相关论文: Can Fractional Time Operators Reproduce Gravitatio…

We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows…

We study the gravitational wave memory effect in spacetimes related to flat space by a conformal transformation. The discussion is general but the gravitational wave length scale is assumed to be small compared with the background curvature…

We revisit the issue of memory effects, i.e. effects giving rise to a net cumulative change of the configuration of test particles, using a toy model describing the emission of radiation by a compact source and focusing on the scalar, hence…

Gravitational wave memory is a nonoscillatory correction to the gravitational wave strain predicted by general relativity, which has yet to be detected. Within general relativity, its dominant component, known as the null memory, can be…

A fractional derivative is a temporally nonlocal operation which is computationally intensive due to inclusion of the accumulated contribution of function values at past times. In order to lessen the computational load while maintaining the…

Gravitational wave memory is said to arise when a gravitational wave burst produces changes in a physical system that persist even after that wave has passed. This paper analyzes gravitational wave bursts in plane wave spacetimes, deriving…

Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…

We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical…

We find new effects for gravitational waves and memory in asymptotically-flat spacetimes of slow decay. In particular, we derive growing magnetic memory for these general systems. These effects do not arise in spacetimes resulting from data…

Gravitational memory is a zero-frequency effect associated with a permanent change in the asymptotic spacetime metric induced by radiation. Although its universal manifestation is a net change in the proper distances between freely falling…

We investigate the Einstein vacuum equations as well as the Einstein-null fluid equations describing neutrino radiation. We find new structures in gravitational waves and memory for asymptotically-flat spacetimes of slow decay. These…

Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the…

Many physical, biological, and engineered systems exhibit memory effects that challenge Markovian models. Fractional calculus provides nonlocal operators to capture hereditary dynamics. This survey connects modeling, analysis, and…

In honor of the great Russian mathematician A. N. Kolmogorov, we would like to draw attention in the present paper to a curious mathematical observation concerning fractional differential equations describing physical systems, whose time…

Gravitational-wave memory is a low-frequency, non-oscillatory component of the radiation field that provides a potentially powerful but as yet undetected probe of strong-field gravity. We present the first calculation of gravitational…

Gravitational-wave (GW) memory effects produce permanent shifts in the GW strain and its time integrals after the passage of a burst of GWs. Their presence is closely tied to symmetries of asymptotically flat spacetimes and fluxes of…

We survay our recent results on fractional gravity theory. It is also provided the Main Theorem on encoding of geometric data (metrics and connections in gravity and geometric mechanics) into solitonic hierarchies. Our approach is based on…

Fractional differential equations model processes with memory effects, providing a realistic perspective on complex systems. We examine time-delayed differential equations, discussing first-order and fractional Caputo time-delayed…

It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old…

Fractional quantum dynamics provides a natural framework to capture nonlocal temporal behavior and memory effects in quantum systems. In this work, we analyze the physical consequences of fractional-order quantum evolution using a Green's…