Microscopic insight on the pump-probe relaxation dynamics of superconductors: Model study of MgB2 relaxation within nonlinear response theory

Here we present a quantum-statistical formulation of third-order polarization P(3)(t), which is induced in a sample by a sequence of incident external fields, and serves as a source of an emitted radiation field detected as a signal in pump-probe (PP) experiments. Our treatment is based on the perturbation expansion of the non-equilibrium density matrix for calculation of multi-time correlation functions, and the corresponding response function, at finite temperature. As a model for our study, the high-temperature superconductor MgB2 has been selected. Knowledge of the electronic structure of the studied system, and of the corresponding Eliashberg function that represents pertinent electron-phonon (EP) interactions, enabled us to distinguish non-equilibrium processes running over different time-periods in a sequence of interactions with laser pulses on a microscopic level. We have also derived temperature-dependent relaxation dynamics as a function of delay time between the pump and probe pulses. For the studied model system of MgB2, we have shown that an abrupt increase of the relaxation time at Tc, as detected by experiments, is the direct consequence of sudden changes in the character of EP coupling in transition from an adiabatic to a stabilized superconducting anti-adiabatic state, as it predicts the anti-adiabatic theory of electron-vibration interactions. The BCS model, which preserves the adiabatic character of EP coupling also below the critical temperature of MgB2, is basically unable to reflect the enormous sudden increase of the relaxation time. Based on diagrammatic perturbation theory, differences in the optical pump-optical probe and the optical pump-terahertz probe settings of MgB2 PP relaxation dynamics are discussed.Comment: 21 pages of the main text with 5 Figures and supplemental material in the form of Appendices A-

Short-term Forecasting Methods Based on the LEI Approach: The Case of the Czech Republic

This paper is aimed at developing short-term forecasting methods based on the LEI (leading economic indicators) approach. We use a set of econometric models (PCA, SURE) that provide estimates of GDP growth for the Czech economy for a co-incident quarter and a few quarters ahead. These models exploit monthly or quarterly indicators such as business surveys, financial or labour market indicators, monetary aggregates, interest rates and spreads, etc. that become available before the release of data on GDP growth itself. Our tests show that the LEIs provide relatively accurate forecasts of GDP fluctuations in the short run.Leading indicators, principal component analysis, seemingly unrelated regression estimate.

Theoretical aspects of high energy elastic nucleon scattering

The eikonal model must be denoted as strongly preferable for the analysis of elastic high-energy hadron collisions. The given approach allows to derive corresponding impact parameter profiles that characterize important physical features of nucleon collisions, e.g., the range of different forces. The contemporary phenomenological analysis of experimental data is, however, not able to determine these profiles unambiguously, i.e., it cannot give the answer whether the elastic hadron collisions are more central or more peripheral than the inelastic ones. However, in the collisions of mass objects (like protons) the peripheral behavior of elastic collisions should be preferred.Comment: 7 pages, 4 figure

Contemporary models of elastic nucleon scattering and their predictions for LHC

The analyses of elastic collisions of charged nucleons have been based standardly on West and Yennie formula. However, this approach has been shown recently to be inadequate from experimental as well as theoretical points of view. The eikonal model seems to be more pertinent as it enables to determine physical characteristics in impact parameter space. The contemporary phenomenological models cannot give, of course, any definite answer as the elastic collisions may be interpreted differently, as central or peripheral processes. Nevertheless, the predictions for the planned LHC energy have been given on their basis and the possibility of exact determination of luminosity has been considered.Comment: 11 pages, 6 figure