![]() We consider the case where the surface S is analytic, i.e., where it can be prescribed by an equation analytically depending on the variables. The null field condition (3.4) is satisfied everywhere inside the scatterer, but as we see below, for the correct application of this condition when solving the boundary-value problems, it is necessary to have the complete information about the singularities of the wave field analytic continuation into the interior of the scatterer. However, some representations of the boundary values of the quantities U | S and ∂ U / ∂ n | S must be used in any attempt to solve these equations, and already in this case, for example, (3.4) means that the sum of the diffraction and incident fields is zero (see below). We note that the word combination “null field condition” does not completely explain the meaning of formulas (3.4) and (1.6), because the integral on the left-hand sides of these relations is not the wave field inside S. This condition allows one to obtain a Fredholm integral equation of the first type with a smooth kernel, and precisely this equation underlies the null field and Т-matrix methods. įormula (3.4) (and (1.6)) is called the null field condition. The scale is kept identical to (b) for clarity.(3.4) ∫ S U ( r → ′ ) ∂ G 0 ( r →, r → ′ ) ∂ n ′ − ∂ U ( r → ′ ) ∂ n ′ G 0 ( r →, r → ′ ) d s ′ + U 0 r → = 0, M r → ∈ D. However, it does give an idea of how the results would have looked, given no fabrication errors. The quantitative outcome this filtering yields is not considered as the main result of the paper. (d) The Sorkin parameter following a Fourier filter (removing frequencies rising above 5 σ of the noise level)-basically eliminating fabrication-related, periodic systematic errors in the measurement. (c) The Sorkin parameter overlaid by an analytical calculation using Eq. ( 4)-plugging in the appropriate parameters d and a derived from our image-processing-based analysis of the mask (see Fig. The oscillations apparent in (b) arise from imperfections in the mask-generating systematic errors which are observable due to our highly accurate measurements. Considering each channel as a separate experiment sets an upper bound on the statistical deviation of | ε | ≤ 2.9 × 10 − 5. The standard deviation for the Sorkin parameter is ε σ = 5.4 × 10 − 4. The error bars are the probability errors arising from finite statistics. The green colored area stands for the shot noise (proportional to the square root of the number of collected counts). The red line represents the mean, which is practically zero. (b) The Sorkin parameter deduced from Eq. ( 5). (a) The diffraction patterns measured for the slits configurations: 100 (green), 110 (blue), 101 (red), and 111 (yellow). Test of multipath interference of H e * in the modified triple-slit experiment. Our value is on the order of the maximal contribution predicted for multipath trajectories by Feynman path integrals. We use a variation of the original triple-slit experiment and accurate single-event counting techniques to provide a new experimental bound of 2.9 × 10 − 5 on the statistical deviation from the commonly approximated null third-order interference term in Born's rule for matter waves. Here we present an experimental test of multipath interference in the diffraction of metastable helium atoms, with large-number counting statistics, comparable to photon-based experiments. In recent years, several studies have challenged the nature of wave-function interference from the perspective of Born's rule-namely, the manifestation of so-called high-order interference terms in a superposition generated by diffraction of the wave functions. Interference experiments have been paramount in our understanding of quantum mechanics and are frequently the basis of testing the superposition principle in the framework of quantum theory. ![]()
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