Asenjo, F. A., Hojman, S. A., MoyaCessa, H. M., & SotoEguibar, F. (2021). Propagation of light in linear and quadratic GRIN media: The Bohm potential. Opt. Commun., 490, 126947.
Abstract: It is shown that field propagation in linear and quadratic gradientindex (GRIN) media obeys the same rules of free propagation in the sense that a field propagating in free space has a (mathematical) form that may be exported to those particular GRIN media. The Bohm potential is introduced in order to explain the reason of such behavior: it changes the dynamics by modifying the original potential . The concrete cases of two different initials conditions for each potential are analyzed.

Asenjo, F. A., Hojman, S. A., MoyaCessa, H. M., & SotoEguibar, F. (2022). Supersymmetric relativistic quantum mechanics in timedomain. Phys. Lett. A, 450, 128371.
Abstract: A supersymmetric relativistic quantum theory in the temporal domain is developed for bispinor fields satisfying the Dirac equation. The simplest timedomain supersymmetric theory can be postulated for fields with timedependent mass, showing an equivalence with the bosonic supersymmetric theory in timedomain. Solutions are presented and they are used to produce probability oscillations between mass states. As an application of this idea, we study the twoneutrino oscillation problem, showing that flavour state oscillations may emerge from the supersymmetry originated by the timedependence of the unique mass of the neutrino.(c) 2022 Elsevier B.V. All rights reserved.

Asenjo, F. A., Hojman, S. A., VillegasMartinez, B. M., MoyaCessa, H. M., & SotoEguibar, F. (2024). Supersymmetric behavior of polarized electromagnetic waves in anisotropic media. Mod. Phys. Lett. A, 39(06), 2450013.
Abstract: A medium with specific anisotropic refractive indices can induce a supersymmetric behavior in the propagation of polarized electromagnetic waves, in an analog fashion to a quantum mechanical system. The polarizations of the wave are the ones which behave as superpartners from each other. For this to happen, the anisotropy of the medium must be transverse to the direction of propagation of the wave, with different refractive indices along the direction of each polarization, being in this way a biaxial medium. These refractive indices must be complex and follow a very specific relation in order to trigger the supersymetric response of the electromagnetic wave, each of them with spatial dependence on the longitudinal (propagation) direction of the wave. In this form, in these materials, different polarized light can be used to test supersymmetry in an optical fashion.

Hojman, S. A., Asenjo, F. A., MoyaCessa, H. M., & SotoEguibar, F. (2021). Bohm potential is real and its effects are measurable. Optik, 232, 166341.
Abstract: We analyze Bohm potential effects both in the realms of Quantum Mechanics and Optics, as well as in the study of other physical phenomena described in terms of classical and quantum wave equations. We approach this subject by using theoretical arguments as well as experimental evidence. We find that the effects produced by Bohm potential are both theoretically responsible for the early success of Quantum Mechanics correctly describing atomic and nuclear phenomena and, more recently, by confirming surprising accelerating behavior of free waves and particles experimentally, for instance.

Hojman, S. J., MoyaCessa, H. M., SotoEguibar, F., & Asenjo, F. A. (2021). Timedependent harmonic oscillators and SUSY in time domain. Phys. Scr., 96(12), 125218.
Abstract: We show that the timedependent harmonic oscillator has a repulsive or inverted oscillator as a time domain SUSYlike partner. Examples of several kinds of supersymmetrical time dependent frequency systems are presented.

MoyaCessa, H. M., Asenjo, F. A., Hojman, S. A., & SotoEguibar, F. (2022). Twomode squeezed state generation using the Bohm potential. Mod. Phys. Lett. B, 36(09), 2250025.
Abstract: We show that twomode squeezed vacuumlike states may be engineered in the BohmMadelung formalism by adequately choosing the phase of the wave function. The difference between our wave function and the one of the squeezed vacuum states is given precisely by the phase we selected. We would like to stress that the engineering of twomode vacuum states is possible due to the existence of the Bohm potential, and it is relevant because of its potential use in the propagation of optical fields, where it may render a variety of applications in optics. The approach to generate nonclassical states, namely, twomode squeezed states of a quantum mechanical system is one of the first applications of the MadelungBohm formalism.

MoyaCessa, H. M., Hojman, S. A., Asenjo, F. A., & SotoEguibar, F. (2022). Bohm approach to the Gouy phase shift. Optik, 252, 168468.
Abstract: By adapting the MadelungBohm formalism to paraxial wave propagation we show, by using ErmakovLewis techniques, that the Gouy phase is related to the form of the phase chosen in order to produce a Gaussian function as a propagated field. For this, we introduce a quantum mechanical invariant, that it is explicitly time dependent. We finally show that the effective Bohm index of refraction generates a GRIN medium that produces the focusing needed for the Gouy phase.

SotoEguibar, F., Asenjo, F. A., Hojman, S. A., & MoyaCessa, H. M. (2021). Bohm potential for the time dependent harmonic oscillator. J. Math. Phys., 62(12), 122103.
Abstract: In the MadelungBohm approach to quantum mechanics, we consider a time dependent phase that depends quadratically on position, and we show that it leads to a Bohm potential that corresponds to a time dependent harmonic oscillator, provided the time dependent term in the phase obeys an Ermakov equation.

VillegasMartinez, B. M., SotoEguibar, F., MoyaCessa, H. M., Hojman, S. A., & Asenjo, F. A. (2024). NonHermitian dynamics from Hermitian systems: Doityourself. Mod. Phys. Lett. B, Early Access.
Abstract: We show that several Hamiltonians that are PT symmetric may be taken to Hermitian Hamiltonians via a nonunitary transformation and vice versa. Therefore, a recipe to produce tractable nonHermitian Hamiltonians is given (a set of instructions to do it yourself). We also show that for some specific Hamiltonians such nonunitary transformations may be associated, via a fractionalWick rotation, to complex time.
