arXiv subjects

Edson C. M. Nogueira

Publications and source records attributed to Edson C. M. Nogueira.

7 recordsLinked to original sources

arXiv2022

Curvature-induced repulsive effect on the lateral Casimir-Polder--van der Waals force

We consider a perfectly conducting infinite cylinder with radius $R$, and investigate the Casimir-Polder (CP) and van der Waals (vdW) interactions with a neutral polarizable particle constrained to move in a plane distant $x_0>R$ from the axis of the cylinder. We show that when the relative curvature $x_0/R \lesssim 6.44$, this particle, under the action of the lateral CP force (which is the projection of the CP force onto the mentioned plane), is attracted to the point on the plane which is closest to the cylinder surface. On the other hand, when $x_0/R \gtrsim 6.44$, we also show that, for certain particle orientations and anisotropy, the lateral CP force can move the particle away from the cylinder. This repulsive behavior of such a component of the CP force reveals a nontrivial dependence of the CP interaction with the surface geometry, specifically of the relative curvature. In the vdW regime, we show that a similar nontrivial repulsive behavior occurs, but for the relative curvature $x_0/R \gtrsim 2.18$, which means that this effect requires a smaller cylinder curvature in the vdW regime than in the CP one. In addition, we also show that there are classical counterparts of these effects, involving a neutral particle with a permanent electric dipole moment. The prediction of such geometric effects on this force may be relevant for a better controlling of the interaction between a particle and a curved surface in classical and quantum physics.

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arXiv2022

Sign inversion in the lateral van der Waals force between an anisotropic particle and a plane with a hemispherical protuberance: an exact calculation

We investigate the lateral van der Waals (vdW) force between an anisotropic polarizable particle and a perfectly conducting plane with a hemispherical protuberance with radius $R$. We predict, via an exact calculation, a sign inversion in the lateral vdW force, in the sense that, instead of pointing to the protuberance, in certain situations this force points to the opposite direction. In the literature, predictions of sign inversions in the lateral vdW force were based on perturbative solutions, valid when the height of the protuberance is very small when compared to the distance $z_0$ between the particle and the plane. Here, taking into account exact formulas, we investigate how such nontrivial geometric effect depends on the ratio $R/z_0$, and how the particle orientation and anisotropy affect this sign inversion.

quant-ph↗

arXiv2022

Introducing the notion of tensors through a variation of a Feynman didactic approach

In one of his books [$\textit{The Feynmann Lectures on Physics}$, vol. 2], Feynman presents a didactic approach to introduce basic ideas about tensors, using, as a first example, the dependence of the induced polarization of a crystal on the direction of the applied electric field, and also presenting the energy ellipsoid as a way of visualizing the polarization tensor. In the present paper, we propose some variations on Feynman's didactic approach, considering as our basic models a single ground-state atom and a carbon dioxide ($\text{CO}_{2}$) molecule, instead of crystals, and introducing a visual representation of tensors based on the ideas of the Lamé stress ellipsoid, instead of the energy ellipsoid. With these changes, the resulting didactic proposal presents a reduction in the prerequisites of physical and mathematical concepts if compared to Feynman's original approach, requiring, for example, no differential calculus and only introductory vector algebra. The text is written so that it can be used directly as a learning tool for students (even those in the beginning of the undergraduate course), as well as for teachers interested in preparing their own materials.

physics.ed-ph↗

arXiv2022

Sign inversion in the lateral van der Waals force

We consider a single slight protuberance in a perfectly conducting plane, and investigate the van der Waals (vdW) interaction between this surface and a neutral polarizable particle. When the protuberance is sufficiently smooth, so that the proximity force approximation (PFA) is well applicable, for a fixed distance of the particle from the plane, the lateral vdW force always points to the protuberance. On the other hand, by making calculations valid beyond the PFA, we show that nontrivial geometric effects arise when we consider an anisotropic particle, and manipulate the ratio between the characteristic widths of the protuberance and the fixed particle-plane distance. We predict that, as this ratio decreases, a sign inversion in the lateral vdW force can occur, in the sense that, instead of pointing to the protuberance, in certain situations the lateral force points to the opposite direction. Moreover, we show that even when such a sign inversion in the lateral vdW force does not occur for a single protuberance, it can arise when two or more protuberances are put together, distinguishing between sign inversions originated by individual or collective effects. In addition, we show that all these effects have their classical counterparts, involving a neutral particle with a permanent electric dipole moment. The prediction of such geometric effects on the lateral vdW force may be relevant for a better controlling of the interaction between a particle and a corrugated surface in classical and quantum physics.

