arXiv subjects

Danilo T. Alves

Publications and source records attributed to Danilo T. Alves.

At least 19 recordsLinked to original sources

arXiv2025

The time-dependent quantum harmonic oscillator: a pedagogical approach via the Lewis-Riesenfeld dynamical invariant method

In quantum mechanics courses, students often solve the Schrödinger equation for the harmonic oscillator with time-independent parameters. However, time-dependent quantum harmonic oscillators are relevant in modeling several problems as, for instance, the description of quantum motion of particles in traps, shortcuts to adiabaticity, generation of squeezed states, as well as quantum scalar fields evolving in expanding universes. In the present paper, we discuss, with a pedagogical approach, the quantum harmonic oscillator with time-dependent frequency via the Lewis-Riesenfeld dynamical invariant method, revisiting the main steps to obtain the wave function associated with this model, and briefly discussing the relation between this oscillator and the generation of squeezed states. As examples of didactic applications of time-dependent harmonic oscillators and the Lewis-Riesenfeld method in quantum mechanics courses, we solve the following problems: the calculation of the transition probability associated with a harmonic oscillator which undergoes jumps in its frequency, and the analysis of the dynamics of a quantum particle in a Paul trap.

quant-ph↗

arXiv2024

Teaching materials aligned or unaligned with the principles of the Cognitive Theory of Multimedia Learning: the choices made by Physics teachers and students

In a recent study [Rev. Bras. Ens. Fís. vol. 45, 2023], the absence of the Cognitive Theory of Multimedia Learning (CTML) in the curricula of Physics teacher education programs at Brazilian public universities was highlighted. Considering this gap, the present study investigates whether, even without any formal prior knowledge of CTML principles (Coherence, Signaling, Spatial Contiguity, Segmentation, Multimedia, and Personalization), Physics teacher trainees and educators tend to choose, among two formats of multimedia materials - one aligned with a given CTML principle and the other not - the materials aligned with these principles. The findings of this case study revealed that, although most participants generally selected materials aligned with the mentioned principles, a significant portion did not. These results underscore the importance of Brazilian universities considering the inclusion of CTML in Physics teacher education curricula.

physics.ed-ph↗

arXiv2024

Curvature effects on the regimes of the lateral van der Waals force

Recently, it has been shown that, under the action of the lateral van der Waals (vdW) force due to a perfectly conducting corrugated plane, 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 the peak, valley, and intermediate regimes, respectively. In the present paper, we calculate the vdW interaction between a polarizable particle and a grounded conducting corrugated cylinder, and investigate how the effects of the curvature of the cylinder affect the occurrence of the mentioned regimes.

quant-ph↗

arXiv2024

Polarization and energy ellipsoids for an introductory visualization of tensors

In ``The Feynman Lectures on Physics'' is discussed an introduction to tensors by means of the polarization tensor, including a way of ``visualizing'' this tensor via the energy ellipsoid, which is drawn by the electric fields which produce the same polarization energy density in an anisotropic crystal. Here, we discuss an alternative way of visualizing the polarization tensor, by means of the polarization ellipsoid, which is based on the ideas of Lamé's stress ellipsoid and is drawn by the polarization vectors produced by electric fields having the same magnitude. We compare both ellipsoids as a first introductory way of visualizing the polarization tensor.

physics.ed-ph↗

arXiv2024

Squeezing equivalence of quantum harmonic oscillators under different frequency modulations

The papers by Janszky and Adam [Phys. Rev. A {\bf 46}, 6091 (1992)] and Chen \textit{et al.} [Phys. Rev. Lett. {\bf 104}, 063002 (2010)] are examples of works where one can find the following equivalences: belonging to the following class: quantum harmonic oscillators subjected to different time-dependent frequency modulations, during a certain time interval $τ$, exhibit exactly the same final null squeezing parameter ($r_f=0$). In the present paper, we discuss a more general case of squeezing equivalence, where the final squeezing parameter can be non-null ($r_f\geq0$). We show that when the interest is in controlling the forms of the frequency modulations, but keeping free the choice of the values of $r_f$ and $τ$, this in general demands numerical calculations to find these values leading to squeezing equivalences (a particular case of this procedure recovers the equivalence found by Jansky and Adams). On the other hand, when the interest is not in previously controlling the form of these frequencies, but rather $r_f$ and $τ$ (and also some constraints, such as minimization of energy), one can have analytical solutions for these frequencies leading to squeezing equivalences (particular cases of this procedure are usually applied in problems of shortcuts to adiabaticity, as done by Chen \textit{et al.}). In this way, this more general squeezing equivalence discussed here is connected to recent and important topics in the literature as, for instance, generation of squeezed states and the obtaining of shortcuts to adiabaticity.

