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A method for calculating the self energy part of the Lamb shift is revisited. When the electron propagator in an external field is represented as an expansion in partial waves, the original method converges relatively slowly, requiring the…
The abundance of functional observations in scientific endeavors has led to a significant development in tools for functional data analysis (FDA). This kind of data comes with several challenges: infinite-dimensionality of function spaces,…
The implementation of weak-value amplification requires the pre- and post-selection of states of a quantum system, followed by the observation of the response of the meter, which interacts weakly with the system. Data acquisition from the…
Instead of sampling a function at a single point, average sampling takes the weighted sum of function values around the point. Such a sampling strategy is more practical and more stable. In this note, we present an explicit method with an…
The optical interferometry has been widely used in various high precision applications. Usually, the minimum precision of an interferometry is limited by various technique noises in practice. To suppress such kind of noises, we propose a…
This paper presents a comprehensive review of the wave-function approach for derivation of the number-resolved Master equations, used for description of transport and measurement in mesoscopic systems. The review contains important…
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
Following the familiar analogy between the optical paraxial wave equation and the Schr\"odinger equation, we derive the optimal, real-valued wave function for focusing in one and two space dimensions without the use of any phase component.…
The main objective of this paper is to look from the unique point of view at some phenomena arising in different areas of probability theory and mathematical statistics. We will try to understand what is common between classical…
Modes generally provide an economical description of waves, reducing complicated wave functions to finite numbers of mode amplitudes, as in propagating fiber modes and ideal laser beams. But finding a corresponding mode description for…
An improvement of the scheme by Brunner and Simon [Phys. Rev. Lett. 105, 010405 (2010)] is proposed in order to show that quantum weak measurements can provide a method to detect ultrasmall longitudinal phase shifts, even with white light.…
A problem of amplitude reconstruction in terms of the given angular distribution is considered. Solution of this problem is not unique. A class of amplitudes, correspondent to one and the same angular distribution, forms a region in…
Weak values arise in quantum theory when the result of a weak measurement is conditioned on a subsequent strong measurement. The majority of the trials are discarded, leaving only very few successful events. Intriguingly those can display a…
We give a simple proof of a pointwise decay estimate in 3+1 dimensions stated in two versions, making advantage of a particular simplicity of inverting the spherically symmetric part of the wave operator and of the comparison theorem. We…
wave solutions to nonlinear partial differential equations. We simplify the so called (G'/G)-expansion method and apply two of those methods to simple physical problems.
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…
In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…
In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of…
We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for…
Many known models, which generally use a factorization hypothesis, give a poor account of the decays B into J/psi + K(*). Usually there is a free overall factor, which is fit to the data, so that tests of the models rely upon ratios. The…