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A. E. Santana

Publications and source records attributed to A. E. Santana.

At least 19 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

Symplectic Representation of the Ginzburg-Landau Theory

In this work, the Ginzburg-Landau theory is represented on a symplectic manifold with a phase space content. The order parameter is defined by a quasi-probability amplitude, which gives rise to a quasi-probability distribution function, i.e., a Wigner-type function. The starting point is the thermal group representation of Euclidean symmetries and gauge symmetry. Well-known basic results on the behavior of a superconductor are re-derived, providing the consistency of representation. The critical superconducting current density is determined and its usual behavior is inferred. The negativety factor associated with the quasi-distribution function is analyzed, providing information about the non-classicality nature of the superconductor state in the region closest to the edge of the superconducting material.

cond-mat.supr-con↗
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↗
arXiv2023

Fractional Effective Quark-Antiquark Interaction in Symplectic Quantum Mechanics

We investigate within the formalism of Symplectic Quantum Mechanics a two-dimensional non-relativistic strong interacting system that represents the bound heavy quark-antiquark state, where it was considered a linear potential in the context of generalized fractional derivatives. For this purpose, it was solved the Schrödinger equation in phase space with the linear potential. The solution (ground state) is obtained, analyzed through the Wigner function comparing with the original solution, the Airy function for the meson $c\overline{c}$. The identified eigenfunctions are connected to the Wigner function via the Weyl product and the Galilei group representation theory in phase space. In some ways, compared to the wave function, the Wigner function makes it simpler to see how the meson system is non-classical.

hep-th↗
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↗
arXiv2021

The Landau Problem and non-Classicality

Exploring the concept of the extended Galilei group G. Representations for field theories in a symplectic manifold have been derived in association with the method of the Wigner function. The representation is written in the light-cone of a de Sitter space-time in five dimensions. A Hilbert space is constructed, endowed with a symplectic structure, which is used as a representation space for the Lie algebra of G. This representation gives rise to the spin-zero Schrödinger (Klein-Gordon-like) equation for the wave functions in phase space, such that the dependent variables have the content of position and linear momentum. This is a particular example of a conformal theory, such that the wave functions are associated with the Wigner function through the Moyal product. We construct the Pauli-Schrödinger (Dirac-like) equation in phase space in its explicitly covariant form. In addition, we analyze the gauge symmetry for spin 1/2 particles in phase space and show how to implement the minimal coupling in this case. We applied to the problem of an electron in an external field, and we recovered the non-relativistic Landau Levels. Finally, we study the parameter of negativity associated with the non-classicality of the system.

hep-th↗
arXiv2021

Representations of Extended Carroll Group

Carroll's group is presented as a group of transformations in a 5-dimensional space ($\mathcal{C}$) obtained by embedding the Euclidean space into a (4; 1)-de Sitter space. Three of the five dimensions of $\mathcal{C}$ are related to $\mathcal{R}^3$, and the other two to mass and time. A covariant formulation of Caroll's group, analogous as introduced by Takahashi to Galilei's group, is deduced. Unit representations are studied.

hep-th↗
arXiv2021

Size-effect at finite temperature in a quark-antiquark effective model in phase space

A quark-antiquark effective model is studied in a toroidal topology at finite temperature. The model is described by a Schrödinger equation with linear potential which is embedded in a torus. The following aspects are analysed: (i) the nonclassicality structure using the Wigner function formalism; (ii) finite temperature and size-effects are studied by a generalization of Thermofield Dynamics written in phase space; (iii) in order to include the spin of the quark, Pauli-like Schrödinger equation is used; (iv) analysis of the size-effect is considered to observe the fluctuation in the ground state. The size effect goes to zero at zero, finite and high temperatures. The results emphasize that the spin is a central aspect for this quark-antiquark effective model.

hep-th↗
arXiv2020

On Regular Black Holes at Finite Temperature

The Thermo Field Dynamics (TFD) formalism is used to investigate the regular black holes at finite temperature. Using the Teleparalelism Equivalent to General Relativity (TEGR) the gravitational Stefan-Boltzmann law and the gravitational Casimir effect at zero and finite temperature are calculated. In addition, the first law of thermodynamics is considered. Then the gravitational entropy and the temperature of the event horizon of a class of regular black holes are determined.

