Related papers: Paths of Least Time for Quantum Scale and a New Ge…
In this paper, the quantum corrections to the kinematics of geometry, specifically geodesics, are presented. This is done by employing the path integral over the geodesics. Interestingly, the geodesics do not see any modifications in this…
The propagation of a light ray in thin layer (film) within geometrical optics is considered. It is assumed that the ray is captured inside the layer due to reflecting walls or total internal reflection (in the case of a dielectric layer).…
Ground-based astro-geodetic observations and atmospheric occultations, are two examples of observational techniques requiring a scrutiny analysis of atmospheric refraction. In both cases, the measured changes in observables are…
In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach, where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and…
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…
New ray-optical elements allow generalized refraction of light rays, but geometry imposes limitations on possible mappings between the positions of an object and its geometric image. Here I study the case of an infinite, planar,…
We present a novel geometric perspective on the latent space of diffusion models. We first show that the standard pullback approach, utilizing the deterministic probability flow ODE decoder, is fundamentally flawed. It provably forces…
We develop the spacetime approach to gravitational lensing by spherically symmetric perturbations of flat, cosmological constant-dominated Friedman-Robertson-Walker metrics. The geodesics of the spacetime are expressed as integral…
We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with…
Geometric optics effectively describes the propagation of electromagnetic waves when the wavelength is much smaller than the characteristic length scale of the medium, making wave phenomena like diffraction negligible. As a result, light…
At present, the theory of light diffraction only has the simple wave-optical approach. In this paper, we study light diffraction with the approach of relativistic quantum theory. We find that the slit length, slit width, slit thickness and…
Light refraction, i.e. the bending of the path of a light wave at the interface between two different dielectric media, is ubiquitous in optics. Refraction arises from the different speed of light and is unavoidable in continuous media…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…
The idea that the quantum space-time of microphysics may be fractal everywhere was intensively investigated recently, and several authors have presented the geodesic equations of different fractal space - times. In the present work we…
Physical systems evolve from one state to another along paths of least energy barrier. Without a priori knowledge of the energy landscape, multidimensional search methods aim to find such minimum energy pathways between the initial and…
We give an accessible introduction and elaboration on the methods used in obtaining a geodesic, which is the curve of shortest length connecting two points lying on the surface of a function. This is found through computing what's known as…
Working by analogy, we use the description of light fluctuations due to random collisions of the radiating atoms to figure out why the reduction of the coherence for light propagating a cosmological distance in the fluctuating background…
We present a full quantum mechanical three dimensional theory describing an electromagnetic field interacting with an ensemble of identical atoms. The theory is constructed such that it describes recent experiments on light-matter quantum…
Based on fundamental properties of light scattering by a particle we reveal the existence of the ultimate upper limit for the light absorption by any partial mode. First, we obtain this result for scattering of a plane wave by a symmetric…
Geometry can fundamentally govern the propagation of light, independent of material constraints. Here, we demonstrate that a fractal phase space, endowed with a non-Euclidean, scale-dependent geometry, can intrinsically induce resonance…