Research

About

My research path has been a workaround between theoretical aspects of Lie algebras applied to discrete systems in my former graduate years, to the description of light-matter interaction using geometric and algebraic approach, with a great doses of numerical simulation. My last three contributions deals with:

(Dec 2024) The analytical and numerical solution of a linear and quadratic coupling optomechanical system, with a forcing term in the field. Currently, as a preprint under peer-reviewing (arXiv preprint: https://doi.org/10.48550/ARXIV.2412.11980)
(Oct 2024) The analytical and numerical solution of a nonlinear Jaynes-Cummings, where deformed field operators were introduced, and the non-stationary spectral response was obtained. Published in PRA: https://doi.org/10.1103/physreva.110.043703
(Sep 2024) The proposal to use a discrete realization of the harmonic oscillator using the angular momentum generator J_{x}, this in advance to use it as a kernel of transformation exploiting the Wigner-Radon theorem via the discrete fractional Fourier transform. Published in JOSAB: https://doi.org/10.1364/josab.533919

Click to see the complete list of manuscripts

Urzúa, A. R., & Wolf, K. B. (2016). Unitary rotation and gyration of pixelated images on rectangular screens. In Journal of the Optical Society of America A (Vol. 33, Issue 4, p. 642). Optica Publishing Group. https://doi.org/10.1364/josaa.33.000642
Urzúa, A. R., & Wolf, K. B. (2017). The U(2) Fourier group for rectangular pixellated images. In Physical and Mathematical Aspects of Symmetries (pp. 367–373). Springer International Publishing. https://doi.org/10.1007/978-3-319-69164-0_55
Ramos-Prieto, I., Urzúa, A. R., Soto-Eguibar, F., & Moya-Cessa, H. M. (2018). KvN mechanics approach to the time-dependent frequency harmonic oscillator. In Scientific Reports (Vol. 8, Issue 1). Springer Science and Business Media LLC. https://doi.org/10.1038/s41598-018-26759-w
Urzúa, A. R., Ramos-Prieto, I., Soto-Eguibar, F., Arrizón, V., & Moya-Cessa, H. M. (2019). Light propagation in inhomogeneous media, coupled quantum harmonic oscillators and phase transitions. In Scientific Reports (Vol. 9, Issue 1). Springer Science and Business Media LLC. https://doi.org/10.1038/s41598-019-53024-5
Urzúa, A. R., Ramos-Prieto, I., Fernández-Guasti, M., & Moya-Cessa, H. M. (2019). Solution to the Time-Dependent Coupled Harmonic Oscillators Hamiltonian with Arbitrary Interactions. In Quantum Reports (Vol. 1, Issue 1, pp. 82–90). MDPI AG. https://doi.org/10.3390/quantum1010009
Urzúa, A. R., Ramos-Prieto, I., Soto-Eguibar, F., & Moya-Cessa, H. (2020). Dynamical analysis of mass–spring models using Lie algebraic methods. In Physica A: Statistical Mechanics and its Applications (Vol. 540, p. 123193). Elsevier BV. https://doi.org/10.1016/j.physa.2019.123193
Ramos-Prieto, I., Urzúa, A. R., Fernández-Guasti, M., & Moya-Cessa, H. M. (2020). Ermakov-Lewis Invariant for Two Coupled Oscillators. In Journal of Physics: Conference Series (Vol. 1540, Issue 1, p. 012009). IOP Publishing. https://doi.org/10.1088/1742-6596/1540/1/012009
Urzúa, A. R., & Moya-Cessa, H. M. (2022). Intrinsic decoherence for the displaced harmonic oscillator. In Pramana (Vol. 96, Issue 2). Springer Science and Business Media LLC. https://doi.org/10.1007/s12043-022-02319-w
Urzúa, A. R., & Wolf, K. B. (2022). Unitary rotation of pixellated polychromatic images. In Journal of the Optical Society of America A (Vol. 39, Issue 8, p. 1323). Optica Publishing Group. https://doi.org/10.1364/josaa.462530
Urzúa, A. R., & Wolf, K. B. (2022). Arbitrary unitary rotation of three-dimensional pixellated images (Version 2). arXiv. https://doi.org/10.48550/ARXIV.2207.13308
Urzúa, A. R., & Moya-Cessa, H. M. (2023). Intrinsic decoherence dynamics in the three-coupled harmonic oscillators interaction. In International Journal of Modern Physics B (Vol. 38, Issue 03). World Scientific Pub Co Pte Ltd. https://doi.org/10.1142/s0217979224500425
Urzúa, A. R., & Moya-Cessa, H. M. (2023). Moving mirror-field dynamics under intrinsic decoherence. In Modern Physics Letters B (Vol. 38, Issue 04). World Scientific Pub Co Pte Ltd. https://doi.org/10.1142/s021798492350238x
Medina-Dozal, L., Récamier, J., Moya-Cessa, H. M., Soto-Eguibar, F., Román-Ancheyta, R., Ramos-Prieto, I., & Urzúa, A. R. (2023). Temporal evolution of a driven optomechanical system in the strong coupling regime. In Physica Scripta (Vol. 99, Issue 1, p. 015114). IOP Publishing. https://doi.org/10.1088/1402-4896/ad15cf
Urzúa, A. R., Ramos-Prieto, I., & Moya-Cessa, H. M. (2024). Integrated optical wave analyzer using the discrete fractional Fourier transform. In Journal of the Optical Society of America B (Vol. 41, Issue 10, p. 2358). Optica Publishing Group. https://doi.org/10.1364/josab.533919
Medina-Dozal, L., Urzúa, A. R., Aranda-Lozano, D., González-Gutiérrez, C. A., Récamier, J., & Román-Ancheyta, R. (2024). Spectral response of a nonlinear Jaynes-Cummings model. In Physical Review A (Vol. 110, Issue 4). American Physical Society (APS). https://doi.org/10.1103/physreva.110.043703
Medina-Dozal, L. A., Urzúa, A. R., & Récamier-Angelini, J. (2024). Temporal evolution of a forced optomechanical system with linear and quadratic field -- mechanical oscillator couplings (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.11980

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