# I. A. Pedrosa's research while affiliated with Universidade Federal da Paraíba and other places

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## Publications (60)

In this work we present a simple and elegant approach to study the adiabatic and nonadiabatic evolution of a generalized damped harmonic oscillator which is described by the generalized Caldirola–Kanai Hamiltonian, in both classical and quantum contexts. Based on time-dependent dynamical invariants, we find that the geometric phase acquired when th...

Based on the time-dependent dynamical invariants, we present a simple and elegant approach to study in both classical and quantum contexts the adiabatic and nonadiabatic evolution of the propagation of electromagnetic waves in a homogeneous time-varying linear material medium in which the permittivity, permeability and conductivity vary exponential...

In this work we study the classical and quantum dynamics of a London superconductor and of a time-dependent mesoscopic or nanoscale LC circuit by assuming that the inductance and capacitance vary exponentially with time at constant rate. Surprisingly, we find that the behavior of these two systems are equivalent, both classically and quantum mechan...

In the present work we discuss the behavior of light in a linear dielectric medium with a time-varying electric permittivity that increases exponentially at a constant rate and of a scalar field in a de Sitter spacetime, in both the classical and quantum contexts. Notably, we find that the behavior of these two systems are identical and can be desc...

In this work we investigate the propagation of electromagnetic waves in a homogenous dielectric linear medium with a time-varying electric permittivity modulated exponentially at a constant rate and in a de Sitter spacetime. We demonstrate that the classical and quantum dynamics of this propagation for both cases are equivalent and can be mapped in...

In this work, we analyze the quantum dynamics of a particle with time-varying mass increasing exponentially in a Paul trap with a trap frequency that decays exponentially with time. By making use of the Lewis-Riesenfeld invariant theory and Fock states, we solve the time-dependent Schrödinger equation for this problem and employ its solutions to co...

In this work, we analyze the quantum dynamics of a generalized pendulum with a time-varying mass increasing exponentially and constant gravitation. By using Lewis–Riesenfeld invariant approach and Fock states, we solve the time-dependent Schrödinger equation for this system and write its solutions in terms of solutions of the Milne–Pinney equation....

We present a simple and direct phenomenological quantization scheme for the London superconductor. Using Maxwell and continuity equations, we show that this quantization can be mapped into a quantum damped harmonic oscillator which is described by the Caldirola-Kanai Hamiltonian. With the help of the dynamic invariant method, we solve the time-depe...

We discuss the quantum theory of an harmonic oscillator with time-dependent mass and frequency submitted to action of a complex time-dependent linear potential with [Formula: see text] symmetry. Combining the Lewis and Riesenfeld approach to time-dependent non-Hermitian Hamiltonians having [Formula: see text] symmetry and linear invariants, we solv...

In this work, we solve the time-independent Schrödinger equation for a Landau system modulated by a non-Hermitian Hamiltonian. The system consists of a spinless particle in a uniform magnetic field submitted to action of a non-𝒫𝒯 symmetric complex potential. Although the Hamiltonian is neither Hermitian nor 𝒫𝒯-symmetric, we find that the Landau pro...

We discuss the extension of the Lewis and Riesenfeld invariant method to cases where the quantum systems are modulated by time-dependent non-Hermitian Hamiltonians having \(\mathcal{PT}\) symmetry. As an explicit example of this extension, we study the quantum motion of a particle submitted to action of a complex time-dependent linear potential wit...

We discuss the problem of a mesoscopic LC circuit with a negative inductance ruled by a time-dependent Hermitian Hamiltonian. Classically, we find unusual expressions for the Faraday’s law and for the inductance of a solenoid. Quantum mechanically, we solve exactly the time-dependent Schrödinger equation through the Lewis and Riesenfeld invariant o...

In this paper, we study the coherent states of Landau–Aharonov–Casher (LAC) levels. These LAC levels are an analogue of the Landau quantization for neutral particles. Afterwards, we investigate some properties of the coherent states, evaluate the uncertainty product and derive the wave functions for our problem. We also discuss the coherent states...

We calculate information measures using the Tsallis, Rényi, and Shannon entropies for two classes (Lane–Emden and Caldirola–Kanai)
of time-dependent mesoscopic RLC circuits. To determine the expressions for the entropies, we used the dynamical invariant
method to obtain the exact Schrödinger wave function $\big (\psi _n (x,t)\big )$. For the state...

We derive quantum solutions of a generalized inverted or repulsive harmonic oscillator with arbitrary time-dependent mass and frequency using the quantum invariant method and linear invariants, and write its wave functions in terms of solutions of a second-order ordinary differential equation that describes the amplitude of the damped classical inv...

