Related papers: Path Integral Formulation for Wave Effect in Multi…
The motivation for the treatment of intrabeam scattering theory given in this paper was to find results which would be convenient for computing the intrabeam scattering growth rates for particle distributions which are more complicated than…
In this paper, we have constructed the Feynman path integral method for non-paraxial optics. This is done by using the mathematical analogy between a non-paraxial optical system and the generalized Schr\"odinger equation deformed by the…
The Heisenberg uncertainty principle gets modified by the introduction of an observer independent minimal length. In this work we have considered the resonant gravitational wave detector in the modified uncertainty principle framework where…
In this paper, we apply the full new method of quantum theory to study the double-slit diffraction of ${C_{60}}$ molecules. We calculate the double-slit wave functions of ${C_{60}}$ molecules by Schr\"{o}dinger equation, and calculate the…
Wavefront aberrations are one of the largest uncertainty factors in present atom interferometers. We present a detailed numerical and experimental analysis of this effect based on measured aberrations from optical windows. By placing…
We develop a formalism for the calculation of the macroscopic dielectric response of composite systems made of particles of one material embedded periodically within a matrix of another material, each of which is characterized by a well…
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…
A mathematical model in terms of partial differential equations (PDE) for the calculation of double freeform surfaces for irradiance and phase control with predefined input and output wavefronts is presented. It extends the results of…
The propagation and absorption of electromagnetic waves in plasma is one of the fundamental issues in plasma physics. The electromagnetic particle-in-cell method with the finite-difference time-domain solver plus Monte Carlo collision model…
This article investigates the velocity dispersion and the spurious reflection of the viscoelastic wave that occur in the numerical integration of the viscoelastic wave equation. For this purpose, the classic finite element of two nodes,…
Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
We continue our study of the optical properties of the solar gravitational lens (SGL). Taking the next step beyond representing it as an idealized monopole, we now characterize the gravitational field of the Sun using an infinite series of…
The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or…
We critically analyze the problem of formulating duality between fringe visibility and which-way information, in multibeam interference experiments. We show that the traditional notion of visibility is incompatible with any intuitive idea…
Physical path integral formulation of motion of particles in Riemannian spaces is outlined and extended to deduce the corresponding field theoretical formulation. For the special case of a zero rest mass particle in Minkowski manifold, it…
Two-photon interference is a fundamental quantum optics effect with numerous applications in quantum information science. Here, we study two-photon interference in multiple transverse-spatial modes along a single beam-path. Besides…
We present a method to synthesize phase screens for multi-wavelength, atmospheric wave optics simulations using fast Fourier transforms. We validate our work by comparing the theoretical, two-wavelength optical path length structure…
Assuming that a formal approximation of multiple waves has been obtained by matched asymptotic methods, we derive a {\em Spatial Shadowing lemma} to construct exact solutions near the formal approximation. In Part I, we consider a general…
We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…