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Europhysics Letters (EPL)

Effects of Lorentz symmetry violation on a spin-(1/2) neutral particle in a doubly anharmonic potential

A. S. Oliveira, K. Okada, H. Belich

Published Feb 26, 2025• 3 citations
Publisher

Abstract

Abstract We investigate the quantum dynamics of a spin-(1/2) neutral particle under the effects of Lorentz symmetry violation, characterized by a fixed time-like background vector and azimuthal electric fields added to the potential of a pure quartic oscillator. These effects, induced by the background vector that defines a preferred spacetime direction, modify the dynamics of the spin-(1/2) neutral particle and give rise to a doubly anharmonic oscillator-like potential. The main challenge is to find analytical solutions to the Schrödinger equation, considering that this nonlinear potential models realistic quantum physics scenarios. Finally, we obtain bound-state solutions in the nonrelativistic limit for the Schrödinger-Pauli equation of a spin-(1/2) neutral particle. An interesting quantum effect is observed: the constant associated with the pure quartic oscillator term is quantized, meaning it depends on the system's quantum numbers.

DOI
10.1209/0295-5075/adba83

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Abstract We investigate the quantum dynamics of a spin-(1/2) neutral particle under the effects of Lorentz symmetry violation, characterized by a fixed time-like background vector and azimuthal electric fields added to the potential of a pure quartic oscillator. These effects, induced by the background vector that defines a preferred spacetime direction, modify the dynamics of the spin-(1/2) neutral particle and give rise to a doubly anharmonic oscillator-like potential. The main challenge is to find analytical solutions to the Schrödinger equation, considering that this nonlinear potential models realistic quantum physics scenarios. Finally, we obtain bound-state solutions in the nonrelativistic limit for the Schrödinger-Pauli equation of a spin-(1/2) neutral particle. An interesting quantum effect is observed: the constant associated with the pure quartic oscillator term is quantized, meaning it depends on the system's quantum numbers.
Abstract We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field. This neutral particle is also under the influence of a background that breaks the Lorentz symmetry. We focus on the Lorentz symmetry violation background determined by a space-like vector field. Then, we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential. Furthermore, we obtain the bound state solutions to the Schrödinger–Pauli equation and show that the spectrum of energy is a function of the Aharonov–Casher geometric quantum phase. Finally, we discuss the arising of persistent spin currents.
The extension of Standard Model of the Fundamental Particles which consider the Lorentz Symmetry Violation governed by a background tensor field presented by Colladay and Kostelecky consider the hypothesis of having a privileged direction in the space-time. Here we investigated a extension of the Schrödinger Equation inspired on that model taking into account a background scalar field. We analyze the behavior of this modified Schrödinger equation on a particle trapped in a well and quantum harmonic oscillator.
In this contribution, we discuss the He–McKellar–Wilkens effect and the scalar Aharonov–Bohm effect for neutral particles based on the Lorentz symmetry violation background, by showing that the background of the Lorentz symmetry violation yields Abelian quantum phases for a neutral particle. We also study the non-relativistic bound states for a neutral particle interacting with a Coulomb-like potential based on the Lorentz symmetry violation background given by a fixed vector field parallel to the radial direction.
The behaviour of the interaction of the induced electric dipole moment of an atom with a uniform magnetic field and a non-uniform electric field are investigated in a rotating reference frame. An interesting aspect of this interaction is that it gives rise to an analogue of a spinless particle subject to the doubly anharmonic oscillator. Then, it is shown that analytical solutions to the Schrödinger equation can be obtained. Another point raised is that the quantum effects on the induced electric dipole moment can be observed if the uniform magnetic field possesses a discrete set of values.
We analyze the nonrelativistic quantum dynamics of a single neutral spin half particle, with non-zero magnetic and electric dipole moments, moving in an external electromagnetic field in presence of Lorentz symmetry violation background. Also, we study the geometric phase for this model taking into account the parameter that breaks the Lorentz symmetry. We investigate the He-McKellar-Wilkens effect in this context and we verify that Lorentz violation parameter contribute to increase the electric dipole moment of the particle.