Related papers: Sum rules and large deviations for spectral matrix…
The Kramers-Kronig relations and various oscillator strength sum rules represent strong constraints on the physical response of materials. In this work, taking inspiration from the well-established equivalence between $f-$sum rules and…
Taking the example of the most popular and well-established Borel / Laplace / Exponential sum rule (LSR), I shortly review some of its recent applications in hadron physics namely the estimates of non-perturbative condensates, the…
The validity of Weinberg's two sum rules for massless QCD, as well as the six additional sum rules introduced into chiral perturbation theory by Gasser and Leutwyler, are investigated for the extended Nambu-Jona-Lasinio chiral model that…
The Gerasimov-Drell-Hearn sum rule is one of several dispersive sum rules that connect the Compton scattering amplitudes to the inclusive photoproduction cross sections of the target under investigation. Being based on such universal…
In this paper, we establish a new law of large numbers with the rate of convergence for special partial sums in a probability space. The proof relies on nonlinear expectation theory, as the uncertainty of random variables in the special…
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…
We derive formulae for Gram matrices arising in the Nyman--Beurling reformulation of the Riemann hypothesis. The development naturally leads upon series of the form $S(x) = \sum_{n\ge 1} R(nx)$ and their reciprocity relations. We give…
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…
In this paper properties of the determinant of a Hermitian matrix are investigated, and determinantal representations of the inverse of a Hermitian coquaternionic matrix are given. By their using, Cramer's rules for left and right systems…
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…
It is shown that at least 50% of the probability mass of a sum of independent Rademacher random variables is within one standard deviation from its mean. This lower bound is sharp, it is much better than for instance the bound that can be…
Images obtained from coherent illumination processes are contaminated with speckle. A prominent example of such imagery systems is the polarimetric synthetic aperture radar (PolSAR). For such remote sensing tool the speckle interference…
The Gerasimov-Drell-Hearn sum rule is a generic relation that has been used to make significant contributions to research in hadronic physics. It connects the spin-dependent cross-section for photoproduction off a particle to the squared…
Consider the random matrix $\Sigma = D^{1/2} X \widetilde D^{1/2}$ where $D$ and $\widetilde D$ are deterministic Hermitian nonnegative matrices with respective dimensions $N \times N$ and $n \times n$, and where $X$ is a random matrix with…
In most versions of beyond the standard model (BSM) physics, the Yukawa couplings of the quarks and charged leptons are not all to the same complex scalar doublet but to different ones. Comparison to the standard model (SM) with only one…
In deep-inelastic scattering experiments, there is a general connection between subtractions in dispersion relations, violations of sum-rules and $\delta$-functions in parton distribution functions. It is explained why one might expect a…
We derive spectral sum rules in the shear channel for conformal field theories at finite temperature in general $d\geq 3$ dimensions. The sum rules result from the OPE of the stress tensor at high frequency as well as the hydrodynamic…
We show that the sum rule recently proved by Uraltsev in the heavy quark limit of QCD holds in relativistic quark models \`a la Bakamjian and Thomas, that were already shown to satisfy Isgur-Wise scaling and Bjorken sum rule. This new sum…
In this work we provide explicit calculations that support the conclusions stated in Phys. Rev. Lett. 111, 039102 (2013) (comment), regarding recent literature on transverse polarization. We also compare and contrast two methods of deriving…
Let m be a unidimensional measure with dimension d. A natural question is to ask if the measure m is comparable with the Hausdorff measure (or the packing measure) in dimension d. We give an answer (which is in general negative) to this…