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The ``spatial interpretation of compositeness'', presented and discussed in [1,2] in the context of non-relativistic potential scattering, is extended to higher partial waves. A particular set of basis states is used to arrive at a slightly…
We explain the collapse of the wavefunction with the notion that, in a measurement, the system observed nucleates a first order phase transition in the measuring device. The possible final states differ by the values of macroscopic…
Achieving higher sensitivity is an earnest purpose for precision metrology. As a response to this goal, the weak value amplification approach has been developed for measuring ultra-small physical effects, realizing sensitivity that had…
A general formalism for joint weak measurements of a pair of complementary observables is given. The standard process of optical three-wave mixing in a nonlinear crystal (such as in parametric down-conversion) is suitable for such tasks. To…
Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we…
In the last five decades, iterative phase retrieval methods draw large amount of interest across the research community as a non-interferometric approach to recover quantitative phase distributions from one (or more) intensity measurement.…
We report on progress concerning the partial wave analysis of higher correlation functions in conformal quantum field theory.
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
By solving the two variable differential equations which arise from finding the eigenfunctions for the Casimir operator for $O(d,2)$ succinct expressions are found for the functions, conformal partial waves, representing the contribution of…
By assuming that the weak value is real, Ferrie and Combes render their result inapplicable to weak measurement experiments which are aimed at enhancing precision.
We develop a new paradigm for finding bifurcations of solutions of nonlinear problems, which is based on the detection of extreme values of new type of variational functional associated with the considering problem. The variational…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
In this work we analyze the variational problem emerging from the Gutzwiller approach to strongly correlated systems. This problem comprises the two main steps: evaluation and minimization of the ground state energy $W$ for the postulated…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
We present here a new approach to determine an accurate variational wavefunction for general quantum antiferromagnets, completely defined by the requirement to reproduce the simple and well known spin-wave expansion. By this wavefunction,…
A factorization formula for wave functions, which is basic in the inverse spectral transform approach to initial-boundary value problems, is proved in greater generality than before. Applications follow. Related compatibility questions for…
The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application to many…
This is a comment on "Strong Measurements Give a Better Direct Measurement of the Quantum Wave Function" which was published as PRL 116, 040502 (2016). We show that there is crucial normalization error in this Letter which invalidates the…
Source extension is a reformulation of inverse problems in wave propagation, that at least in some cases leads to computationally tractable iterative solution methods. The core subproblem in all source extension methods is the solution of a…
It is widely claimed that the quantile function is equivariant under increasing transformations. We show by a counterexample that this is not true (even for strictly increasing transformations). However, we show that the quantile function…