arXiv subjects

R. R. Luz

Publications and source records attributed to R. R. Luz.

4 recordsLinked to original sources

arXiv2026

Symplectic Pauli-Schrödinger Equation for the Quark-Antiquark Interaction System

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.

quant-ph↗

arXiv2024

On the Fractional Quark-Antiquark Confinement and Symplectic Quantum Mechanics

Using the formalism of generalized fractional derivatives, a two-dimensional non-relativistic meson system is studied. The mesons are interacting by a Cornell potential. The system is formulated in the domain of the symplectic quantum mechanics by means of the generalized fractional Nikiforov-Uvarov method. The corresponding Wigner function and the energy eigenvalues are then derived. The effect of fractional parameters $α$ and $β$ with the ground state solution is analyzed through the Wigner function for the charm-anticharm, bottom-antibottom and $b\overline{c}$ mesons. One of the fundamental achievements of such Cornell model is the determination of heavy quarkonia mass spectra. We have computed these masses and the

hep-ph↗

arXiv2022

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

In this paper, we study within the structure of Symplectic Quantum Mechanics a bi-dimensional non-relativistic strong interaction system which represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which consists of Coulomb-type plus linear potentials. First, we solve the Schrödinger equation in the phase space with the linear potential. The solution (ground state) is obtained and analyzed by means of the Wigner function related to Airy function for the $c\overline{c}$ meson. In the second case, to treat the Schrödinger-like equation in the phase space, a procedure based on the Bohlin transformation is presented and applied to the Cornell potential. In this case, the system is separated into two parts, one analogous to the oscillator and the other we treat using perturbation method. Then, we quantized the Hamiltonian with the aid of stars operators in the phase space representation so that we can determine through the algebraic method the eigenfunctions of the undisturbed Hamiltonian (oscillator solution), and the other part of the Hamiltonian was the perturbation method. The eigenfunctions found (undisturbed plus disturbed) are associated with the Wigner function via Weyl product using the representation theory of Galilei group in the phase space. The Wigner function is analyzed, the non-classicality of ground state and first excited state is studied by the non-classicality indicator or negativity parameter of the Wigner function for this system. In some aspects, we observe that the Wigner function offers an easier way to visualize the non-classic nature of meson system than the wavefunction does.

hep-ph↗

arXiv2020

Analytical Solution for Gross-Pitaevskii Equation in Phase Space and Wigner Function

In this work we study symplectic unitary representations for the Galilei group. As a consequence a Non-Linear Schrödinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using the group theory approach as a guide a physically consistent theory is constructed in phase space. The state is described by a quasi-probability amplitude that is in association with the Wigner function. With these results, we solve the Gross-Pitaevskii equation in phase space and obtained the Wigner function for the system considered.

math-ph↗