Sub-Planck scale structures in the P{\"o}schl-Teller potential and their sensitivity to perturbations

TL;DR

This paper demonstrates the existence of sub-Planck scale structures in the P{"o}schl-Teller potential and shows their high sensitivity to perturbations, similar to harmonic oscillators, through phase space analysis.

Contribution

It reveals sub-Planck structures in an exactly solvable P{"o}schl-Teller potential and analyzes their sensitivity to perturbations using Wigner distributions.

Findings

Sub-Planck structures are present in P{"o}schl-Teller potential.

These structures exhibit high sensitivity to phase-space displacements.

Sensitivity is comparable to that observed in harmonic oscillator systems.

Abstract

We find the existence of sub-Planck scale structures in the P{\"o}schl-Teller potential, which is an exactly solvable potential with both symmetric and asymmetric features. We analyze these structures in both cases by looking at the Wigner distribution of the state evolved from an initial coherent state up to various fractional revival times. We also investigate the sensitivity to perturbations of the P{\"o}schl-Teller potential and we verify that, similar to the harmonic oscillator, the presence of sub-Planck structure in phase space is responsible for a high sensitivity to phase-space displacements.