Related papers: Sum rules in multiphoton coincidence rates
We revisit the photo-absorption sum rule for real Compton scattering from the proton and from nuclear targets. In analogy with the Thomas-Reiche-Kuhn sum rule appropriate at low energies, we propose a new "constituent quark model" sum rule…
We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…
We present a general simplification of quantified SMT formulas using variable elimination. The simplification is based on an analysis of the ground terms occurring as arguments in function applications. We use this information to generate a…
We provide an asymptotically tight, computationally efficient approximation of the joint spectral radius of a set of matrices using sum of squares (SOS) programming. The approach is based on a search for an SOS polynomial that proves…
We show a simple method for constructing larger matrices but preserving the spectral radius. This yields a sufficient criteria for two square matrices of arbitrary dimension have the same spectral radius, a way to compare spectral radii of…
We discuss oscillations of atmospheric and solar neutrinos into sterile neutrinos in the 2+2 scheme. A zeroth order sum rule requires equal probabilities for oscillation into nu_s and nu_tau in the solar+atmospheric data sample. Data does…
The problem of convergence in law of normed sums of exchangeable random variables is examined. First, the problem is studied w.r.t. arrays of exchangeable random variables, and the special role played by mixtures of products of stable laws…
The iterative method of Sinkhorn allows, starting from an arbitrary real matrix with non-negative entries, to find a so-called 'scaled matrix' which is doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and with all…
We present a theoretical model which allows to keep track of all photons in an interferometer. The model is implemented in a numerical scheme, and we simulate photon interference measurements on one, two, four, and eight slits. Measurements…
Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…
In this paper, we investigate property testing whether or not a degree d multivariate poly- nomial is a sum of squares or is far from a sum of squares. We show that if we require that the property tester always accepts YES instances and…
Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random…
Testing the unimodular equivalence of two full-dimensional integral simplices can be reduced to testing unimodular permutation (UP) equivalence of two nonsingular matrices. We conduct a systematic study of UP-equivalence, which leads to the…
We experimentally demonstrate a versatile technique for performing dual-comb interferometry using a single frequency comb. By rapid switching of the repetition rate, the output pulse train can be delayed and heterodyned with itself to…
A method used previously to calculate the masses of the vector mesons is extended to the calculation of the nucleon resonances. The method is based on the choice of integration kernels which eliminate the unknown parts of the spectrum. We…
A comprehensive study is made for the magnetic moments of octet baryons in the method of QCD sum rules. A complete set of QCD sum rules is derived using the external field method and generalized interpolating fields. For each member, three…
Universal multiport interferometers (UMIs) have emerged as a key tool for performing arbitrary linear transformations on optical modes, enabling precise control over the state of light in essential applications of classical and quantum…
Some consequences of spatio-temporal symmetry for the deterministic decomposition of complex light fields into factorized components are considered. This enables to reveal interrelations between spatial and temporal coherence properties of…
The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we…
Integrals for the product of unitary-matrix elements over the U(n) group will be discussed. A group-theoretical formula is available to convert them into a multiple sum, but unfortunately the sums are often tedious to compute. In this…