Continued-fraction representation of the Kraus map for non-Markovian reservoir damping

Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes-Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field

Modified atomic decay rate near absorptive scatterers at finite temperature

The change in the decay rate of an excited atom that is brought about by extinction and thermal-radiation effects in a nearby dielectric medium is determined from a quantummechanical model. The medium is a collection of randomly distributed thermally-excited spherical scatterers with absorptive properties. The modification of the decay rate is described by a set of correction functions for which analytical expressions are obtained as sums over contributions from the multipole moments of the scatterers. The results for the modified decay rate as a function of the distance between the excited atom and the dielectric medium show the influence of absorption, scattering and thermal-radiation processes. Some of these processes are found to be mutually counteractive. The changes in the decay rate are compared to those following from an effective-medium theory in which the discrete scatterers are replaced by a continuum

Damping and dispersion of oscillating modes of a multicomponent ionic mixture in a magnetic field

The collective-mode spectrum of a multicomponent magnetized ionic mixture for small wave number k is studied with the use of magnetohydrodynamics and formal kinetic theory. Apart from the usual thermal and diffusive modes, the spectrum contains a set of four oscillating modes. By evaluating the k^2 contributions to the eigenfrequencies, the damping and the dispersion of these oscillating modes are determined. The long-range nature of the Coulomb interactions is shown to imply that Burnett terms with higher-order gradients in the linear phenomenological laws have to be taken into account in order to obtain a full description of all damping and dispersion effects.Comment: 25 page

Cross-linguistic influence in simultaneous and early sequential bilingual children: A meta-analysis

Although cross-linguistic influence at the level of morphosyntax is one of the most intensively studied topics in child bilingualism, the circumstances under which it occurs remain unclear. In this meta-analysis, we measured the effect size of cross-linguistic influence and systematically assessed its predictors in 750 simultaneous and early sequential bilingual children in 17 unique language combinations across 26 experimental studies. We found a significant small to moderate average effect size of cross-linguistic influence, indicating that cross-linguistic influence is part and parcel of bilingual development. Language dominance, operationalized as societal language, was a significant predictor of cross-linguistic influence, whereas surface overlap, language domain and age were not. Perhaps an even more important finding was that definitions and operationalisations of cross-linguistic influence and its predictors varied considerably between studies. This could explain the absence of a comprehensive theory in the field. To solve this issue, we argue for a more uniform method of studying cross-linguistic influence

Atomic decay near a quantized medium of absorbing scatterers

The decay of an excited atom in the presence of a medium that both scatters and absorbs radiation is studied with the help of a quantum-electrodynamical model. The medium is represented by a half space filled with a randomly distributed set of non-overlapping spheres, which consist of a linear absorptive dielectric material. The absorption effects are described by means of a quantized damped-polariton theory. It is found that the effective susceptibility of the bulk does not fully account for the medium-induced change in the atomic decay rate. In fact, surface effects contribute to the modification of the decay properties as well. The interplay of scattering and absorption in the total decay rate is discussed.Comment: 20 pages, 1 figur

Field quantization in inhomogeneous anisotropic dielectrics with spatio-temporal dispersion

A quantum damped-polariton model is constructed for an inhomogeneous anisotropic linear dielectric with arbitrary dispersion in space and time. The model Hamiltonian is completely diagonalized by determining the creation and annihilation operators for the fundamental polariton modes as specific linear combinations of the basic dynamical variables. Explicit expressions are derived for the time-dependent operators describing the electromagnetic field, the dielectric polarization and the noise term in the latter. It is shown how to identify bath variables that generate the dissipative dynamics of the medium.Comment: 24 page