Quantum information entropies for a soliton at hyperbolic well

TL;DR

This paper analyzes quantum information entropies like Shannon and Fisher for a soliton with position-dependent mass in hyperbolic potentials, providing analytical solutions relevant to semiconductor heterojunctions.

Contribution

It introduces an analytical approach to compute Shannon and Fisher entropies for solitonic mass distributions in hyperbolic potentials using Zhu-Kroemer ordering.

Findings

Calculated Shannon and Fisher entropies for the system

Derived analytical solutions in position and momentum space

Applied results to semiconductor heterojunctions

Abstract

In this work, the probability uncertainties related to a stationary quantum system with solitonic mass distribution when subjected to deformable hyperbolic potentials are studied. Shannon's entropy and Fisher's information of a position-dependent mass are calculated. To investigate the concept of Shannon and Fisher entropies of the solitonic mass distribution subject to the hyperbolic potential, it is necessary to obtain the analytic solutions at position and momentum space. For the Hamiltonian operator to be Hermitian, we consider the stationary Schr\"odinger equation ordered by Zhu-Kroemer. This ordering is known to describe abrupt heterojunctions in semiconductor materials.