Exactly solvable dynamical models with a minimal length uncertainty

TL;DR

This paper provides exact solutions to classical equations of motion considering a minimal length, revealing increased particle speeds and frequencies in various systems due to this fundamental length scale.

Contribution

It offers the first analytical solutions for multiple classical systems incorporating a minimal length, highlighting its effects on dynamics and characteristic frequencies.

Findings

Minimal length increases free particle speed.

Minimal length accelerates fall in linear potential.

Characteristic frequencies tend to increase with minimal length.

Abstract

We present exact analytical solutions to the classical equations of motion and analyze the dynamical consequences of the existence of a minimal length for the free particle, particle in a linear potential, anti-symmetric constant force oscillator, harmonic oscillator, vertical harmonic oscillator, linear diatomic chain, and linear triatomic chain. It turns out that a minimal length increases the speed of a free particle and the rate of fall of a particle that is subject to the influence of a linear potential. Our results suggest that the characteristic frequency of systems tend to increase when there is a minimal length. This is a common feature that we observed for the oscillator systems that we have considered.