We present an alternative quantum treatment for a generalized mesoscopic RLC circuit with time-dependent resistance, inductance and capacitance. Taking advantage of the Lewis and Riesenfeld quantum invariant method and using quadratic invariants we obtain exact nonstationary Schrödinger states for this electromagnetic oscillation system. Afterwards...

In this paper, we study the generalized harmonic oscillator with arbitrary time-dependent mass and frequency subjected to a linear velocity-dependent frictional force from classical and quantum points of view. We obtain the solution of the classical equation of motion of this system for some particular cases and derive an equation of motion that de...

In this paper, we use Hermitian linear invariants and the Lewis and Riesenfeld invariant method to obtain the general solution of the Schrödinger equation for a mesoscopic RLC circuit with time-dependent resistance, inductance, capacitance and a power source and represent it in terms of an arbitrary weight function. In addition, we construct Gaussi...

In this paper, we present a comprehensive quantum description of a
mesoscopic RLC circuit with time-dependent resistance, inductance and
capacitance. Based on the dynamical invariant method and using quadratic
invariants, we derive exact nonstationary quantum states for this
circuit and write them in terms of solutions of the Milne-Pinney
equation....

We discuss the Lewis and Riesenfeld invariant method for cases where the invariant has continuous eigenvalues and use it to find the Schrödinger wave functions of an inverted pendulum under time-dependent gravitation. As a particular case, we consider an inverted pendulum with exponentially increasing mass and constant gravitation. We also obtain t...

We discuss the extension of the Lewis and Riesenfeld method of solving the time-dependent Schrödinger equation to cases where the invariant has continuous eigenvalues and apply it to the case of a generalized time-dependent inverted harmonic oscillator. As a special case, we consider a generalized inverted oscillator with constant frequency and exp...

In this work we investigate classical and quantum properties of light
propagating in curved spacetimes determined by the Robertson-Walker
metric. As a special case we consider the classical de Sitter spacetime.
Afterwards, based on a quadratic invariant and the dynamical invariant
method, we solve the Schrödinger equation for this problem and
write...

In this contribution, we discuss quantum effects on relic gravitons
described by the Friedmann-Robertson-Walker (FRW) spacetime background
by reducing the problem to that of a generalized time-dependent harmonic
oscillator, and find the corresponding Schrödinger states with the
help of the dynamical invariant method. Then, by considering a quadrati...

We use the time-dependent invariant method in order to study the behavior of a scalar field placed in an anisotropic universe. The existence of coherent and squeezed states is discussed.

By making use of linear and quadratic invariants and the invariant operator formulation of Lewis and Riesenfeld, the complete exact solutions of the Schrödinger equation for the generalized time-dependent harmonic oscillator are obtained. It is shown that the general solution of the system under consideration contains both the discrete and continuo...

In this work we study the classical electrodynamics in homogeneous conducting and nonconducting time-dependent linear media in the absence of charge sources. Surprisingly, we find that a time dependence in the permittivity gives rise to an additional term in the Ampere-Maxwell equation and the presence of extra terms, non-analogous between themselv...

In this work, we present a quantum description of electromagnetic waves propagating through time-dependent homogeneous nondispersive linear media without sources. By using the Coulomb gauge, we show that this description can be perfomed in terms of a time-dependent quantum harmonic oscillator. In addition, we construct conherent states for the quan...

We present a quantum description of a mesoscopic RLC circuit. Based on the Caldirola-Kanai Hamiltonian and quantum invariant method we solve the Schrödinger equation for this circuit and write the corresponding wave functions in terms of a particular solution of the Milne-Pinney equation. In addition, we construct coherent and squeezed states for t...

We investigate the light propagation through time-dependent dielectric linear media in the absence of free charges and in curved spacetimes. Remarkably, we find that the light propagation in the two cases present amazing similarities, both classically and quantum mechanically. We also establish the connection between a permittivity with an exponent...

We present a quantum description of electromagnetic waves propagating through time-dependent homogeneous nondispersive conducting and nonconducting linear media without charge sources. Based on the Coulomb gauge and the quantum invariant method, we find the exact wave functions for this problem. In addition, we construct coherent and squeezed state...

In this work, we investigate the quantum effects of relic gravitons from a Schrödinger-picture point of view. By considering the gravity-wave equations in the Friedmann–Robertson–Walker cosmological background, we reduce the problem to that of a generalized time-dependent harmonic oscillator and find the corresponding exact analytic wave functions...

In this work, we study quantum effects of a massive scalar field in the de Sitter spacetime. We reduce the problem to that of a time-dependent harmonic oscillator and use exact linear invariants and the dynamic invariant method to derive the corresponding Schrödinger states in terms of solutions of a second order ordinary differential equation. Aft...

