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

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 ;

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

Glassy dynamics and domains: exact results for the East model

A general matrix-based scheme for analyzing the long-time dynamics in kinetically constrained models such as the East model is presented. The treatment developed here is motivated by the expectation that slowly-relaxing spin domains of arbitrary size govern the highly cooperative events that lead to spin relaxation at long times. To account for the role of large spin domains in the dynamics, a complete basis expressed in terms of domains of all sizes is introduced. It is first demonstrated that accounting for single domains of all possible sizes leads to a simple analytical result for the two-time single-spin correlation function in the East model that is in excellent quantitative agreement with simulation data for equilibrium spin up density values c greater or equal to 0.6. It is then shown that including also two neighboring domains leads to a closed expression that describes the slow relaxation of the system down to c approximately 0.3. Ingredients of generalizing the method to lower values of c are also provided, as well as to other models. The main advantage of this approach is that it gives explicit analytical results and that it requires neither an arbitrary closure for the memory kernel nor the construction of an irreducible memory kernel. It also allows one to calculate quantities that measure heterogeneity in the same framework, as is illustrated on the neighbor-pair correlation function and the distribution of relaxation times.Comment: 17 pages, 5 figures (best viewed in color). Submitted to J. Chem. Phy