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arXiv:2607.04519

Schrodinger Oscillator and its Thermal Properties in a Dynamical Noncommutative Space

Ilyas Haouam

quant-phmath-phSubmitted Jul 5, 2026• Announced Jul 7, 2026
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Abstract

In this paper, we study the two-dimensional Schrodinger oscillator within a dynamical noncommutative (DNC) space. By leveraging perturbation theory, we derive the energy eigenvalues and eigenvectors and systematically analyze the effects of both dynamical and non-dynamical noncommutative settings. First-order corrections to the eigensystem are obtained, revealing that the energy shift explicitly depends on the DNC parameter tau. Furthermore, we explore the thermal properties of the system by employing the partition function. Numerical results are presented to provide a comprehensive analysis of the system behavior under the considered effects. Notably, in the DNC framework, the commutation relations and the deformation parameter are position-dependent. Using the two-dimensional Bopp-shift, we effectively map the noncommutative problem to its commutative counterpart.

Comments
29 pages, 16 figures

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We study graphene in an external magnetic field within a noncommutative (NC) framework. A gauge-invariant NC Hamiltonian is derived, and the system is analyzed using the ladder-operator formalism, yielding deformed Landau levels and eigenstates. A mapping to the anti-Jaynes-Cummings model is established, providing a bridge to quantum-optical interpretation. The thermal properties of gauge-invariant NC graphene are then investigated via the partition function, constructed using Euler and zeta functions. Analytical expressions for the partition function, free energy, internal energy, entropy, and specific heat are obtained and numerically evaluated. The results show that the NC phase-space deformation modifies the effective Landau-level spacing and consequently alters the thermal behavior of the graphene system. In particular, the deformation suppresses the thermal accessibility of excited states and produces measurable deviations from the commutative case while preserving the correct low- and high-temperature asymptotic limits.
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