Related papers: Wide-angle x-ray diffraction theory versus classic…
Complex numbers are basic. An inconsistency would question Wigner's unreasonable effectiveness of mathematics. A vehicle to study this question is Kirchoff's scalar diffraction theory. In the paper, an inconsistency in complex phase angle…
It is shown how Adler's trace dynamics can be applied to stochastic mechanics and other complex classical dynamical systems. Emergent non-commutivity due to the fractal nature of sample trajectories is closely related to the fact that the…
A general reformulation of classical sharp-edge diffraction theory is proposed within paraxial approximation. The, not so much known, Poincar\'e vector potential construction is employed directly inside Fresnel's 2D integral in order for it…
A new method for investigation of x-ray propagation in a rough narrow dielectric waveguide is proposed on the basis of the numerical integration of the quazioptical equation. In calculations a model rough surface was used with the given…
Well-known Kato's theory of the Laue diffraction of spherical x-ray waves is generalized to the case of the neutron diffraction in strongly absorbing crystals, taking into consideration both the potential and the resonant scattering of…
Dynamical systems of the gauge glass are investigated by the method of the gauge transformation.Both stochastic and deterministic dynamics are treated. Several exact relations are derived among dynamical quantities such as equilibrium and…
Structured x-rays carrying an orbital angular momentum break spatial inversion symmetry and have been proposed as a means to probe chirality. We theoretically investigate twisted non-resonant x-ray diffraction from chiral molecules and…
A direct comparison of quantum and classical dynamical systems can be accomplished through the use of distribution functions. This is useful for both fundamental investigations such as the nature of the quantum-classical transition as well…
The location of the beam focus when monochromatic x-ray radiation is diffracted by a thin bent crystal is predicted by "crystal lens equation". We derive this equation in a general form valid for Bragg and Laue geometries. This equation has…
Fresnel theory is used to derive the complex electric-fields above and below an X-ray reflecting interface that separates two materials with differing indices of refraction. The interference between the incident and reflected waves produces…
Accurate and efficient prediction of three-dimensional (3D) fields in wave interactions with large, complex-shaped objects is essential for applications in electromagnetic computation, computer graphics, optical metrology, and freeform…
In this paper we develop a general conceptual approach to the problem of existence of action-angle variables for dynamical systems, which establishes and uses the fundamental conservation property of associated torus actions: anything which…
A very small amount of K\"ahler algebra (i.e. Clifford algebra of differential forms) in the real plane makes x + ydxdy emerge as a factor between the differentials of the Cartesian and polar coordinates, largely replacing the concept of…
We introduce a class of variational wavefunctions that capture the long-range interaction between neutral systems (atoms and molecules) without changing the diagonal of the density matrix of each monomer. The corresponding energy…
The analytical generalization of the classical dynamical friction formula (derived under the assumption that all the field particles have the same mass) to the case in which the masses of the field particles are distributed with a mass…
The use of classical thermal field to approximate real-time quantum thermal field theory is discussed. For a \lambda\phi^4 theory, it is shown that the classical Rayleigh-Jeans divergence can be canceled with the appropriate counterterms,…
The binary radix expansion of a real number can be used to code the outcome of any series of coin tosses, a fact that provides an intriguing link between number theory, measure theory and statistical physics. Inspired by this fact, a…
Integer-order differential operators were originally used to describe local and isotropic effects, in both space and time. However, in fields like biology, the modelling of complex phenomena with spatial heterogeneity necessitates more…
In conventional scattering theory, by large-distance asymptotics, at the cost of losing the information of the distance between target and observer, one imposes a large-distance asymptotics to achieve a scattering wave function which can be…
Quantum electrodynamics predicts x-ray diffractions under a high-intensity laser field via virtual charged particles, and this phenomenon is called as vacuum diffraction (VD). In this paper, we derive a new formula to describe VD in a…