Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology

A key symmetry of classical $p$-branes is invariance under worldvolume diffeomorphisms. Under the assumption that the worldvolume, at fixed values of the time, is a compact, quantisable K\"ahler manifold, we prove that the Lie algebra of volume-preserving diffeomorphisms of the worldvolume can be approximated by $su(n)$, for $n\to\infty$. We also prove, under the same assumptions regarding the worldvolume at fixed time, that classical Nambu brackets on the worldvolume are quantised by the multibrackets corresponding to cocycles in the cohomology of the Lie algebra $su(n)$.Comment: This is a contribution to the Special Issue on Deformation Quantization, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

On the effect of the maximal proper acceleration in the inertia

The effect of an hypothetical maximal proper acceleration on the inertial mass of charged particles is investigated in the context of particle accelerators. In particular, it is shown that maximal acceleration implies a reduction of the luminosity of the bunches relative with respect to the expected luminosity in the relativistic models of the bunches. This relative loss in luminosity is of the order $10^{-7}$ for the LHC and of order $10^{-4}$ for current laser plasma accelerators facilities. Although this effect is small, it increases with the square of the number of particles in the bunch.Comment: 10 page

Applications of mathematical models in energy problems: From research to spin-off generation

[ES] En este trabajo se presentan diversas aplicaciones del modelado matemático a problemas de interés en el campo de la Energía, desarrolladas en el seno de nuestro grupo de investigación. Entre ellas podemos destacar desde el estudio de los sistemas de climatización geotérmica de edificios, la trasmisión de calor en el proceso de rectificado industrial o las soluciones fotónicas para aumentar la eficiencia de los paneles solares hasta el modelado del metabolismo de sistemas microbianos para la producción de biocombustibles de última generación. Así mismo, se hace especial hincapié en un ejemplo de transferencia tecnológica a la sociedad, impulsado desde el grupo de investigación y materializado en la creación de una spin-off: Energesis Ingeniería, una empresa que no sólo está implantando sistemas geotérmicos de climatización en edificios, sino que apuesta por una fuerte presencia de las actividades de I+D entre sus tareas centrándose, fundamentalmente, en dos campos: el ahorro energético en la edificación y el uso del suelo como foco de intercambio térmico. Ambos campos requieren el despliegue de sofisticados modelos de simulación numérica, tanto de los intercambios energéticos en edificios como de la trasmisión de calor en suelos.[EN] This paper presents various applications of mathematical modeling to several problems of interest in the field of Energy, all of them developed in our research group. Among these are geothermal heat pumps, heat transfer in grinding process, photonic solutions to increase the efficiency of solar panels and metabolic modeling of microbial systems for production of next-generation biofuels. Furthermore, we focus on an example of technology transfer to society, promoted by our research group and resulting in the creation of a spin-off: Energesis Engineering, a company that not only is implementing geothermal HVAC systems in buildings, but which is also developing strong R&D activity, mainly on two areas: energy efficiency in buildings and the use of the soil as a focus for heat exchange. Both fields require the development of sophisticated numerical simulation models.Fernández De Córdoba, P. (2012). Aplicaciones del modelado matemático en problemas energéticos: Un recorrido desde la investigación a la creación de empresas. Revista de la Academia Colombiana de Ciencias Exactas Físicas y Naturales. 36(138):79-89. http://hdl.handle.net/10251/107331S79893613

Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology

[EN] The holographic principle sets an upper bound on the total (Boltzmann) entropy content of the Universe at around 10123kB (kB being Boltzmann¿s constant). In this work we point out the existence of a remarkable duality between nonrelativistic quantum mechanics on the one hand, and Newtonian cosmology on the other. Specifically, nonrelativistic quantum mechanics has a quantum probability fluid that exactly mimics the behaviour of the cosmological fluid, the latter considered in the Newtonian approximation. One proves that the equations governing the cosmological fluid (the Euler equation and the continuity equation) become the very equations that govern the quantum probability fluid after applying the Madelung transformation to the Schroedinger wavefunction. Under the assumption that gravitational equipotential surfaces can be identified with isoentropic surfaces, this model allows for a simple computation of the gravitational entropy of a Newtonian Universe.This research was supported by grant no. ENE2015-71333-R (Spain).Fernández De Córdoba, P.; Isidro, J. (2018). Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology. Proceedings. 2(4):155-159. https://doi.org/10.3390/ecea-4-050081551592

