We consider the states with extremum products and sums of the uncertainties in non-commuting observables. These are illustrated by two specific examples of harmonic oscillator and the angular momentum states. It shows that the coherent states of the harmonic oscillator are characterized by the minimum uncertainty sum 〈(Δq)²〉 + 〈(Δp)²〉. The extremum values of the sums and products of the uncertainties of the components of the angular momentum are also obtained.

We give the theory of the free induction decay of two-level saturation resonances in the time-resolved laser saturation spectroscopy. The saturating and probe fields may be either co- or counter-propagating. The change-signal line-shape is analysed in detail in two cases of practical importance, namely when the saturating field is either strong or weak. The time evolution of the change-signal exhibits many interesting features which include Ramsey-type fringes, oscillatory decay, narrow resonances, line-narrowing etc. It is shown that by analysing the decay of the change-signal in time one can distinguish (i) various laser interaction processes such as population effects, coherence effects, three-photon Raman-type process, dynamic Stark splitting, power-broadening etc., and (ii) various relaxation mechanisms such as phase-changing collisions, etc.

The superposition of the non-abelian potentials of the formA′^μ=Aα^μ+aβ^μ andB′^μ=Bγ^μ+bη^μ are considered and the necessary as well as the sufficient conditions are obtained. The significance of the conditions is discussed and the constrained isotopic spins of the perturbation potentials (aβ^μ,bη^μ) are shown to be necessary for the superposition of these potenitals.

The theory of the coherent, two-photon resonant interaction of a monochromatic field with N atoms is given. It is seen that the dynamics of the atom-field system can be completely determined when the field is “strong”. Two specific examples are given: (i) two-photon absorption by atoms in ground state, and (ii) stimulated two-photon emission by fully excited atoms, assuming a coherent field in both cases. In case (ii), the field shows photon-antibunching after the decay of half of the atoms. The merits of our approach are shown by comparing with other treatments. Our results can also be applied to certain degenerate four-wave mixing processes which are described by a similar Hamiltonian.

The near-edge processes, such as X-ray absorption fine structure (XAFS) andresonant Raman scattering (RRS), are not incorporated in the available theoretical attenuation coefficients, which are known to be reliable at energies away from the shell/subshell ionization thresholds of the attenuator element. Theoretical coefficients are generally used to estimate matrix corrections in routine quantitative elemental analysis based on various X-ray emission techniques. A tabulation of characteristic X-ray energies across the periodic table is provided where those X-rays are expected to alter the attenuation coefficients due to XAFS from a particular shell/subshell of the attenuator element. The influence of XAFS to the attenuation coefficient depends upon the atomic environment and the photoelectron wave vector, i.e., difference in energies of incident X-ray and the shell/subshell ionization threshold of the attenuator element. Further, the XAFS at a shell/subshell will significantly alter the total attenuation coefficient if the jump ratio at that shell/subshell is large, e.g., the K shell, L₃ subshell and M$_5$ subshell. The tabulations can be considered as guidelines so as to know what can be expected due to XAFS in typical photon-induced X-ray emission spectrometry.

We investigate the relaxation dynamics of photogenerated carriers in silicon nanowires consisting of a crystalline core and a surrounding amorphous shell, using femtosecond time resolved differential reflectivity and transmission spectroscopy at 3.15 eV and 1.57 eV photon energies. The complex behaviour of the differential transmission and reflectivity transients is the mixed contributions from the crystalline core and the amorphous silicon on the nanowire surface and the substrate where competing effects of state-filling and photoinduced absorption govern the carrier dynamics. Faster relaxation rates are observed on increasing the photogenerated carrier density. Independent experimental results on crystalline silicon-on-sapphire (SOS) help us in separating the contributions from the carrier dynamics in crystalline core and the amorphous regions in the nanowire samples. Further, single-beam z-scan nonlinear transmission experiments at 1.57 eV in both open- and close-aperture configurations yield two-photon absorption coefficient 𝛽 (∼3 cm/GW) and nonlinear refraction coefficient 𝛾 ($−2.5 × 10^{−4}$ cm² /GW).

We apply random matrix theory (RMT) to investigate the structure of cross-correlation in 20 global financial time series after the global financial crisis of 2008. We find that the largest eigenvalue deviates from the RMT prediction and is sensitive to the financial crisis. We find that the components of eigenvectors corresponding to the second largest eigenvalue changes sign in response to the crisis. We show that 20 global financial indices exhibit multifractality. We find that the origin of multifractality is due to the long-range correlations as well as broad probability function in the financial indices, with the exception of the index of Taiwan, as in all other indices the multifractal degree for shuffled and surrogate series is weaker than the original series. We fit the binomial multifractal model to the global financial indices.

Cross-sections for one- and multinucleon transfer reactions, namely, ⁵⁸Ni(¹²C, ¹³C), ⁵⁸Ni(¹²C, ¹¹C), ⁵⁸Ni(¹²C, ¹¹B), ⁵⁸Ni(¹²C, ¹⁰B), ⁵⁸Ni(¹²C, ¹⁰Be), ⁵⁸Ni(¹²C, ⁹Be), ⁵⁸Ni(¹²C, ⁸Be_𝑔.s.), ⁵⁸Ni(¹²C, ⁷Be), ⁵⁸Ni(¹²C, ⁷Li) and ⁵⁸Ni(¹²C, ⁶Li) have been measured at an incident energy of 60 MeV. The reaction cross-section for the corresponding transfer channels in the system ¹²C+⁵⁶Fe have also been measured under the same kinematical conditions. Angular distribution of the elastic scattering cross-section is measured at 60 MeV. The measured elastic scattering angular distributions for these two systems have been analysed using the optical model search code SFRESCO and the potential parameters are extracted. The multinucleon transfer data are analysed to obtain cross-section dependence on the number of nucleons transferred and on the ground state 𝑄-values. The transfer probabilities for multinucleon stripping are extracted. A detailed comparison in the multiparticle stripping and elastic scattering cross-sections between these two systems are made to understand the mechanism of multinucleon transfer and possible role of two extra protons in ⁵⁸Ni target nucleus as compared to the ⁵⁶Fe core.

Spintronic heterostructures are considered to be the new generation terahertz (THz) sources because of their capability of producing high power and broadband THz radiation. Here, we provide a brief review on the state-of-the-art in this field. The optically excited bi- and tri-layer combinations of ferromagnetic and non-magnetic thin films have become increasingly popular. Towards optimising the THz conversion efficiency and broadband gapless spectrum from these THz emitters, various control parameters need to be taken into consideration. The inverse spin Hall effect in the heavy metal layer of the heterostructure is primarily responsible for the generation of THz pulses. A few new results on iron-, platinum- and tantalum-based heterostructures have also been reported here. It is observed that the Ta(2 nm)/Fe(2 nm)/Pt(2 nm) tri-layer heterostructure generates ~40(250)% stronger THz signal than the counterpart Fe(2 nm)/Pt(2 nm) (Fe(3 nm)/Ta(2 nm)) bi-layer heterostructure.