data indicate that the complex is non-rigid in solution