Noticia de la maravilla que ha obrado Nuestro Señor por laintercession de... San Ignacio... en su Santa Casa de Loyola, el dia 13 de mayo deste presente año de 1690

Autor tomado de Uriarte, Catálogo razonado..., I, p. 471Sign.: A

Schroedinger vs. Navier-Stokes

[EN] Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier-Stokes equation for viscous fluid flow. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out that the (state-dependent) viscosity of this fluid is proportional to Planck's constant, while the volume density of entropy is proportional to Boltzmann's constant. Stationary states have zero viscosity and a vanishing time rate of entropy density. On the other hand, the nonzero viscosity of nonstationary states provides an information-loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier-Stokes equation) gives rise to an emergent theory (a quantum particle governed by the Schroedinger equation).Fernández De Córdoba, P.; Isidro San Juan, JM.; Vazquez Molina, J. (2016). Schroedinger vs. Navier-Stokes. Entropy. 18(1):1-11. doi:10.3390/e18010034S11118

The small-world of 'Le Petit Prince': Revisiting the word frequency distribution

[EN] Many complex systems are naturally described through graph theory, and different kinds of systems described as networks present certain important characteristics in common. One of these features is the so-called scale-free distribution for its node s connectivity, which means that the degree distribution for the network s nodes follows a power law. Scale-free networks are usually referred to as small-world because the average distance between their nodes do not scale linearly with the size of the network, but logarithmically. Here we present a mathematical analysis on linguistics: the word frequency effect for different translations of the Le Petit Prince in different languages. Comparison of word association networks with random networks makes evident the discrepancy between the random Erdo¿s-Re¿ny model for graphs and real-world networks.Gamermann ., D.; Moret-Tatay, C.; Navarro Pardo, E.; Fernández De Córdoba, P. (2016). The small-world of 'Le Petit Prince': Revisiting the word frequency distribution. Digital Scholarship in the Humanities. 32(2):301-311. doi:10.1093/llc/fqw005S30131132

Forward-backward equations for nonlinear propagation in axially-invariant optical systems

We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse inhomogeneities. With a minimum amount of approximations, we obtain a system of two first-order equations for forward and backward components explicitly showing the nonlinear couplings among them. The modal approach used allows for an effective reduction of the dimensionality of the original problem from 3+1 (three spatial dimensions plus one time dimension) to 1+1 (one spatial dimension plus one frequency dimension). The new equations can be written in a spinor Dirac-like form, out of which conserved quantities can be calculated in an elegant manner. Finally, these new equations inherently incorporate spatio-temporal couplings, so that they can be easily particularized to deal with purely temporal or purely spatial effects. Nonlinear forward pulse propagation and non-paraxial evolution of spatial structures are analyzed as examples.Comment: 11 page

Hyperbolic space in the Newtonian limit: The cosmological constant

[EN] In this paper, the cosmological constant and the Boltzmann entropy of a Newtonian Universe filled with a perfect fluid are computed, under the assumption that spatial sections are copies of 3-dimensional hyperbolic space.This research was supported by Grant No. RTI2018-102256-B-I00 (Spain).Castro-Palacio, JC.; Fernández De Córdoba, P.; Gallego Torromé, R.; Isidro, J. (2022). Hyperbolic space in the Newtonian limit: The cosmological constant. International Journal of Modern Physics D. 31(09):2250072-1-2250072-11. https://doi.org/10.1142/S02182718225007292250072-12250072-11310

The irreversible quantum

We elaborate on the existing notion that quantum mechanics is an emergent phenomenon, by presenting a thermodynamical theory that is dual to quantum mechanics. This dual theory is that of classical irreversible thermodynamics. The linear regime of irreversibility considered here corresponds to the semiclassical approximation in quantum mechanics. An important issue we address is how the irreversibility of time evolution in thermodynamics is mapped onto the quantum-mechanical side of the correspondence.Fernández De Córdoba Castellá, PJ.; Isidro San Juan, JM.; Perea-Córdoba, MH.; Vázquez Molina, J. (2015). The irreversible quantum. International Journal of Geometric Methods in Modern Physics. 12(1). doi:10.1142/S0219887815500139S12