High Dimensional Atomic States of Hydrogenic Type: Heisenberg-like and Entropic Uncertainty Measures

This work has been partially supported by the Grant PID2020-113390GB-I00 of the Agencia Estatal de Investigacion (Spain)) and the European Regional Development Fund (FEDER), and the Grant FQM-207 of the Agencia de Innovacion y Desarrollo de Andalucia.High dimensional atomic states play a relevant role in a broad range of quantum fields, ranging from atomic and molecular physics to quantum technologies. The D-dimensional hydrogenic system (i.e., a negatively-charged particle moving around a positively charged core under a Coulomblike potential) is the main prototype of the physics of multidimensional quantum systems. In this work, we review the leading terms of the Heisenberg-like (radial expectation values) and entropy-like (Rényi, Shannon) uncertainty measures of this system at the limit of high D. They are given in a simple compact way in terms of the space dimensionality, the Coulomb strength and the state’s hyperquantum numbers. The associated multidimensional position–momentum uncertainty relations are also revised and compared with those of other relevant systems.Agencia Estatal de Investigacion (Spain)) PID2020-113390GB-I00European Commission FQM-207Agencia de Innovacion y Desarrollo de Andalucia FQM-20

Rényi Entropies of Multidimensional Oscillator and Hydrogenic Systems with Applications to Highly Excited Rydberg States

Funding: Research partially supported by the grants P20-00082 (Junta de Andalucía), PID2020- 113390GB-I00 (Agencia Estatal de Investigación (Spain), the European Regional Development Fund (FEDER)), and the Grant FQM-207 of the Agencia de Innovación y Desarrollo de Andalucía.The various facets of the internal disorder of quantum systems can be described by means of the Rényi entropies of their single-particle probability density according to modern density functional theory and quantum information techniques. In this work, we first show the lower and upper bounds for the Rényi entropies of general and central-potential quantum systems, as well as the associated entropic uncertainty relations. Then, the Rényi entropies of multidimensional oscillator and hydrogenic-like systems are reviewed and explicitly determined for all bound stationary position and momentum states from first principles (i.e., in terms of the potential strength, the space dimensionality and the states’s hyperquantum numbers). This is possible because the associated wavefunctions can be expressed by means of hypergeometric orthogonal polynomials. Emphasis is placed on the most extreme, non-trivial cases corresponding to the highly excited Rydberg states, where the Rényi entropies can be amazingly obtained in a simple, compact, and transparent form. Powerful asymptotic approaches of approximation theory have been used when the polynomial’s degree or the weight-function parameter(s) of the Hermite, Laguerre, and Gegenbauer polynomials have large values. At present, these special states are being shown of increasing potential interest in quantum information and the associated quantum technologies, such as e.g., quantum key distribution, quantum computation, and quantum metrology.Grant P20-00082 (Junta de Andalucía)PID2020- 113390GB-I00 (Agencia Estatal de Investigación (Spain)European Regional Development Fund (FEDER)Grant FQM-207 of the Agencia de Innovación y Desarrollo de Andalucí

Parameter and q asymptotics of Lq-norms of hypergeometric orthogonal polynomials

The three canonical families of the hypergeometric orthogonal polynomials in a continuous real variable (Hermite, Laguerre, and Jacobi) control the physical wavefunctions of the bound stationary states of a great number of quantum systems [Correction added after first online publication on 21 December, 2022. The sentence has been modified.]. The algebraic Lq-norms of these polynomials describe many chemical, physical, and information theoretical properties of these systems, such as, for example, the kinetic and Weizsäcker energies, the position and momentum expectation values, the Rényi and Shannon entropies and the Cramér-Rao, the Fisher-Shannon and LMC measures of complexity. In this work, we examine review and solve the q-asymptotics and the parameter asymptotics (i.e., when the weight function's parameter tends towards infinity) of the unweighted and weighted Lq-norms for these orthogonal polynomials. This study has been motivated by the application of these algebraic norms to the energetic, entropic, and complexity-like properties of the highly excited Rydberg and high-dimensional pseudo-classical states of harmonic (oscillator-like) and Coulomb (hydrogenic) systems, and other quantum systems subject to central potentials of anharmonic type (such as, e.g., some molecu- lar systems) [Correction added after first online publication on 21 December, 2022. Oscillatorlike has been changed to oscillator-like.].The work of J.S. Dehesa has been partially supported by the grant I+D+i of Junta de Andalucia with ref. P20-00082, and the grant PID2020-113390GB-I00 of the Agencia Estatal de Investigación (Spain) and the European Regional Development Fund (FEDER). The work of N. Sobrino has been partially supported by the grant IT1249-19 of Basque Government and UPV/EHU

El manto de Nuestra Señora de la Soledad de Burgos: la indumentaria de las vírgenes de vestir en su advocación de la soledad

