https://hdl.handle.net/10481/31015 Sat, 11 Apr 2026 00:53:15 GMT 2026-04-11T00:53:15Z https://hdl.handle.net/10481/103478 Unbalanced droplets of one-dimensional mixtures of fermions Gordillo, María Carmen By means of a diffusion Monte Carlo technique, we study one-dimensional unbalanced mixtures of fermionic Ytterbium atoms (173Yb, 171 Yb). This means clusters in which the total number of 173Yb particles is different from the sum of all the atoms belonging to the 171 Yb isotope. Our aim will be to check the possibility of having self-bound arrangements beyond the balanced compositions reported in previous literature rather than exploring all the situations in which that could be possible. In that vein, we focused mainly on mixtures in which the atoms belonging to one isotope are spin-polarized, while the spins of the particles in the other isotope are evenly distributed in two sets. What we found was that, even tough self-bound droplets are possible for different compositions, the most stable ones are clusters with a slight excess of attractively interacting 171Yb particles with different spins with respect to the number of spin-polarized 173 Yb atoms. Clusters in which the number of repulsively interacting unequal-spin 173Yb atoms are in excess with respect to the spin-polarized 171Yb particles have a very narrow stability range. We acknowledge financial support from the Ministerio de Ciencia e Innovación MCIN/AEI/10.13039/501100011033 (Spain) under Grant No. PID2020-113565GB-C22 and from the Junta de Andalucía Group PAIDI-205. We also acknowledge the use of the C3UPO computer facilities at the Universidad Pablo de Olavide. https://hdl.handle.net/10481/103478 https://hdl.handle.net/10481/102903 Capturing magic angles in twisted bilayer graphene from information theory markers Calixto Molina, Manuel; Mayorgas Reyes, Alberto; Castaños, Octavio Zero energy eigenstates ψ0(θ) of the twisted bilayer graphene Hamiltonian at the Dirac point show a high sensitivity to the twist angle θ near the magic angles where the effective Fermi velocity vanishes. We use information theory markers, like fidelity-susceptibility and entanglement entropy of the reduced density matrix to the layer sector, to capture this quantum criticality of zero modes at magic twist angles. We thank the support of Spanish MICIU through the project PID2022-138144NB-I00. AM thanks the Spanish MIU for the predoctoral grant FPU19/06376 at the University of Granada in the early stages of this work, and also thanks the Polytechnic University of Cartagena, Spain for a contract under the European Commission project C-QuENS (ID: 101135359). OC was on sabbatical leave at Granada University, Spain, from September 2023 to August 2024. OC thanks support from the program PASPA from DGAPA-UNAM . https://hdl.handle.net/10481/102903 https://hdl.handle.net/10481/102632 Information-Theoretic Concepts to Elucidate Local and Non-Local Aspects of Chemical Phenomena Esquivel, Rodolfo O. This review explores the application of information theory in understanding chemical reactions, focusing on concepts like Shannon entropy, Fisher information, and complexity measures. By analyzing elementary chemical reactions, significant patterns in reactivity were identified, revealing chemically important regions and providing insights into reaction mechanisms. Further investigation extends to amino acids and pharmacological molecules, classifying them based on information-theoretic measures such as Shannon entropy and Fisher information. The proposed Information-Theoretic Space unveils unique aspects of many-electron systems, suggesting a universal 3D chemical space. Furthermore, we investigate the partitioning of molecules into constituent parts using Atoms-In-Molecules (AIM) schemes and their information-theoretic justifications. We validated popular AIM schemes like Hirshfeld, Bader's topological dissection, and the quantum approach within the Information Theory framework. Additionally, the study delves into the quantum origin of correlation energy, exploring the relationship between correlation energy and quantum entanglement. It also examines quantum entanglement features in dissociation processes of diatomic molecules, shedding light on critical points along reaction paths. Overall, this research highlights the utility of information theory in analyzing molecular complexity, providing insights into chemical processes and molecular behavior across various systems.; En esta revisión se examina la aplicación de la Teoría de la información tanto clásica como cuántica para entender las reacciones químicas. Se centra principalmente en el estudio de la entropía de Shannon, la información de Fisher, el Desequilibrio y las distintas medidas de complejidad. Se analizaron algunas reacciones químicas seleccionadas y se identificaron importantes patrones de reactividad, lo que permitió descubrir regiones de relevancia química y comprender mejor los mecanismos de reacción. El estudio se amplía al análisis de aminoácidos y moléculas farmacológicas. Para clasificarlos, se utilizó la entropía de