Quantumlike Diffusion over Discrete Sets

TL;DR

This paper introduces a discrete differential calculus framework for dynamical systems on graphs, deriving uncertainty principles and Schrödinger-like equations without traditional quantization, bridging classical discrete models and quantum-like behavior.

Contribution

It presents a novel discrete calculus approach that models quantum-like dynamics on arbitrary graphs without quantization procedures.

Findings

Derived Heisenberg-like uncertainty inequalities

Formulated Schrödinger-like equations for discrete systems

Established a link between discrete calculus and quantum dynamics

Abstract

In the present paper, a discrete differential calculus is introduced and used to describe dynamical systems over arbitrary graphs. The discretization of space and time allows the derivation of Heisenberg-like uncertainty inequalities and of a Schrodinger-like equation of motion, without need of any quantization procedure.