| Issue |
EPL
Volume 152, Number 1, October 2025
|
|
|---|---|---|
| Article Number | 11002 | |
| Number of page(s) | 7 | |
| Section | Statistical physics and networks | |
| DOI | https://doi.org/10.1209/0295-5075/ae0961 | |
| Published online | 14 October 2025 | |
Tsallis-Kaniadakis homotopy of position-dependent mass functions
1 Departamento de Ciências Exatas e Naturais, Universidade Estadual do Sudoeste da Bahia BR 415, Itapetinga, BA, 45700-000, Brazil
2 PROFÍSICA, Programa de Pós-Graduação em Física, Universidade Estadual de Santa Cruz 45650-000 Ilhéus, BA, Brazil
3 Instituto Federal de Educação, Ciência e Tecnologia do Sertão Pernambucano, Rua Maria Luiza de Araújo Gomes Cabral s/n - 56316-686 Petrolina, Pernambuco, Brazil
Received: 20 July 2025
Accepted: 19 September 2025
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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