Related papers: Fractional Schr\"odinger equation in gravitational optics

Fractional Schr\"odinger equation in gravitational optics

URL: http://arxiv.org/abs/2101.11920v1
Date: Thu, 28 Jan 2021 10:45:21 GMT
Title: Fractional Schr\"odinger equation in gravitational optics
Authors: Alexander Iomin
Abstract summary: This paper addresses issues surrounding the concept of fractional quantum mechanics, related to lights propagation in inhomogeneous nonlinear media. We have also concerned with linear and nonlinear Airy beam accelerations in flat and curved spaces and fractal photonics.
Score: 91.3755431537592
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: This paper addresses issues surrounding the concept of fractional quantum mechanics, related to lights propagation in inhomogeneous nonlinear media, specifically restricted to a so called gravitational optics. Besides Schr\"odinger Newton equation, we have also concerned with linear and nonlinear Airy beam accelerations in flat and curved spaces and fractal photonics, related to nonlinear Schr\"odinger equation, where impact of the fractional Laplacian is discussed. Another important feature of the gravitational optics' implementation is its geometry with the paraxial approximation, when quantum mechanics, in particular, fractional quantum mechanics, is an effective description of optical effects. In this case, fractional-time differentiation reflexes this geometry effect as well.

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