We present a quantization scheme for the electromagnetic field in time-dependent homogeneous nondispersive conducting and nonconducting linear media without sources. Using the Coulomb gauge, we demonstrate this quantization can be mapped into a damped (attenuated) time-dependent quantum harmonic oscillator. Remarkably, we find that the time depende...

In this contribution, we investigate quantum effects of relic gravitons in a Friedmann–Robertson–Walker (FRW) cosmological background. We reduce the problem to that of a generalized time-dependent harmonic oscillator and find the corresponding exact Schrödinger states with the help of linear invariants and of the dynamical invariant method. Afterwa...

In this work we investigate the quantization of electromagnetic waves propagating through homogeneous conducting linear media with no charge density. We use Coulomb's gauge to reduce the problem to that of a time-dependent harmonic oscillator, which is described by the Caldirola–Kanai Hamiltonian. Furthermore, we obtain the corresponding exact wave...

In this work we investigate the quantum dynamics of a particle trapped by oscillating fields. With the help of quadratic invariants and of the invariant method we solve analytically and exactly the Schrödinger equation for this system and write the corresponding wave functions in terms of solutions of the Milne–Pinney equation. We also construct co...

In this work, we use linear invariants and the dynamical invariant method to obtain exact solutions of the Schrödinger equation for the generalized time-dependent forced harmonic oscillator in terms of solutions of a second order ordinary differential equation that describes the amplitude of the classical unforced damped oscillator. In addition, we...

In this paper, we use the Coulomb gauge, linear invariants and the dynamical invariant method in the framework of the Schrödinger equation to obtain a quantum description of light propagation through homogeneous conducting linear media with no charge density. We obtain exact wavefunctions for this problem in terms of solutions of a second-order ord...

In this contribution we use linear invariants and the dynamical invariant method in the framework of the linear Schrödinger equation to study scalar fields in a Friedman–Robertson–Walker spacetime, obtaining exact wave functions to this problem. In addition, we construct Gaussian wave packet solutions and calculate the quantum fluctuations as well...

The exact wavefunctions for a particle trapped by oscillating fields are obtained in terms of Mathieu functions with the help of linear invariants and the dynamical invariant method. In addition, we construct Gaussian wave packet solutions and calculate the quantum fluctuations in the coordinate and momentum as well as the quantum correlations betw...

We obtain the Schrödinger wave functions of a generalized pendulum under time-dependent gravitation by making use of the Lewis and Riesenfeld invariant method. As an example, we consider a generalized pendulum with constant gravitation and exponentially increasing mass. We also present a canonical approach to the generalized time-dependent pendulum...

In this work we study scalar fields in a Friedmann-Robertson-Walker space-time. We use the invariant operator formulation of Lewis and Riesenfeld in order to study the behavior of scalar fields placed in the Friedmann-Robertson-Walker space-time. In addition, we construct the coherent states in this background and establish the existence of squeeze...

By using canonical and unitary transformations and the Lewis–Riesenfeld invariant method, the generalized invariant and the exact Schrödinger wave functions for a time-dependent parametric oscillator with and without an inverse quadratic potential are obtained.

Time-dependent mass and frequency inverted harmonic oscillator is discussed in light of the Lewis and Reisenfeld invariant method. The wave function is found in terms of the Weber function. As an example, we derive the wave function of the inverted Caldirola-Kanai oscillator.

We use the Lewis and Riesenfeld invariant method to obtain the exact
Schrödinger wave functions for a time-dependent harmonic oscillator
with and without an inverse quadratic potential. As a particular case we
also obtain the wave functions for the Caldirola-Kanai oscillator.

We use the Lewis and Riesenfeld invariant method [J. Math. Phys. 10, 1458 (1969)] to obtain the exact Schr\"odinger wave functions for a harmonic oscillator with time-dependent mass and frequency. Exact coherent states for such system are also constructed.

It is shown that the squeezed states derived from different unitary squeeze operators do not exhibit exactly the same results.

The correct wave function for the problem of a harmonic oscillator of time-dependent mass and frequency is obtained following the same approach used in the paper of Dantas et al. [Phys. Rev. A 45, 1320 (1992)].

It is shown that the Hamiltonian governing the dynamics of a harmonic oscillator in expanding universes belongs to the class
of quadratic Hamiltonians that generates squeezed states.

A simple treatment to the problem of finding exact invariants and related auxiliary equations for time‐dependent oscillators with friction is presented. The treatment is based on the use of a time‐dependent canonical transformation and an auxiliary transformation.

