A Note on the Quantum-Mechanical Ricci Flow

Abstract

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

A Mechanics for the Ricci Flow

“…Recent works [5][6][7][8] have shed light on applications of the Ricci flow to foundational issues in quantum mechanics. The present contribution is a continuation of previous research [1,[14][15][16] on the exciting interrelation between Ricci flow, quantum mechanics, and gravity. We can state our results more precisely as follows.…”

On stability, fluctuations, and quantum mechanics

“…There have been many studies of stochastic and hydrodynamic models, or fractal situations, involving such situations and we mention in particular [9,10,11,12,13,17,18,23,24,29,30,31,32,33,42,43,47,48,49,51,52,54,56,61,62,63]; a survey of some of this appears in [9]. For various geometrical considerations related to the emergence question see also [3,7,8,19,35,36,37,38,39,40,41,46].…”