Shannon y la información de Fisher lo cual permitió representar un nuevo espacio teórico-informacional, con el cuál se descubrieron características únicas en sistemas multilectróncos, lo que sugiere la existencia de un espacio químico universal en varias dimensiones. También se exploró la constitución molécular en sus componentes atómicos, empleando esquemas de Átomos en Moléculas (AIM) asociados a sus fundamentos teórico informacionales. Así, pudimos validar los principales esquemas AIM: el método "stockholder" de Hirshfeld, la disección topológica de Bader y el enfoque informacional de tipo cuántico, todos dentro del marco de la Teoría de la Información. Esta revisión profundiza también en los fundamentos cuánticos de la energía de correlación, estudiando su conexión con el fenómeno del entrelazamiento cuántico. Además, se analizan las características del entrelazamiento cuántico en el proceso de disociación en las moléculas diatómicas, indentificando los puntos críticos de estos procesos. En conclusión, este trabajo demuestra la valía de la teoría de la información para estudiar la complejidad molecular. Los resultados ofrecen importantes perspectivas sobre procesos químicos y el comportamiento de las moléculas en diferentes sistemas. Financial support was granted from Mexican agencies: CONACYT, PIFI, PROMEP-SEP and Spanish MICINN projects: FIS-2008- 02380, FQM-4643 and P06-FQM-2445 of Junta de Andalucía and to the Andalusian research group FQM-020. I also wish to acknowledge financial support from the Ministerio de Educación of Spain through grant SAB2009-0120. Allocation of supercomputing time from Laboratorio de Supercómputo y Visualización at UAM, Sección de Supercomputacion at CSIRC Universidad de Granada, and Departamento de Supercómputo at DGSCA-UNAM is gratefully acknowledged. https://hdl.handle.net/10481/102632 https://hdl.handle.net/10481/102430 Reduction of unitary operators, quantum graphs and quantum channels Salcedo Moreno, Lorenzo Luis Given a unitary operator in a finite dimensional complex Hilbert space, its unitary reduction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the reduction allows to generate the scattering matrices of new quantum graphs from assembling of simpler graphs. The reduction of quantum channels is also defined. The implementation of the quantum gates corresponding to the reduced unitary operator is investigated, although no explicit construction is presented. The situation is different for the reduction of quantum channels for which explicit implementations are given. This work has been partially supported by MCIN/AEI/10.13039/501100011033 under grant PID2020-114767 GB-I00, and by the Junta de Andalucía under grant No. FQM-225, and Spanish Ministerio de Ciencia, Innovacion y Universidades under grant PID2023-147072N https://hdl.handle.net/10481/102430 https://hdl.handle.net/10481/102391 Nambu–Jona-Lasinio model with a fractal inspired coupling Megías Fernández, Eugenio; Teixeira, M. J.; Timóteo, V. S.; Deppman, A. The Nambu–Jona-Lasino model is modified by the inclusion of a running-coupling that was obtained by a fractal approach to Quantum Chromodynamics. The coupling follows a q-exponential function and, in the context of high energy collisions, explains the origin of the Tsallis non-extensive statistics distributions. The parameter q is completely determined in terms of the number of colours and the number of quark flavours. We study several aspects of the extended model and compare our results to the standard NJL model, where a constant coupling is used in combination with a sharp cutoff to regularize the gap equation. We show that the modified coupling regularizes the model in a smooth cutoff fashion and reproduces the pion mass and decay constant, providing an almost identical Gell Mann-Oakes-Renner relation as in the standard NJL model. In both models the relation is satisfied in similar cutoff scales. An important novelty of this work is the physical explanation, in terms of the fractal QCD vacuum, for a running coupling that renormalizes the quark condensate. The work of E M is supported by the project PID2020-114767GB-I00 and by the Ramón y Cajal program under Grant RYC-2016-20678 funded by MCIN/AEI/10.13039/501100011033 and by “FSE Investing in your future”, by the FEDER/Junta de Andalucía-Consejería de Economía y Conocimiento 2014-2020 Operational Program under Grant A-FQM-178-UGR18, by Junta de Andalucía under Grant FQM-225, by the Consejería de Conocimiento, Investigación y Universidad of the Junta de Andalucía and European Regional Development Fund (ERDF) under Grant SOMM17/6105/UGR, and by the “Prórrogas de Contratos Ramón y Cajal” Program of the University of Granada. M J T is supported by São Paulo Research Foundation (FAPESP) grant 2021/12954-5. V S T is supported by FAPESP grant 2019/010889-1 and by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) grant 305004/2022-0. A D is partially supported by the CNPq, grant 304244/2018-0, by Project INCT-FNA Proc. No. 464 898/2014-5, and by FAPESP grant 2016/17612-7. https://hdl.handle.net/10481/102391