---
abstract: 'We find the existence of sub-Planck scale structures in the P[ö]{}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[ö]{}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.'
author:
- 'Utpal Roy,$^{\mathrm{1}}$[^1] Suranjana Ghosh,$^{\mathrm{1}}$[^2] P. K. Panigrahi,$^{\mathrm{2,3}}$[^3] and David Vitali,$^{\mathrm{1}}$[^4]'
title: 'Sub-Planck scale structures in the P[ö]{}schl-Teller potential and their sensitivity to perturbations'
---

Introduction
============

The Wigner distribution $W(x,p)$ is a useful tool for visualizing quantum interference phenomena in phase space. Non-local superposition states show interference and the presence of phase space regions where $W(x,p)$ is negative is an unambiguous signature of quantum behavior. The oscillatory structures resulting from quantum interference can have a dimension much smaller than the Planck’s constant $\hbar$, and these sub-Planck scale structures were first found by Zurek in quantum chaotic systems [@zurek]. Sub-Planck scale structures usually appear as alternate small ’tiles’ 