Nonextensive statistics for a 2D electron gas in noncommutative spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912729691848704 |
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| author | Adewi, Bienvenu Gnim Aremua, Isiaka |
| author_facet | Adewi, Bienvenu Gnim Aremua, Isiaka |
| contents | This work investigates a quantum system described by a Hamiltonian operator in a two dimensional noncommutative space. The system consists of an electron subjected to a perpendicular magnetic field $\mathbf{B}$, coupled to a harmonic potential and an external electric field $\mathbf{E}$, within the context of non-extensive statistical thermodynamics. The noncommutative geometry introduces a fundamental minimal length that modifies the phase space structure. The thermodynamics of this quantum system is developed within the framework of Tsallis statistics through the derivation of $q$-generalized versions of the partition function, magnetization, and magnetic susceptibility, following the application of a generalized Hilhorst transformation adapted to non-commutative geometry. The combined effects of the non-extensivity parameter $q$ and the noncommutativity parameter $θ$ are analyzed by considering the limit $q \rightarrow 1$, revealing new thermodynamic regimes and anomalous electromagnetic properties specific to quantum systems in non-commutative geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20822 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonextensive statistics for a 2D electron gas in noncommutative spaces Adewi, Bienvenu Gnim Aremua, Isiaka Quantum Physics This work investigates a quantum system described by a Hamiltonian operator in a two dimensional noncommutative space. The system consists of an electron subjected to a perpendicular magnetic field $\mathbf{B}$, coupled to a harmonic potential and an external electric field $\mathbf{E}$, within the context of non-extensive statistical thermodynamics. The noncommutative geometry introduces a fundamental minimal length that modifies the phase space structure. The thermodynamics of this quantum system is developed within the framework of Tsallis statistics through the derivation of $q$-generalized versions of the partition function, magnetization, and magnetic susceptibility, following the application of a generalized Hilhorst transformation adapted to non-commutative geometry. The combined effects of the non-extensivity parameter $q$ and the noncommutativity parameter $θ$ are analyzed by considering the limit $q \rightarrow 1$, revealing new thermodynamic regimes and anomalous electromagnetic properties specific to quantum systems in non-commutative geometry. |
| title | Nonextensive statistics for a 2D electron gas in noncommutative spaces |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2511.20822 |