12 research outputs found
Complex density of continuum states in resonant quantum tunneling
We introduce a complex-extended continuum level density and apply it to
one-dimensional scattering problems involving tunneling through finite-range
potentials. We show that the real part of the density is proportional to a real
"time shift" of the transmitted particle, while the imaginary part reflects the
imaginary time of an instanton-like tunneling trajectory. We confirm these
assumptions for several potentials using the complex scaling method. In
particular, we show that stationary points of the potentials give rise to
specific singularities of both real and imaginary densities which represent
close analogues of excited-state quantum phase transitions in bound systems.Comment: 6 pages, 3 figure
Strong impact of light induced conical intersections on the spectrum of diatomic molecules
We show that dressing of diatomic molecules by running laser waves gives rise
to conical intersections (CIs). Due to presence of such CIs, the rovibronic
molecular motions are strongly coupled. A pronounced impact of the CI on the
spectrum of molecule is demonstrated via numerical calculation for weak
and moderate laser intensity, and an experiment is suggested on this basis. The
position of the light induced CI and the strength of its non-adiabatic
couplings can be chosen by changing the frequency and intensity of the used
running laser wave. This offers new possibilities to control the photo-induced
rovibronic molecular dynamics.Comment: 4 pages, 7 figure
A New Generalized Inequality for Covariance in N Dimensions
Inspired by the work of Zhefei He and Mingjin Wang which was published in the Journal of Inequalities and Applications in 2015, this paper further generalizes some related results to the case of multidimensional random variables. The resulting inequality for covariance is then applied to different multidimensional statistical distributions (multiuniform, multinomial, and multinormal). Coordinate dependence of the inequality is also examined. The obtained formulas could be useful for making estimates in multivariate statistics