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

... 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. ...

... 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]. ...

... 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]. ...