# Compared study of Shannon, Tsallis and Gaussian entropy of bound magnetopolaron in nanostructures

## TL;DR

This study compares Shannon, Tsallis, and Gaussian entropies in nanostructures, revealing their relative effectiveness in analyzing decoherence and information dynamics in quantum dots under various conditions.

## Contribution

It provides a comparative analysis of three entropy measures in nanostructures, highlighting their different sensitivities and suitability for evaluating quantum decoherence and information exchange.

## Key findings

- Gaussian entropy amplitude is greater than Tsallis and Shannon.
- Gauss entropy is more suitable for evaluating average information.
- Shannon entropy shows more significant amplitude with increasing delta length.

## Abstract

Many methods have been experimented to study decoherence in nanostructures. Tsallis, Shannon and Gaussian entropy have been used to study decoherence separately; in this paper, we compared the results of the sus-mentioned entropies in nanostructures. The linear combination operator and the unitary transformation was used to derive the magnetopolaron spectrum that strongly interact with the LO phonons in the presence of electric field in the pseudo harmonic and delta quantum dot. Numerical results revealed for the quantum pseudo dot that: (i) The amplitude of Gauss entropy is greater than the amplitude of Tsallis entropy which inturn is greater than the amplitude of Shannon entropy. The Tsallis entropy is not more significant in nanostructure compared to Shannon and Gauss entropies, (ii) With an increase of the zero point, the dominance of the Gauss entropy on the Shannon entropy was observed on one hand and the dominance of the Shannon entropy on the Tsallis entropy on the other hand ; this suggested that in nanostructures, Gauss entropy is more suitable in the evaluation of the average of information in the system, for the delta quantum dot it was observed that (iii) when the Gauss entropy is considered, a lot of information about the system is missed. The collapse revival phenomenon in Shannon entropy was observed in RbCl and GaAs delta quantum dot with the enhancement of delta parameter; with an increase in this parameter, the system in the case of CsI evolved coherently; with Shannon and Tsallis entropies , information in the system is faster and coherently exchanged; (iv) The Shannon entropy is more significant because its amplitude outweighs on the others when the delta dimension length enhances. The Tsallis entropy involves as wave bundle; which oscillate periodically with an increase of the oscillation period when delta dimension length is improved.

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Source: https://tomesphere.com/paper/1703.09158