Nonlinear Model of non-Debye Relaxation

We present a simple nonlinear relaxation equation which contains the Debye equation as a particular case. The suggested relaxation equation results in power-law decay of fluctuations. This equation contains a parameter defining the frequency dependence of the dielectric permittivity similarly to the well-known one-parameter phenomenological equations of Cole-Cole, Davidson-Cole and Kohlrausch-Williams-Watts. Unlike these models, the obtained dielectric permittivity (i) obeys to the Kramers-Kronig relation; (ii) has proper behaviour at large frequency; (iii) its imaginary part, conductivity, shows a power-law frequency dependence \sigma ~ \omega^n where n<1 corresponds to empirical Jonscher's universal relaxation law while n>1 is also observed in several experiments. The nonlinear equation proposed may be useful in various fields of relaxation theory

Deflection of field-free aligned molecules

We consider deflection of polarizable molecules by inhomogeneous optical fields, and analyze the role of molecular orientation and rotation in the scattering process. It is shown that molecular rotation induces spectacular rainbow-like features in the distribution of the scattering angle. Moreover, by pre-shaping molecular angular distribution with the help of short and strong femtosecond laser pulses, one may efficiently control the scattering process, manipulate the average deflection angle and its distribution, and reduce substantially the angular dispersion of the deflected molecules. This opens new ways for many applications involving molecular focusing, guiding and trapping by optical and static fields.Comment: 4 pages, 4 figure

Radiative orbital electron capture by the atomic nucleus

The rate for the photon emission accompanying orbital 1S electron capture by the atomic nucleus is recalculated. While a photon can be emitted by the electron or by the nucleus, the use of the length gauge significantly suppresses the nuclear contribution. Our calculations resolve the long standing discrepancy of theoretical predictions with experimental data for $\Delta J=2$ forbidden transitions. We illustrate the results by comparison with the data established experimentally for the first forbidden unique decays of $^{41}$Ca and $^{204}$Tl.Comment: 18 pages, 2 figures, submitted to Phys. Rev.

Short-time fluctuations of displacements and work

A recent theorem giving the initial behavior of very short-time fluctuations of particle displacements in classical many-body systems is discussed. It has applications to equilibrium and non-equilibrium systems, one of which is a series expansion of the distribution of work fluctuations around a Gaussian function. To determine the time-scale at which this series expansion is valid, we present preliminary numerical results for a Lennard-Jones fluid. These results suggest that the series expansion converges up to time scales on the order of a picosecond, below which a simple Gaussian function for the distribution of the displacements can be used.Comment: 10 pages, 3 figure

Non-equilibrium Thermodynamics and Fluctuations

In the last ten years, a number of ``Conventional Fluctuation Theorems'' have been derived for systems with deterministic or stochastic dynamics, in a transient or in a non-equilibrium stationary state. These theorems gave explicit expressions for the ratio of the probability to find the system with a certain value of entropy (or heat) production to that of finding the opposite value. A similar theorem for the fluctuations of the work done on a system has recently been demonstrated experimentally for a simple system in a transient state, consisting of a Brownian particle in water, confined by a moving harmonic potential. In this paper we show that because of the interaction between the stochastic motion of the particle in water and its deterministic motion in the potential, very different new heat theorems are found than in the conventional case. One of the consequences of these new heat Fluctuation Theorems is that the ratio of the probability for the Brownian particle to absorb heat from rather than supply heat to the water is much larger than in the Conventional Fluctuation Theorem. This could be of relevance for micro/nano-technology.Comment: 10 pages, 6 figures. Some corrections in the text were made. Submitted to Physica

ICT-Investment, Knowledge Accumulation and Endogenous Growth

In this paper we present an endogenous growth model based on Lucas (1988). We have extended the Lucas model by incorporating ICT-capital next to human capital. We take account of spillovers from ICT use in human capital formation to final output production. The effects on growth of these spillovers depend very much on whether they are external or completely internalised. We find that welfare is positively affected, the stronger these spillovers are, but also the more these spillovers are internalised. In addition, we find that in the case of limited internalised knowledge spillovers, we may face a multiple equilibria steady state growth situation, that has an inherent tendency to select the non-optimum (high growth) equilibrium in which all types of capital are ‘over accumulated’, including ICT-capital. This suggests that there is room for policy intervention here, because there exists an ‘optimum’ value of the knowledge-spillover parameter where both equilibria coincide and over accumulation does not happen.economics of technology ;

Endogenous Technical Change and Skill Biases in Employment Opportunities

In this paper we present a model that addresses the issue of the uneven distribution ofemployment opportunities over low- and high-skilled workers in a context of skill-biasedendogenous technical change. In our model, technical change consists in part of productinnovation. There is also process innovation to the extent that new products can be producedin two different ways, either using high-skilled workers, or using low-skilled workers afteradapting the production process of a new product. The model combines elements fromKrugman’s (1979) North-South framework, Vernon’s (1966) life-cycle hypothesis andAghion and Howitt’s (1992) work on creative destruction. We show that from a growth pointof view, lowering the relative wages for low-skilled workers does indeed reduceunemployment in the short run, as expected, but it also lowers growth. This is reminiscent ofKleinknecht’s (1998) contention that moderate wage growth makes for slow technical change.economics of technology ;

A Simple Endogenous Growth Model With Asymmetric Employment Opportunities by Skill

In this paper we present the outlines of an endogenous growth model that focuses on the labour market- and skill-aspects of economic policy measures that may have an impact on technological change, and hence on the long term effectiveness of the policy measures concerned. The link between skills and technology is two-fold. On the one hand, new technology is high-skilled intensive, while on the other hand, process R&D may actively change the skill-mix of existing production technologies in the direction of a more intensive use of least-cost production factors/skills. Hence, we endogenise both product R&D and process R&D decisions. The product R&D generates new varieties of goods with a higher quality than older varieties. New and older varieties are assumed to be imperfect substitutes, so that new varieties only gradually replace older varieties. Process R&D in turn is geared towards downscaling the skill-requirements of the jobs associated with producing the different varieties of output. Because high-skilled labour has different uses (it is an input to final output production, but also into product and process R&D activities), whereas low-skilled labour is used only in final output generation, we can show how various alternative policy measures may affect R&D decisions, hence growth performance, but also the distribution of income between skills. We also show that the promotion of process R&D in particular has beneficial effects both for the employment perspectives of low-skilled workers and for growth in general. In simulation experiments with the model we show that the model, even in its present state, is able to mimic the stylised facts reported by Acemoglu (1997), who observed for the US that an increase in the supply of high-skilled labour does not necessarily imply a fall in the relative wage rate of high-skilled workers in the long run. We show that the ensuing increase in R&D activity creates its own demand for high-skilled workers when new products arrive on the market that are high-skilled intensive during the first phase of their life-cycle, as we assume it to be the case. This in turn invokes endogenous process R&D reactions that change the long term composition of the demand for labour by skill and by sector. In various experiments we found that the model generates an interesting interplay between both types of R&D that may have important consequences for the distribution of income between skills, for growth and more generally for the design of economic policy.economics of technology ;