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Symplectic Pauli-Schr\"odinger Equation for the Quark-Antiquark Interaction System
arXiv:2507.20045v4 Announce Type: replace Abstract: We investigate the quantum behavior of a quark-antiquark bound system under the influence of a magnetic field within the symplectic formulation of quantum mechanics. Employing a perturbative approach, we obtain the ground and first excited states of the system described by the Cornell potential, which incorporates both confining and non-confining interactions. After performing a Levi-Civita mapping in phase space, we solve the time-independent symplectic Pauli-Schr\"odinger-type equation and determine the corresponding Wigner function. Special attention is given to the observation of the confinement of the quark-antiquark, that is revealed in the phase space structure. Due to the presence of spin in the Hamiltonian, the results reveal that the magnetic field enhances the non-classicality of the Wigner function, signaling stronger quantum interference and a departure from classical behavior. The experimental mass spectra is used to estimate the intensity of the external field, leading to a value that is in order of the transiet magnetic field measured in non-central heavy-ion collisions at RHIC and LHC.
Abstract:We investigate the quantum behavior of a quark-antiquark bound system under the influence of a magnetic field within the symplectic formulation of quantum mechanics. Employing a perturbative approach, we obtain the ground and first excited states of the system described by the Cornell potential, which incorporates both confining and non-confining interactions. After performing a Levi-Civita mapping in phase space, we solve the time-independent symplectic Pauli-Schrödinger-type equation and determine the corresponding Wigner function. Special attention is given to the observation of the confinement of the quark-antiquark, that is revealed in the phase space structure. Due to the presence of spin in the Hamiltonian, the results reveal that the magnetic field enhances the non-classicality of the Wigner function, signaling stronger quantum interference and a departure from classical behavior. The experimental mass spectra is used to estimate the intensity of the external field, leading to a value that is in order of the transiet magnetic field measured in non-central heavy-ion collisions at RHIC and LHC.
arXiv:2507.20045 [quant-ph]
(or arXiv:2507.20045v4 [quant-ph] for this version)
From: Renato Rodrigues Luz Dr. [view email] [v1] Sat, 26 Jul 2025 19:34:32 UTC (50 KB) [v2] Tue, 27 Jan 2026 14:19:33 UTC (79 KB) [v3] Mon, 22 Jun 2026 20:29:26 UTC (54 KB) [v4] Tue, 18 Aug 2026 21:04:57 UTC (59 KB)
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