相关论文: Fractional Schr\"odinger equation in gravitational…
We consider the nonunitary quantum dynamics of neutral massless scalar particles used to model photons around a massive gravitational lens. The gravitational interaction between the lensing mass and asymptotically free particles is…
The propagation of high-frequency gravitational waves can be analyzed using the geometrical optics approximation. In the case of large but finite frequencies, the geometrical optics approximation is no longer accurate, and…
In this paper we regard the dynamics obtained from Fermat principle as begin the classical theory of light. We (first-)quantize the action and show how close we can get to the Maxwell theory. We show that Quantum Geometric Optics is not a…
The fractional Schr\"{o}dinger equation (FSE) -- a natural extension of the standard Schr\"{o}dinger equation -- is the basis of fractional quantum mechanics. It can be obtained by replacing the kinetic-energy operator with a fractional…
Frequency-dependent gravitational lens effects are found for trajectories of electromagnetic rays passing through a distribution of plasma near a massive object. Ray propagation through plasma adds extra terms to the equations of motion…
Fractional derivatives are nonlocal differential operators of real order that often appear in models of anomalous diffusion and a variety of nonlocal phenomena. Recently, a version of the Schr\"odinger Equation containing a fractional…
Using a sharp Gagliardo-Nirenberg type inequality, well-posedness issues of the initial value problem for a fractional inhomogeneous Schrodinger equation are investigated.
Fractional electromagnetic field theory describes electromagnetic wave propagation through the complex, nonlocal, dissipative, fractal and also recent artificially engineered materials know as fractional metamaterials. In this theory using…
We compute the gravitational birefringence of light as it undergoes gravitational lensing. To this end we re-derive the Souriau-Saturnini equations in the Schwarzschild metric and solve them numerically and perturbatively. Our main result…
We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically,…
When gravitational waves travel from their source to an observer, they interact with matter structures along their path, causing distinct deformations in their waveforms. In this study we introduce a novel theoretical framework for wave…
We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness…
The geometrical approximation of the extended Maxwell equation in curved spacetime incorporating interactions induced by the vacuum polarization effects is considered. Taking into account these QED interactions and employing the analogy…
The Nelson stochastic mechanics of inhomogeneous quantum diffusion in flat spacetime with a tensor of diffusion can be described as a homogeneous one in a Riemannian manifold where this tensor of diffusion plays the role of a metric tensor.…
The kinematical effect induced by the transversal motion of a gravitational lens on the frequency shift of light has been investigated in detail, while the effect of the radial motion is thought to be much smaller than the transversal one…
In this paper we study the pointwise convergence problem along a tangential curve for the fractional Schr\"odinger equations in one spatial dimension and estimate the capacitary dimension of the divergence set. We extend a prior paper by…
The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system of equations describing in terms of ray trajectories a very wide family of wave-like phenomena (including diffraction and interference) going much beyond…
Considered is the Schr\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting…
Interactions incorporating the vacuum polarization effects in curved backgrounds modify the null cone structure in such a way that the photon trajectories would not be the space-time geodesics anymore. The gravitational birefringence…
We study the quantum mechanical phases associated with the propagation of neutrinos in gravitational fields under the WKB approximation for Dirac equation. Applying the result, the investigations are made for gravitational effects on the…