相关论文: Ricci flow and quantum theory

We indicate some formulas connecting Ricci flow and the Perelman entropy functional to Fisher information, differential entropy, and the quantum potential.

We discuss in rather general terms quantum field theories dealing with spaces of maps between Riemannian manifolds. In particular we explore the well--known connection between the renormalization group flow for non--linear sigma models and…

The idea is considered that a quantum wormhole in a spacetime foam can be described as a Ricci flow. In this interpretation the Ricci flow is a statistical system and every metric in the Ricci flow is a microscopical state. The probability…

This article reports recent developments of the research on Hamilton's Ricci flow and its applications.

We obtain Schroedinger quantum mechanics from Perelman's functional and from the Ricci flow equations of a conformally flat Riemannian metric on a closed 2-dimensional configuration space. We explore links with the recently discussed…

We elaborate on the existing idea that quantum mechanics is an emergent phenomenon, in the form of a coarse-grained description of some underlying deterministic theory. We apply the Ricci flow as a technical tool to implement dissipation,…

Some situations are discussed where subquantum oscillations in momentum arise in connectiion with Fisher information and the quantum potential.

In this paper the relation between quantum covariances and quantum Fisher informations are studied. This study is applied to generalize a recently proved uncertainty relation based on quantum Fisher information. The proof given…

We describe a few elementary aspects of the circle of ideas associated with a quantum field theory (QFT) approach to Riemannian Geometry, a theme related to how Riemannian structures are generated out of the spectrum of (random or quantum)…

I survey some of the developments in the theory of Ricci flow and its applications from the past decade. I focus mainly on the understanding of Ricci flows that are permitted to have unbounded curvature in the sense that the curvature can…

In previous papers we have shown how Schrodinger's equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field. The…

In this note we explain how a flow in the space of Riemmanian metrics (including Ricci's \cite{mt}) induces one in the space of pseudoconnections.

We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher…

In Riemannian geometry, the Ricci flow is the analogue of heat diffusion; a deformation of the metric tensor driven by its Ricci curvature. As a step towards resolving the problem of time in quantum gravity, we attempt to merge the Ricci…

In previous papers we have shown how Schr\"{o}dinger's equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field.…

The Ricci flow equation of a conformally flat Riemannian metric on a closed 2-dimensional configuration space is analysed. It turns out to be equivalent to the classical Hamilton-Jacobi equation for a point particle subject to a potential…

We give some heuristic results for FRW situations with Ricci flow.

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…

We introduce the notion of contact Ricci flow associated with the Reeb vector field. Using it, we give a simple proof of the Poincare conjecture.

We survey several problems concerning Riemannian manifolds with positive curvature of one form or another. We describe the PIC1 notion of positive curvature and argue that it is often the sharp notion of positive curvature to consider.…