hep-th↗
arXiv2019

Zeeman Effect in Phase Space

The two-dimensional hydrogen atom in an external magnetic field is considered in the context of phase space. Using solution of the Schrödinger equation in phase space the Wigner function related to the Zeeman effect is calculated. For this purpose, the Bohlin mapping is used to transform the Coulomb potential into a harmonic oscillator problem. Then it is possible to solve the Schrödinger equation easier by using the perturbation theory. The negativity parameter for this system is realised.

quant-ph↗
arXiv2019

Non-abelian gauge symmetry for fields in phase space: a realization of the Seiberg-Witten non-abelian gauge theory

The Seiberg-Witten formalism has been realized as an electrodynamics in phase space (associated to the Dirac equation written in phase space) and this fact is explored here with non-abelian gauge group. First, a physically heuristic presentation of the Seiberg-Witten approach is carried out for non-abelian gauge in order to guide the calculation procedures. These results are realized by starting with the Lagrangian density for the free Dirac field in phase space. Then a field strength is derived, where the non-abelian gauge group is the SU(2), corresponding to an isospin (non-abelian) field theory in phase space. An application to nucleon is then discussed.

hep-th↗
arXiv2016

Approximative Wigner function for the Helium atom and dissipation

The Schrödinger equation in phase space is used to calculate the Wigner function for the Helium atom in the approximation of a system of two oscillators. Dissipation effect is analysed and the non-classicality of the state is studied by the non-classicality indicator of the Wigner function, which is calculated as a function of the dissipation parameter.

quant-ph↗
arXiv2016

Hénon-Heiles Interaction for Hydrogen Atom in Phase Space

Using elements of symmetry, as gauge invariance, several aspects of a Schrödinger equation represented in phase-space are introduced and analyzed under physical basis. The Hydrogen atom is explored in the same context. Then we add a Hénon-Heiles potential to the Hydrogen atom in order to explore chaotic features.

quant-ph↗
arXiv2015

Thermofield qubits, generalized expectations and quantum information protocols

Thermofield dynamics (TFD) approach is a real time quantum field method for dealing with finite temperature quantum states in a purified version of usual density operator formalism at finite temperature. In the domain of quantum information, TFD represents a quite promising direction for dealing with qubits under thermal influence and can also be associated to Gaussian states. Here, we propose a generalized TFD mean expectation for the case of thermofield qubits considering the action of gate operators. We propose quantum teleportation protocols involving thermofield states, considering thermal-to-thermal and thermal-to-non-thermal transfering cases. In particular, we discuss the case in which Alice and Bob are at different temperatures. Action of gate operators on the result of the Mandel parameter for thermofields and on Gibbs-like density operators are also discussed. The no-cloning and non-broadcasting theorems in TFD are also considered and cases of superposed thermofield states and maps connecting thermofield vacua at different temperatures are also addressed and associated to metastable and non-equilibrium scenarios.

quant-ph↗
arXiv2014

Quantum field theory on toroidal topology: algebraic structure and applications

The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordström, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a torus, such that Einstein and Maxwell equations would be unified. Many developments were carried out considering cosmological problems in association with particles physics, leading to methods that are useful for areas of physics, in which size effects play an important role. This interest in finite size effect systems has been increasing rapidly over the last decades, due principally to experimental improvements. In this review, the foundations of compactified quantum field theory on a torus are presented in a unified way, in order to consider applications in particle and condensed matted physics.

hep-th↗
arXiv2014

Scaling of the dynamics of homogeneous states of one-dimensional long-range interacting systems

Quasi-Stationary States of long-range interacting systems have been studied at length over the last fifteen years. It is known that the collisional terms of the Balescu-Lenard and Landau equations vanish for one-dimensional systems in homogeneous states, thus requiring a new kinetic equation with a proper dependence on the number of particles. Here we show that previous scalings described in the literature are due either to small size effects or the use of improper variables to describe the dynamics. The correct scaling is proportional to the square of the number of particles and deduce the kinetic equation valid for the homogeneous regime and numerical evidence is given for the Hamiltonian Mean Field and ring models.

cond-mat.stat-mech↗
arXiv2014

Realization of the Noncommutative Seiberg-Witten Gauge Theory by Fields in Phase Space

Representations of the Poincaré symmetry are studied by using a Hilbert space with a phase space content. The states are described by wave functions ( quasi amplitudes of probability) associated with Wigner functions (quasi probability density). The gauge symmetry analysis provides a realization of the Seiberg-Witten gauge theory for noncommutative fields.

hep-th↗