Quantum-Like Behavior of Nonlinear Classical Oscillator

TL;DR

This paper constructs a classical dynamical system exhibiting quantum-like properties, including an energy-time uncertainty relation, and offers a classical explanation for phenomena typically considered quantum, such as the Franck-Hertz experiments.

Contribution

It introduces a classical system that mimics quantum behaviors, providing new insights into quantum phenomena through classical dynamics.

Findings

The system exhibits an energy-time uncertainty relation.

The system can explain Franck-Hertz experiment results classically.

The behavior demonstrates quantum-like features in a purely classical context.

Abstract

We construct the classical dynamical system which has a quantum-like behavior. We have shown that the energy-time uncertainty relation takes place for the system and it has purely classical nature. We investigate the behavior of the system and discuss a "classical" explanation of Franck-Hertz experiments.