Poincaré’s Relativistic Physics: Its Origins and Nature

Henri Poincaré (1854–1912) developed a relativistic physics by elevating the empirical inability to detect absolute motion, or motion relative to the ether, to the principle of relativity, and its mathematics ensured that it would be compatible with that principle. Although Poincaré’s aim and theory were similar to those of Albert Einstein (1879–1955) in creating his special theory of relativity, Poincaré’s relativistic physics should not be seen as an attempt to achieve Einstein’s theory but as an independent endeavor. Poincaré was led to advance the principle of relativity as a consequence of his reflections on late nineteenth-century electrodynamics; of his conviction that physics should be formulated as a physics of principles; of his conventionalistic arguments on the nature of time and its measurement; and of his knowledge of the experimental failure to detect absolute motion. The nonrelativistic theory of electrodynamics of Hendrik A.Lorentz (1853–1928) of 1904 provided the means for Poincaré to elaborate a relativistic physics that embraced all known physical forces, including that of gravitation. Poincaré did not assume any dynamical explanation of the Lorentz transformation, which followed from the principle of relativity, and he did not seek to dismiss classical concepts, such as that of the ether, in his new relativistic physics. Shaul Katzir teaches in the Graduate Program in History and Philosophy of Science, Bar Ilan University.     

Many-body effects in molecular photoionization in intense laser fields; time-dependent Hartree-Fock simulations

The time evolution of the reduced single electron density matrix for eight electrons in a one-dimensional finite box potential driven by an intense laser field is calculated by numerically integrating the time-dependent Hartree-Fock equations. We study the effects of the Coulomb interaction, field intensity, and frequency on the time profile of the ionization process. Our computed saturation ionization intensity (Isat) is in good agreement with experimental results for decatetraene [Ivanov et al. J. Chem. Phys. 117, 1575 (2002)].     

The effect of adsorbed oxygen on the surface potential of n-GaAs(110)

Potential variations on semiconductor surfaces are often mapped using a combination of constant current topographic and local surface photo-voltage (SPV) imaging. SPV imaging provides a direct measurement of surface-potential variations at large lateral distances from a charged defect or adsorbate. However, directly above the defect, variations in the SPV signal need to be interpreted in terms of surface screening, traps, and band bending. We have examined these effects using isolated oxygen atoms on a GaAS(110) surface, which is free of surface states. We interpret variations in the SPV signal in terms of a simple electrostatic model which considers the oxygen-induced Coulomb potential and corresponding image potential, both of which affect the surface density of states.     

Reduced equations of motion for collision-induced intersystem crossing

A model is proposed for collision-induced intersystem crossing in “intermediate case” and small molecules. The collisions are assumed to cause dephasing (T₂) among the zero order singlet and triplet molecular states. The combined effect of the intramolecular spin-orbit coupling (μ) and the collisional dephasing, results in the experimentally observable relaxation of populations (T₁). The basic assumption of the present model is that the duration of a collision τ_c is short compared to the intramolecular coupling (μτ_c ? 1). Reduced equations of motion for the molecular density matrix are derived and conditions for observing nonexponential relaxations are discussed. The model demonstrates the equivalence of T₁ and T₂ processes, depending on our choice of a basis set.     

On the dynamics of excitations in disordered systems

A new, time-local (TL) reduced equation of motion for the probability distribution of excitations in a disordered system is developed. ToO(k²) the TL equation results in a Gaussian spatial probability distribution, i.e, P(r, t) = [(2)^1/2]^–dexp(-r²/2²), where = (t) is a correlation length, andr = ¦r¦. The corresponding distribution derived from the Hahn-Zwanzig (HZ) equation is more complicated and assumes the asymptotic (r ) form: P(r, s)(s ^d )^–1exp(–r/) · (r/)^(1-d)/2 where = (s),d is the space dimensionality, ands is the Laplace transform variable conjugate tot. The HZ distribution generalizes the scaling form suggested by Alexanderet al. ford= 1. In the Markov limit (t)t, (s)1/s, and the two distributions are identical (ordinary diffusion).     

Nonlinear optical properties of confined excitons in clusters

Size effects in femtosecond photon echo spectroscopy of neat clusters are calculated using a quasiparticle representation of the nonlinear response. We extend our previous study of cooperative effects on the nonlinear response of assemblies of two level molecules [J. A. Leegwater and S. Mukamel, Phys. Rev. A46, 452 (1992)] to allow for nuclear motion and to have an s-p model of polarizable atoms. Photon echos in Benzene/Argon clusters are calculated using a semiclassical phase averaging procedure [L. E. Fried and S. Mukamel, Adv. Chem. Phys. (in Press)].     

Critical concentrations for intermolecular interpenetration and entanglements

In this paper it is shown that three critical concentrations, observable through light scattering, solution and melt viscosity, exist for high molecular weight polymers: C_i, observed through light scattering, reflects the onset of intermolecular interpenetration at the point of complete space-filling, the point where all the available space is taken up by segments with no change in the intramolecular segmental density; C_ep, observed through solution viscosity determination, reflects the appearance of dynamically measurable quantities of entanglements in the peripheral regio of the molecular coils; and C_ec, obtained from melt viscosity measurements, reveals the appearance of such entanglements in the core regions of the coils. The relationship between these critical concentrations is C_i < C_ep < C_ec. This reflects the fact that intermolecular interpenetration occurs at significantly lower concentrations than intermolecular entanglements, and that the static light scattering is insensitive to entanglements while the dynamic viscosity measurements are sensitive to entanglements but do not sense intermolecular interpenetrations. A tentative explanation of these observations, based on the macromolecular domain model, is proposed.