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February 5, 20260 citations

Tsallis-Kaniadakis homotopy of position-dependent mass functions

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IGIgnacio S. GomezJRJoão A. A. S. dos ReisBCBruno G. da Costa

Key Points

  • The aim is to connect Tsallis and Kaniadakis statistics using homotopy applied to position-dependent mass functions.
  • Developed homotopic connections between position-dependent mass functions of Tsallis and Kaniadakis statistics.
  • Generated a continuous family of homotopic canonical transformations.
  • Presented a family of Schrödinger equations related to the homotopic position-dependent mass functions.
  • Analyzed eigenfunctions for the infinite well to explore their inhomogeneous properties.
  • Established a continuous family of position-dependent mass functions linking Tsallis and Kaniadakis cases.
  • Demonstrated that eigenfunctions display a mixture of inhomogeneities.
  • Recovered specific statistical cases at the parameters λ = 0 and λ = 1.

Abstract

We present a method for linking Tsallis and Kaniadakis statistics based on the concept of homotopy of curves. By homotopically connecting the position-dependent mass (PDM) functions from the Tsallis and Kaniadakis algebras, we generate a continuous family of homotopic PDM functions along with their associated homotopic canonical transformations. A homotopy family of Schrödinger equations associated to the homotopic PDM is presented. We work out the spectrum for the infinite well whose eigenfunctions are shown to manifest a mixture of inhomogeneities. The Kaniadakis and Tsallis cases are recovered for the homotopic parameter λ = 0 and λ = 1, respectively.

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Cite This Study

Gomez et al. (2025) studied this question.

synapsesocial.com/papers/6984349af1d9ada3c1fb2ed8https://doi.org/10.1209/0295-5075/ae0961/pdf
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