Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method

For non-zero $\ell$ values, we present an analytical solution of the radial Schr\"{o}dinger equation for the rotating Morse potential using the Pekeris approximation within the framework of the Asymptotic Iteration Method. The bound state energy eigenvalues and corresponding wave functions are obtained for a number of diatomic molecules and the results are compared with the findings of the super-symmetry, the hypervirial perturbation, the Nikiforov-Uvarov, the variational, the shifted 1/N and the modified shifted 1/N expansion methods.Comment: 15 pages with 1 eps figure. accepted for publication in Journal of Physics A: Mathematical and Genera

Fluctuation-dissipation relationship in chaotic dynamics

We consider a general N-degree-of-freedom dissipative system which admits of chaotic behaviour. Based on a Fokker-Planck description associated with the dynamics we establish that the drift and the diffusion coefficients can be related through a set of stochastic parameters which characterize the steady state of the dynamical system in a way similar to fluctuation-dissipation relation in non-equilibrium statistical mechanics. The proposed relationship is verified by numerical experiments on a driven double well system.Comment: Revtex, 23 pages, 2 figure

Environment-induced dynamical chaos

We examine the interplay of nonlinearity of a dynamical system and thermal fluctuation of its environment in the ``physical limit'' of small damping and slow diffusion in a semiclassical context and show that the trajectories of c-number variables exhibit dynamical chaos due to the thermal fluctuations of the bath.Comment: Revtex, 4 pages and 4 figure

Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions

Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {\it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their co-ordinates and momenta we derive a generalized quantum Langevin equation in $c$-numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski equations are the {\it exact} quantum analogues of their classical counterparts. The present work is {\it independent} of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (Smoluchowski equation being considered in the overdamped limit).Comment: RevTex, 16 pages, 7 figures, To appear in Physical Review E (minor revision

Law enforcement and legal presumptions

We compare two alternative legal presumptions, one more pro-defendant than the other, with the objective of reducing bureaucratic corruption to any target level at minimum social costs, broadly defined to include law enforcement costs, trial costs, and verdict error costs. In the absence of collusion possibilities between law enforcers and offenders, presumption of innocence involves lower social costs for low corruption targets while presumption of guilt has a cost advantage for high corruption targets. Allowing for collusion enlarges the corruption range over which the presumed innocence rule will dominate. However, there are two possible exceptions to this outcome, namely, if the government's law enforcement budget is limited and if the offenders can be penalized only up to a maximum permissible limit. In each of these cases, presumption of guilt may become the cost-effective rule. © 2001 Elsevier Science

SCARS: Suturing wounds due to conflicts between non-functional requirements in autonomous and robotic systems

In autonomous and robotic systems, the functional requirements (FRs) and non-functional requirements (NFRs) are gathered from multiple stakeholders. The different stakeholder requirements are associated with different components of the robotic system and with the contexts in which the system may operate. This aggregation of requirements from different sources (multiple stakeholders) often results in inconsistent or conflicting sets of requirements. Conflicts among NFRs for robotic systems heavily depend on features of actual execution contexts. It is essential to analyze the inconsistencies and conflicts among the requirements in the early planning phase to design the robotic systems in a systematic manner. In this work, we design and experimentally evaluate a framework, called SCARS, providing: (a) a domain-specific language extending the ROS2 Domain Specific Language (DSL) concepts by considering the different environmental contexts in which the system has to operate, (b) support to analyze their impact on NFRs, and (c) the computation of the optimal degree of NFR satisfaction that can be achieved within different system configurations. The effectiveness of SCARS has been validated on the iRobot (Formula presented.) Create (Formula presented.) 3 robot using Gazebo simulation

Towards fully integrated photonic displacement sensors

Funding: European Union Horizon 2020 research and innovation programme under the Future and Emerging Technologies Open grant agreement Super-pixels No 829116.The field of optical metrology with its high precision position, rotation and wavefront sensors represents the basis for lithography and high resolution microscopy. However, the on-chip integration a task highly relevant for future nanotechnological devices necessitates the reduction of the spatial footprint of sensing schemes by the deployment of novel concepts. A promising route towards thisgoal is predicated on the controllable directional emission of the fundamentally smallest emitters of light, i.e. dipoles, as an indicator. Here we realize an integrated displacement sensor based on the directional emission of Huygens dipoles excited in an individual dipolar antenna. The position of the antenna relative to the excitation field determines its directional coupling into a six-way crossing of photonic crystal waveguides. In our experimental study supported by theoretical calculations, we demonstrate the first prototype of an integrated displacement sensor with a standard deviation of the position accuracy below λ=300 at room temperature and ambient conditions.Publisher PDFPeer reviewe

Reactivity of Phenylacetylene toward Unsymmetrical Disilenes: Regiodivergent [2+2] Cycloaddition vs. CH Addition

We report the regiodivergent reaction of phenylacetylene with a selection of disilenes Tip2Si=SiTipR as well as bridged tetrasiladienes Tip2Si=SiTip−LU−SiTip=SiTip2 (Tip=2,4,6-iPr3C6H2, R=aryl groups; LU=arylene linkers). The regioselectivity of the [2+2] cycloaddition as determined by NMR spectroscopy and X-ray crystallography is shown to strongly depend on the nature of the substituent R. The small size of the substituents compared to the Tip groups in both cases suggests a change in mechanism between the substrates with only hydrogen in the ortho-positions of R and LU and those with either ortho-methyl groups or condensed aromatic rings. In contrast, the presence of catalytic quantities of base completely suppresses cycloaddtion in favor of the formal CH addition of phenylacetylene. Quenching reactions with either MeI or MeOH after the stoichiometric application of deprotonated phenylacetylene as well as NMR studies at low temperature prove the intermediacy of an alkynyl-substituted disilanyl lithium and thus suggest a carbolithiation pathway for the net CH addition