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

• URL: http://arxiv.org/abs/2606.22107v1
• Date: Sat, 20 Jun 2026 15:43:06 GMT
• Title: Spectral and thermodynamic properties of supersymmetric quantum systems with self-adjoint deformed momentum
• Abstract summary: We build a rigorous framework for quantum systems with geometric deformations by constructing a strictly self-adjoint deformed momentum operator.<n>We provide the first complete thermodynamic characterization of such systems by analytically evaluating the partition function.<n>These results establish geometric deformation as a tunable parameter for engineering quantum thermodynamic responses in curved nanostructures.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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