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arXiv:2606.22107

Spectral and thermodynamic properties of supersymmetric quantum systems with self-adjoint deformed momentum

J. A. Oke, F. A. Dossa

quant-phSubmitted Jun 20, 2026• Announced Jun 23, 2026• Revised Jun 30, 2026 (v2)
v1 · Jun 20, 2026v2 · Jun 30, 2026
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Abstract

We establish a rigorous framework for quantum systems with geometric deformations by constructing a strictly self-adjoint deformed momentum operator through the generalized extended momentum operator (GEMO) formalism. Unlike previous approaches relying on boundary-condition hermiticity, our method ensures intrinsic self-adjointness for both linear ($μ(x)=αx$) and quadratic ($μ(x)=αx^{2}$) deformations within a unified non-Hermitian supersymmetric factorization scheme. This yields exact analytical spectra while revealing hidden $\mathfrak{su}(1,1)$ symmetry structures. Crucially, we provide the first complete thermodynamic characterization of such systems by analytically evaluating the partition function via the Euler--Maclaurin approximation. Geometric deformation fundamentally reshapes the density of states $ρ(E)$, producing distinct thermal signatures: a divergent heat capacity peak for linear deformation due to state accumulation near a maximal energy, and a saturation $C/k_{\mathrm{B}}\to 0.6$ (below the Dulong--Petit limit) for quadratic deformation. These results establish geometric deformation as a tunable parameter for engineering quantum thermodynamic responses in curved nanostructures.

Journal reference
Condens. Matter Phys., vol. 29, no. 2, p. 23704, Jun. 2026
DOI
10.5488/cmp.29.23704
Comments
14 pages, 3 figures

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