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arXiv2022

Introducing corrugated surfaces in electromagnetism problems via perturbative approach

Problems involving boundary conditions on corrugated surfaces are relevant to understand nature, since, at some scale, surfaces manifest corrugations that have to be taken into account. In introductory level electromagnetism courses, a very common and fundamental exercise is to solve Poisson's equation for a point charge in the presence of an infinity perfectly conducting planar surface, which is usually done by image method. Clinton, Esrick and Sacks [Phys. Rev. B 31, 7540 (1985)] added corrugation to this surface, and solved the problem by a perturbative analytical calculation of the corresponding Green's function. In the present paper, we make a detailed pedagogical review of this calculation, aiming to popularize their results. We also present an original contribution, extending this perturbative approach to solve the Laplace's equation for the electrostatic potential for a corrugated neutral conducting cylinder in the presence of a uniform electric field (without corrugation, this is another very common model considered as an exercise in electromagnetism courses). All these calculations can be used as pedagogical examples of the application of the present perturbative approach in electromagnetism courses.

physics.ed-ph↗

arXiv2021

Regimes of the lateral van der Waals force in the presence of dielectrics

In a recent paper, it was shown that, under the action of the lateral van der Waals (vdW) force due to a perfectly conducting corrugated surface, a neutral anisotropic polarizable particle in vacuum can be attracted not only to the nearest corrugation peak, but also to a valley, or an intermediate point between a peak and a valley, with such behaviors called peak, valley and intermediate regimes, respectively. In the present paper, we investigate how these regimes are affected by the consideration of two non-dispersive semi-infinite dielectrics $ε_{1}$ and $ε_{2}$, separated by a corrugated interface. Specifically, we study the vdW interaction between a neutral anisotropic polarizable particle, embedded in the dielectric $ε_{2}$, and the dielectric $ε_{1}$. We show that when $ε_{2}<ε_{1}$ the peak, valley and intermediate regimes have, unless numerical factors, behaviors similar to those found for the situation where the particle is in vacuum and interacting with a conducting medium. For the case $ε_{2}>ε_{1}$, one might expect a mere permute between the peak and valley regimes, in comparison to the case $ε_{2}<ε_{1}$. Surprisingly, we find that when $ε_{2}>ε_{1}$ the regimes exhibit a very different and nontrivial behavior. Moreover, we show that similar regimes arise in the classical case involving a neutral polarized particle. The description of how the peak, valley and intermediate regimes are affected by the presence of dielectrics may be relevant for a better understanding of the interaction between anisotropic particles and corrugated surfaces.

quant-ph↗

arXiv2021

Peak, valley and intermediate regimes in the lateral van der Waals force

We study the van der Waals (vdW) interaction between a polarizable particle and a grounded conducting corrugated surface. For sinusoidal corrugations, one knows that, under the action of the lateral vdW force, an isotropic particle is always attracted to the nearest corrugation peak, with such behavior called in the present paper as peak regime. Here, considering an anisotropic polarizable particle, and making analytical calculations valid beyond the proximity force approximation (PFA), we show that the attraction is not only toward the peaks, but, for certain particle orientations and distances from the surface, the lateral force attracts the particle to the nearest corrugation valley (valley regime), or even to an intermediate point between a peak and a valley (intermediate regime). We also show that in the configurations of transition between the peak and valley regimes the lateral vdW force vanishes, even in the presence of a corrugated surface. In addition, we find that these new regimes occur in general, for periodic and nonperiodic corrugated surfaces. Moreover, we demonstrate that similar regimes arise in the classical interaction between a neutral polarized particle and a rough surface. The description of these valley and intermediate regimes, which are out of reach of the predictions based on the PFA, may be relevant for a better understanding of the interaction between anisotropic particles and corrugated surfaces in classical and quantum physics, with experimental verifications feasible in both domains.

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