The experience in Hamiltonian Dynamical Systems with applications to Chemistry of the PI starts in 1978 with his PhD thesis on collisions, when acquired a solid background in Computational Quantum Chemistry, semiclassical treatments, and scattering theory. Some results were published in the high impact journal Phys. Rev. Lett. (1981), something extremely uncommon in the Spanish University of those days. In 1983 he made a postdoc in the USA, working on semiclassical quantization of chaotic systems, something which supposed his first contact with Nonlinear Dynamical Systems with unpredictable complex behavior. Relevant mathematical tools on nonlinear dynamics and chaos were added to the PI’s background. This work (J. Chem. Phys. 1985) has attracted great attention with more than 181 citations, extended during many years, having being referenced in the advanced monograph books by Gutzwiller and Child. Back in Spain, the PI created a research group at UAM, which has been leader at national and international levels on some aspects of quantum chaos.

During this period, the Investigator have had collaborations with Profs. Ezra (Cornell), Uzer (Georgia Tech), Jaffé (West Virginia), Ozorio de Almeida (Brazil), Martens (Irvine) and Saraceno (BsAs, Argentina) having made research in different aspects of the Classical- Quantum Correspondence (quantum chaos, Gutzwiller’s trace formula and the (alternative) Bohmian Theory of Quantum Mechanics). The most relevant contribution of the PI is to the so- called scar theory, i.e. unexpected, according to the Ergodic Theory, localization of the quantum density in unstable periodic orbits, and their homoclinic and heteroclinic manifolds (Phys. Rev. Lett. 1994, Phys. Rev. Lett. 1998, Phys. Rev. Lett. 2005, Phys. Rev. Lett. 2006). Another relevant research line, both in Chemistry and Mathematics, has been recently started in collaboration with Profs. Hernandez (Johns Hopkins U, Baltimore) and Bartsch (Appl Math, Loughborough, UK) on the study of chemical reactivity in solution (transition state theory in the Langevin equation) using numerical massive computer simulations and sophisticated geometrical theories developed using Celestial Mechanics techniques (Phys. Rev. Lett. 2008). In 2012, the PI made a sabbatical stay in the prestigious Media Lab at the MIT (Cambridge, USA) with the aim of making a serious advance in his career in the field of Complexity. There, a mathematical model for economical transactions embedded in the social networks, published in Nature Scientific Reports (2014), were developed and studied. It should be remarked that the PI’s professional trajectory constitutes a true effort of multidisciplinary, bringing chemical applications to the field of Dynamical Systems, also participating in the i-MATH Consolider, SIMUMAT and ICMAT-Severo Ochoa projects, he is member of the Red Matemática DANCE, and staff of ICMAT since its foundation. Recently, the PI has started a new line of research in Machine Learning, using the new Reservoir Computing method, applied to solving the Schrödinger eq. (see C.1.1) and with applications to prediction agri-commodity prices in Precision Agriculture, and optimization in (rotogravure printing) Industry 4.0 (see C.4), with CDTI and FUAM knowledge transfer projects. Finally, the PI is also researching on the effect of noisy gates in Quantum (Reservoir) Computing. Finally, the Investigator has a long and intense trajectory in the popularization of science, having organized many scientific events, TV courses, MOOC (9 eds) on chaos, being author of 12 chapters in the textbooks Química Física (Editorial Ariel) and Problemas de Química Física (Editorial Delta), participated 4 years in the Catálogo de Conferencias del CSIC, and in EL PAÍS-Café y Teoremas.