La Cofradía de Nuestra Señora de la Soledad y de San - tiago, de la iglesia de Santiago y Santa Águeda, de Burgos, actuando en cumplimiento del legado que hizo una devota, encargó en 2012 un manto al taller del bordador Salvador Oliver Urdiales. Realizado en oro fino y terciopelo negro según diseño del artista Jesús Ruiz Ce - brero, en 2013 pasó a formar parte del patrimonio de la cofradía enriqueciendo la Semana Santa burgalesa. Al hilo de la confección de este manto se hace un repaso a la historia de la talla de la Virgen de la Soledad y a la indumentaria de las vírgenes de vestir de esta advocación.Nuestra Señora de la Soledad y de Santiago brotherhood, belonging to Santiago and Santa Águeda church in Burgos, acomplishing a devout's bequest, ordered in the year 2012 a cape to Salvador Oliver Urdiales' workshop. Made in fine gold and black velvet according to the design of Jesús Ruiz Cebrero, it become part of the brotherhood's heritage in the year 2013, enriching the burgalese Holy Week. In connection to the making of this cape, a review of the Virgen de la Soledad sculpture history and the clothing of this advocacy virgins is made

Historia corregida y aumentada de Gregorio Mayoral, verdugo de la Audiencia Territorial de Burgos

Gregorio Mayoral Sendino (Cabia, 1861-Burgos, 1928) fue nombrado ejecutor de la Justicia de la Audiencia Territorial de Bur gos en 1890. En sus 38 años de ejercicio del cargo dio garrote a 60 reos de la pena capital. La ejecución del anarquista Miguel Ángelo Rinaldi, Angiolillo, asesino de Cánovas, y de otros célebres encausados, su precisión y firmeza en el patíbulo y su dedicación al perfeccionamiento del instrumental de las ejecuciones para evitar innecesarios sufrimientos a los ajusticiados, hicieron tristemente famoso a este bur - galés, condenado por su penoso oficio al rechazo social y a la soledad.Gregorio Mayoral Sendino (Cabia, 1861-Burgos, 1928) was appointed Justice executioner at the Provincial Audience of Burgos, in 1890. During his 38 years of practice he used the cudgel against 60 sentenced to death prisoners. The execution of the anarchist Miguel Ángelo Rinaldi, Angiolillo, Canovas murderer, and of other famous convicts, his precision and determination at the scaffold and his dedication to the improvement of the execution tools aiming to avoid innecesary suffering of the prisoners, made this burgalese sadly famous, condemned to social rejection and lonesomeness by his sorry job

Martín Domínguez Berrueta y la catedral de Burgos (II): el cuaderno de notas del profesor

Fue deseo de Martín Domínguez Berrueta escribir un libro sobre la catedral de Burgos, truncado por su prematura muerte. Las notas que tomó el profesor a tal fin se recogen en los veintiocho capítulos de un cuaderno manuscrito, inédito hasta ahora, que completa los artículos de prensa que publicó sobre el monumento burgalés en distintos medios de la prensa nacional.Martín Domínguez Berrueta had the desire of writing a book about the Burgos Cathedral, but he never achieved it because of his premature death. The notes he took with that purpose are compiled on the twenty eight chapters of an until now unpublished notebook, which completes the press articles that he published about the burgalese monument on different media of the Spanish national press

"El rebaño": drama en tres jornadas y verso estrenado en Burgos con ocasión del VII centenario de la catedral

En 1921, para solemnizar la conmemoración del VII Centenario de la colocación de la primera piedra de la catedral de Burgos, se confeccionó un amplio programa de actividades religiosas y cívicas. Entre estas últimas se incluyeron seis representaciones teatrales, destacando entre ellas el estreno del poema dramático titulado El rebaño, del poeta modernista Fernando López Martín, que fue llevado a escena por la compañía teatral del notable actor Enrique Borrás con gran éxito. La acción transcurre en Burgos, durante el levantamiento de las Comunidades de Castilla.In 1921, in order to solemnise the commemoration of the 7th Centenary of the laying of the first stone of the Burgos cathedral, a broad programme of religious and civic activities was scheduled. Among the latter were included six theatrical plays, standing out the premiere of the dramatic poem titled The flock by the modernist poet Fernando López Martín, wich was staged by the great actor Enrique Borrás with a big success. The play takes part in Burgos, during the Castillan Communities uprising

"Aspectos burgaleses": María Cruz Ebro en "El Día de Palencia" (1929-1930)

El 14 de noviembre de 1929 la escritora burgalesa María Cruz Ebro (1881-1967) inició una breve colaboración periodística en El Día de Palencia, que finalizó en marzo de 1930. En los cuatro meses que van entre ambas fechas, remitió once crónicas bajo el epígrafe «Aspectos burgaleses» y una más encabezada por el título genérico «Ráfagas históricas», que se insertó en un especial sobre Bur - gos del citado medio palentino.On November 14th, 1929, the burgalese writer María Cruz Ebro (1881-1967) started a brief journalistic collaboration at the newspaper El Día de Palencia, which finished in March 1930. During the four months comprised between both dates, she sent eleven columns under the epigraph «Aspectos burgaleses» and one more, headed by the generic title «Ráfagas históricas» which was inserted into a special number of the referred palentine newspaper which dealed with Burgos