quant-ph↗

arXiv2024

Vacuum energy around particles

The creation of particles by the excitation of the quantum vacuum in a cavity with a moving mirror was predicted in 1969. Here, we investigate that, in addition to real particles, the excitation of the quantum vacuum in a dynamical cavity can also result in the creation of a certain amount of positive vacuum energy around these particles. We show that while in the case of a single mirror moving in a free space, with the field in the vacuum state, all the energy transferred from the mirror to the field is converted into real particles, on the other hand, when considering a second and static mirror forming a cavity with the first, the same movement of the first mirror can lead to less energy being converted into real particles, with the difference being converted into positive vacuum energy around these particles.

hep-th↗

arXiv2023

Renormalization of the band gap in 2D materials near an interface between two dielectrics

We investigate how the renormalization of the band gap in a planar 2D material is affected by the consideration of two nondispersive semi-infinite dielectrics, with dielectric constants $ε_1$ and $ε_2$, separated by a planar interface. Using the pseudo quantum electrodynamics to model the Coulomb interaction between electrons, we show how the renormalization of the band gap depends on $ε_1$ and $ε_2$, and also of the distance between the 2D material and the interface between the two dielectrics. In the appropriate limits, our results reproduce those found in the literature for the band gap renormalization when a single dielectric medium is considered.

hep-th↗

arXiv2023

Exact solution of a time-dependent quantum harmonic oscillator with two frequency jumps via the Lewis-Riesenfeld dynamical invariant method

Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency $ω_0$, that undergoes a sudden jump to a frequency $ω_1$ and, after a certain time interval, suddenly returns to its initial frequency. Using the Lewis-Riesenfeld method of dynamical invariants, we present expressions for the mean energy value, the mean number of excitations, and the transition probabilities, considering the initial state different from the fundamental. We show that the mean energy of the oscillator, after the jumps, is equal or greater than the one before the jumps, even when $ω_1<ω_0$. We also show that, for particular values of the time interval between the jumps, the oscillator returns to the same initial state.

quant-ph↗

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.

quant-ph↗

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

A simple mathematical model underlying Keller's individualized teaching method

Keller's article entitled ``Good-bye teacher...'' [J. Appl. Behav. Anal. \textbf{1}, 79-89 (1968)] was fundamental for the development and dissemination of Keller's Personalized System of Instruction (PSI), which was one of the central issues in the discussions on psychology and education in the 1970s and 1980s, and nowadays has attracted attention in the context of the increasing use of online education. Belonging to a class of approaches usually named as mastery learning, PSI and modified PSI courses (Keller-type courses) present several interesting results, such as final grade distributions where the majority of students achieve the highest grades. Here, we present a simple mathematical model underlying Keller-type individualized teaching methods, describing, in terms of average characteristic parameters, the time evolution of the distribution of students per unit of content, and that most students achieve the highest grades at the end of the course. By applying this model to a real case of an introductory electromagnetism Keller-type course, we obtained its characteristic parameters with which we showed good agreement between the predictions and observations. The model presented here results in a simple formula, which is very accessible for use by a wide audience interested in planning or investigating Keller-type or other mastering learning methods.

physics.ed-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.

quant-ph↗

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

Dynamical Casimir effect enhanced by decreasing the mirror reflectivity

In the present paper, we show that a partially reflecting static mirror with time-dependent properties can produce, via dynamical Casimir effect in the context of a massless scalar field in $1+1$ dimensions, a larger number of particles than a perfectly reflecting one. As particular limits, our results recover those found in the literature for a perfect static mirror imposing a generalized or an usual time-dependent Robin boundary condition.

quant-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.

quant-ph↗

arXiv2020

Relativistic bands in the discrete spectrum of created particles in an oscillating cavity

We investigate the dynamical Casimir effect for a one-dimensional resonant cavity, with one oscillating mirror. Specifically, we study the discrete spectrum of created particles in a region of frequencies above the oscillation frequency $ω_0$ of the mirror. We focus our investigation on an oscillation time equal to $2L_0/c$, where $L_0$ is the initial and final length of the cavity, and $c$ is the speed of light. For this oscillation duration, a field mode, after perturbed by the moving mirror, never meets this mirror in motion again, which allows us to exclude this effect of re-interaction on the particle creation process. Then, we describe the evolution of the particle creation with frequencies above $ω_0$ only as a function of the relativistic aspect of the mirror's velocity. In other words, we analyze the formation of relativistic bands in a discrete spectrum of created particles.

quant-ph↗