Exact coherent states for the time-dependent harmonic oscillator are constructed. These new coherent states have most, but not all, of the properties of the coherent states for the time-independent oscillator. For example, these coherent states give the exact classical motion, but they are not minimum uncertainty states.

We study a many-body system consisting of a central harmonic oscillator linearly coupled to a reservoir of a large number of oscillators. To get the quantal description of the central oscillator we use normal-ordering operators and the coherent-state representation in order to solve the Schrödinger equation for the complete system. Then, it is show...

No presente trabalho, usamos operadores invariantes lineares à luz do método de invariantes dinâmicos para encontrar as soluções exatas da equação de Schrödinger para o oscilador harmônico forçado dependente do tempo de Caldirola-Kanai em termos das soluções de uma equação diferencial de segunda ordem que descreve a amplitude de um oscilador harmôn...

Hartley and Ray have constructed and studied coherent states for the time-dependent oscillator. Here we show how to construct coherent states for more general time-dependent systems. We also show that these states are equivalent to tl;e well-known squeezed states.

A general treatment of the quanta1 harmonic oscillator with time-dependent mass and fre-quency is presented. The treatment is based on the use of some time-dependent transfor-matiois and in the method of invariants of Lewis and Riesenfeld. Exact coherent states for such a. system are also constructed.

## Citations

... The Hamilton function associated to a system of trapped ions has been investigated in a large number of papers, both analytically and experimentally [27,145,220,221,231,261,262,280,286,288,[298][299][300][301][302][303][304][305][306][307]. The non-integrability of a trapped ion system in 2D is investigated in [148] by employing the Lyapunov and Ziglin-Morales-Ramis theory [147,308,309]. ...

... The quantum harmonic oscillator potential with time-dependent parameters is relevant in modeling several problems in physics, and it has been investigated [1][2][3][4][5][6][7][8][9]. For example, the interaction between a spinless charged quantum particle and a time-dependent external classical electromagnetic field can be studied through a harmonic potential whose frequency depends explicitly on time [4,[10][11][12][13], and this is used to model the quantum motion of this particle in a trap [14][15][16][17][18][19]. In the context of quantum electrodynamics, this potential is useful, for instance, to describe the free electromagnetic field in nonstationary media [8,9,20]. ...

... Note that the authors of Ref. [30] emphasize that in nonrelativistic quantum mechanics and in relativistic quantum field theory, the time coordinate t is a parameter and thus the time-reversal operator T does not actually reverse the sign of t. Some authors adopt the fact that the operator T changes also the sign of time t → −t [7,[31][32][33][34][35][36][37][38][39][40], this case could lead sometimes to incorrect results. ...

... This apparent result leads us to the hypothesis of complex energy eigenvalues. Nonetheless, as discussed by Ramos et al. [38], although the system may be non-Hermitian, the eigenenergies of the system may be real. For more details on non-Hermitian theories, see Refs. ...

Reference: Non-Hermitian fermions with effective mass

... where β i (t) are arbitrary complex functions to be determined. By inserting the Expressions (19) and (21) in Equation 17, the following system of equations can be found: ...

... The inverted harmonic potential, a less known parabolic potential, has attracted some attention over the years [1][2][3][4][5][6][7][8][9][10][11][12] because it has a wide range of application in many branches of physics. For example, an LC circuit with negative inductance and capacitance in quantum mesoscopic system is described by a model with an effective inverted harmonic potential [13]. The inverted harmonic potential is also used in the study of fast frictionless cooling of ultracold atomic mixtures [14][15][16] and and light propagation in inhomogeneous media [17]. ...

Reference: Quantum inverted harmonic potential

... The transition to the free particle (the zero magnetic field limit) in the coherent states (15.15) was studied in [30,31]. Some generalizations were considered recently in [32]. ...

... With the development of nanometer techniques and microelectronics, classical and quantum effects of mesoscopic or nanoscale circuits have attracted a lot of interest from physicists [14][15][16][17][18][19][20]. In the study of mesoscopic circuits, an LC (inductance L and capacitance C) circuit represents a fundamental cell. ...

... Some other information measures (including the joint entropy and the Fisher information) for special cases of frequencies and states (mainly related to the ground state) were analysed in Refs. [18][19][20][21][22][23]. In the present work, see Sect. ...

... Lewis et al in their original work [12] presented a method to obtain a set of exact wave-functions for the time-dependent harmonic oscillator in Hilbert space. Later, this approach has been applied in several applications such as in mesoscopic R(t)L(t)C(t) electric circuits where the quantum evolution is described [15]. As well as in engineering, in shortcuts and adiabaticity [16]. ...