相关论文: Sum rules in the oscillator radiation processes
It is shown that the well known sum rules for oscillator strengths for Hydrogen atom can be generalised to a whole class of sum rules. The sum rules have contributions from the discrete and the continuum parts of the spectrum neither of…
Sum rules are elegant formulas that relate entropy functionals to coefficients associated with orthogonal polynomials [Sim11]. In a series of paper (see for example [GNR16], [GNR17], [BSZ18a], [BSZ18b]), interesting connections have been…
Generating functions and sum rules are discussed for transition probabilities between quantum oscillator eigenstates with time-dependent parameters.
Uncertainties $(\Delta x)^2$ and $(\Delta p)^2$ are analytically derived in an $N$-coupled harmonic oscillator system when spring and coupling constants are arbitrarily time-dependent and each oscillator is in an arbitrary excited state.…
The status of our understanding of relativistic sum rules is reviewed. The recent development of new theoretical methods for the evaluation of these sum rules offers hope for further advances in this challenging field. These new techniques…
A sum rule is an identity connecting the entropy of a measure with coefficients involved in the construction of its orthogonal polynomials (Jacobi coefficients). Our paper is an extension of Gamboa, Nagel and Rouault (2016), where we have…
I derive new sum rules for the electronic oscillator strengths in a periodic or nearly periodic potential, which apply within a single energy band and between any two bands. The physical origin of these sum rules is quite unlike that of…
The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary…
A formal derivation of the polarization correlations between the incident electron and the scattered electron is given for a general class of transition operators. In correspondence to the case of bremsstrahlung emission, three sum rules…
We derive two model-independent sum rules relating the transition matrix elements for radiative and strong decays of excited heavy mesons to properties of the lowest-lying heavy mesons. The sum rule for the radiative decays is an analog of…
We calculate transition amplitudes and probabilities between the coherent and Fock states of a quantum harmonic oscillator with a moving center for an arbitrary law of motion. These quantities are determined by the Fourier transform of the…
The calculations of masses and decay constants of the radial excitations of light pseudoscalar and scalar mesons within QCD sum rules method are briefly reviewed. The predictions are based on the $1/N_c$-supported model spectra, which…
Truncated sum rules have been used to calculate the fundamental limits of the nonlinear susceptibilities; and, the results have been consistent with all measured molecules. However, given that finite-state models result in inconsistencies…
The nonlinear oscillator model allows a basic understanding of all nonlinear processes and can be adopted to analyse optical vibrational modes and electronic transition in molecules and crystals, in order to derive general properties of…
One-dimensional problem for quantum harmonic oscillator with "regular+random" frequency subjected to the external "regular+random" force is considered. Averaged transition probabilities are found.
The interrelation between the condensation energy and the optical sum rules has been investigated. It has been shown that the so called 'partial' sum rule violation is related mainly to a temperature dependence of the relaxation rate rather…
We introduce a new, probability-level approach to calculations in scalar field particle scattering. The approach involves the implicit summation over final states, which makes causality manifest since retarded propagators emerge naturally.…
Classical sum rules arise in a wide variety of physical contexts. Asymptotic expressions have been derived for many of these sum rules in the limit of long orbital period (or large action). Although sum rule convergence may well be…
An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal…
A class of sum rules for inelastic light scattering is developed. We show that the first moment of the non-resonant response provides information about the potential energy in strongly correlated systems. The polarization dependence of the…