Equivalence between classical and quantum dynamics. Neutral kaons and electric circuits

TL;DR

This paper establishes a precise isomorphism between the quantum dynamics of neutral kaons and classical electric networks, enabling a novel classical simulation of quantum CP violation phenomena.

Contribution

It introduces a unique classical electric network model that exactly replicates the quantum dynamics of neutral kaons, including CP violation effects.

Findings

Complete mapping between kaon Hamiltonian and network parameters

Determination of CP violation parameter from network characteristics

Classical networks can simulate quantum neutral kaon behavior

Abstract

An equivalence between the $\mathrm{Schr\ddot{o}dinger}$ dynamics of a quantum system with a finite number of basis states and a classical dynamics is presented. The equivalence is an isomorphism that connects in univocal way both dynamical systems. We treat the particular case of neutral kaons and found a class of electric networks uniquely related to the kaon system finding the complete map between the matrix elements of the effective Hamiltonian of kaons and those elements of the classical dynamics of the networks. As a consequence, the relevant $\epsilon$ parameter that measures CP violation in the kaon system is completely determined in terms of network parameters.