Between 2009 and 2014 I worked on Applied Mathematics, within the research group FQM-316: ‘PDE’s in Kinetic Theory, Quantum-Kinetics, Fluid Mechanics and Developmental Biology (website).
During this period, my research was focused on:
- Nonlinear Schödinger equations: Schödinger-Langevin, logarithmic and Doebner-Goldin family
- Kinetic partial differential equations and viscous quantum hydrodynamic systems
- Open Quantum Systems and applications: semiconductor devices design, light-harvesting phenomena in photosynthesis
- Quantum diffusive and dissipative phenomena
Selected papers in this period:
Guerrero, P., López, J. L. , Montejo-Gámez, J. (2014). A wavefunction description of quantum Fokker-Planck dissipation: derivation and numerical approximation of transient dynamics, J. Physics A: Math Theor 47, 035303. https://doi.org/10.1088/1751-8113/47/3/035303
Guerrero, P., López, J. L. , Montejo-Gámez, J., Nieto, J. J. (2012). Wellposedness of a nonlinear Schrödinger equation of logarithmic type modeling quantum dissipation, Journal of Nonlinear Science, 22, 231-263. https://doi.org/10.1007/s00332-012-9123-8
López, J. L., Montejo-Gámez, J. (2012). On viscous quantum hydrodynamics associated with nonlinear Schrödinger–Doebner–Goldin models, Kinetic and Related Models, 5 (3), 517–536. https://doi.org/10.3934/krm.2012.5.517
Jüngel, A., López, J. L., Montejo–Gámez, J. (2011). A new derivation of the quantum Navier-Stokes equations in the Wigner-Fokker-Planck approach, Journal of Statistical Physics, 145(6), 1661-1673. https://doi.org/10.1007/s10955-011-0388-3
López, J. L., Montejo–Gámez, J. (2011). On a rigorous interpretation of the quantum Schrödinger-Langevin operador in bounded domains with applications, Journal of Mathematical Analysis and Applications 383 (2), 365-378. https://doi.org/10.1016/j.jmaa.2011.05.024
Montejo-Gámez, J. (2011). Estudio de procesos cuánticos disipativos mediante ecuaciones en derivadas parciales en la formulación de Schrödinger. PhD dissertation (online version) at the University of Granada, supervised by Dr. José Luis López (personal website).
López, J. L., Montejo–Gámez, J. (2009). A hydrodynamic approach to multidimensional dissipation-based Schrödinger models from quantum Fokker–Planck dynamics, Physica D 238, 622-644. https://doi.org/10.1016/j.physd.2008.12.006
