Related papers: Quantum wormhole as a Ricci flow
We study the quantum backflow problem of a relativistic charged Dirac fermion constrained to move on a ring of radius $R$. Using the relativistic current operator we compute the probability flux through a generic time interval to show…
Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure. Besides coordinate invariance, its key features are…
We establish a short-time existence theory for complete Ricci flows under scaling-invariant curvature bounds, starting from rotationally symmetric metrics on $\mathbb{R}^{n+1}$ that are noncollapsed at infinity, without assuming bounded…
We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional…
Quantum backflow is an interference effect in which a matter-wave packet comprised of only plane waves with non-negative momenta exhibits negative probability flux. Here we show that this effect is mathematically equivalent to the…
We consider a static wormhole as a waveguide and determine the conditions for full transmission through the wormhole waveguide for a quantum particle with zero angular momentum. We find that the waveguide is transparent when the de Broglie…
We define the Ricci curvature, as a measure, for certain singular torsion-free connections on the tangent bundle of a manifold. The definition uses an integral formula and vector-valued half-densities. We give relevant examples in which the…
The Ricci flow is a parabolic evolution equation in the space of Riemannian metrics of a smooth manifold. To some extent, Einstein equations give rise to a similar hyperbolic evolution. The present text is an introductory exposition to…
We review different notions of synthetic Ricci flow that apply to time-dependent families of metric measure spaces and which are based on properties of the heat flow, ideas from optimal transport, and the asymptotic behaviour of volumes.…
In this article, we study the Ricci flow neckpinch in the context of metric measure spaces. We introduce the notion of a Ricci flow metric measure spacetime and of a weak (refined) super Ricci flow associated to convex cost functions (cost…
First a Friedmann-Robertson-Walker (FRW) universe filled with dust and a conformally invariant scalar field is quantized. For the closed model we find a discrete set of wormhole quantum states. In the case of flat spacelike sections we find…
In this work we seek to generalize the connection between traversable wormholes and quantum channels. We do this via a connection between traversable wormholes and graph geometries on which we can perform quantum random walks for signal…
We model the spacetime foam picture by a gas of wormholes in Euclidean field theory. It is shown that at large distances the presence of such a gas leads merely to a renormalization of mass and charge values. We also demonstrate that there…
We derive the interesting result that the two asymptotically flat Universes classically linked by the Einstein-Rosen bridge may also be quantum mechanically connected in their far out regions. This would be felt by the Newtonian potential…
It is assumed that the quantum state that may describe a macroscopic system at a given instant of time is one of the eigenstates of the reduced density matrix calculated from the wave function of the system plus its environment. This…
Small crystallites form when finite quantal systems are set highly rotating. This crystallization is independent of the statistics of the particles, and occurs for both trapped bosons and fermions. The spin degree of freedom does not change…
We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with…
A model of space-time foam, made by $N$ wormholes is considered. The Casimir energy leading to such a model is computed by means of the phase shift method which is in agreement with the variational approach used in Refs.[9-14]. The…
Until recently, Ricci flow was viewed almost exclusively as a way of deforming Riemannian metrics of bounded curvature. Unfortunately, the bounded curvature hypothesis is unnatural for many applications, but is hard to drop because so many…
Quantum foam, also known as spacetime foam, has its origin in quantum fluctuations of spacetime. Its physics is intimately linked to that of black holes and computation. Arguably it is the source of the holographic principle which severely…