[en] The decay of orthopositronium to three photons can be studied using a method of covariant amplitudes previously used to calculate the Z → 3γ partial decay rate. Three independent amplitudes are needed to describe the decay. The orthopositronium decay amplitudes were calculated analytically to one-loop order using the method of Passarino and Veltman for evaluating one-loop integrals. The amplitudes are given in terms of dilogrithms, logarithms, and other elementary functions. These amplitudes were used to find new, higher precision results for the one-loop decay rate and the contribution to the two-loop decay rate coming from the squares of the one-loop amplitudes

[en] The law for spontaneous transmutations, such as radioactive decay processes in atomic and nuclear physics, has been derived for the general case where the decay rates may be time dependent. The general formula for the ingrowth and decay in successive steps of radioactive decay chains, with multiple branches at each step, are given. As an example of current interest, the formalism is applied to the decay cascade of highly excited nuclei, where a time delay of the fission decay width is caused by the dynamics of the fission process. Several frequently used forms of the time dependence of the fission decay width are explored and discussed in connection with measurements of pre-scission γ- and particle emission

[en] We have studied the effects of colored multiplicative noises incorporated into the damping and the frequency term on the decay ratio (DR). It is clarified that the colored multiplicative noises can induce a long-time correlation and non-stationarity (random switching between unstable state and stable one) which give rise to the estimation errors of the DR

[en] The ill-conditioned nature of sums-of-exponentials analyses is confirmed and quantified, using synthetic noisy data. In particular, the magnification of errors is plotted for various two-exponential models, to illustrate its dependence on the ratio of decay constants, and on the ratios of amplitudes of the contributing terms. On moving from two- to three-exponential models, the condition deteriorates badly. It is also shown that the use of 'direct' Prony-type analyses (rather than general iterative nonlinear optimisation) merely aggravates the condition. (author)

[en] This work presents an analysis of synchronization and amplitude death (oscillation decay) phenomena in a pair of coupled Van der Pol oscillators under two types of conjugate couplings. The coupling is through diffusive flow of the conjugate or dissimilar variables and referred to as type 1 and type 2 coupling respectively. The analytical conditions for in-phase and out-of-phase synchronizations and amplitude death are determined. It is found that the amplitude death occurs only with type 2 coupling over a region of coupling strength. In this region, with decaying amplitude the oscillators approach a stationary state of negligible amplitude in anti-phase fashion. Beyond this range, on lower side the stable in-phase synchronization occurs if the frequencies of both the oscillators are equal, and on higher side uncontrolled amplitude growth occur. The type 1 coupling produces stable in-phase synchronization for positive coupling strength values and stable anti-phase synchronization for negative values under the condition that the coupling strength must be greater than or equal to the frequency detuning. In coupled systems the synchronization conditions are achieved maintaining the linear phase characteristics similar to the uncoupled oscillators. This study may be of interest in modeling the behavior of coupled biological and electrical oscillators. (paper)

[en] The properties of a simples quantum mechanical model for the decay of two equal mass particles are studied and related to some recent work on complex energy eigenvalues. It consists essentially in a generalization of the Lee-Friedrichs model for an unstable particle and gives a highly idealized version of the K⁰-anti K⁰ system, including CP violations. The model is completely solvable, thus allowing a comparison with the well known Weisskopf-Wigner formalism for the decay amplitudes. A different model, describing the same system is also briefly outlined. (Author)

[en] Relativistic corrections of order α² to the decay width of orthopositronium are calculated using the local quasipotential equation. Necessary contributions coming from the amplitude of the three-photon decay of orthopositronium and from the normalization of the wave function, as well as second-order perturbative corrections, are taken into account. 20 refs., 2 figs

[en] The decay properties of overlapping compound nucleus resonances are discussed. It is argued that the correlation width of Agassi,Weidenmuller and Mantzouranis is to be identified with the average total width of Kawai, Kerman and McVoy. It is also shown that in the very strong coupling limit, the compound system behaves like a system with isolated resonances (weak absorption). (Author)

[en] A self-consistent theory of slowly evolving potential waves in non magnetized homogeneous collisionless plasma is presented. The theory includes: 1) description of the evolution of the particle distribution function at an arbitrary but slow, as compared to oscillations of trapped particles, change in the shape, phase velocity and energy of the wave; 2) corroboration of the fact that in the process of the slow evolution the waveform remains symmetrical relative to extreme points whose number is retained if the initial distribution function does not include singularities; 3) examination of the evolution of the shape and phase velocity of the wave in a first approximation of the found iteration procedure; 4) derivation and analysis of the fundamental evolution equation from which the criteria of stationarity and stability of the waves follow. On the basis of the theory a study has been made into the evolution of waves in bounded plasma with a fast beam whose initial velocity exceeds the maximum phase velocity of the waves. It is found that the waves lose stability in such a system. The optimum initial beam particle distribution function over velocities is found

[en] Part 3 of the paper mostly discusses the problem of justifying the approximation in which the reduced resolvent is replaced by the pole term alone. Imposing additional regularity assumptions on the function v, which specifies the interaction, it is possible to estimate the difference in the corresponding reduced propagators. The result is used to derive the estimate of the deviations from the exponential decay law which results from the pole approximation. With the exception of very small and very large times, the obtained bound is proportional to the fourth power of the coupling constant. The Fermi golden rule was proved for the model under consideration, and the present method compared to the one previously used by Demuth. (author). 7 refs