Nonextensive thermodynamic functions in the Schr\"odinger-Gibbs ensemble

Schr\"odinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schr\"odinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system. In this work we focus on one of the best known of these distributions, and we prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schr\"odinger's idea can not be used to construct an appropriate quantum equilibrium thermodynamics.Comment: 32 pages, revtex 4.1 preprint style, 5 figures. Published version with several changes with respect to v2 in text and reference

Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Ref. 1. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space $D$, and on the number of classical trajectories $N$ of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.Comment: Revtex 4-1, 14 pages, 2 figures. Final published versio

La sostenibilidad en la arquitectura industrializada: cerrando el ciclo de los materiales

The condition of sustainability, from a physical point of view, can be defined as the closure of the material cycle. This is reached in determined systems, in the absence of residual flows, and in which resources are constantly recycled. Such systems can encounter serious obstacles in the productive model that characterises the majority of contemporary industry. The productive model, born during the Industrial Revolution, can be summarised by the following lineal sequence: extraction > manufacture > use > residue. In contrast, this research focuses on a productive model from the ecological industry, based on the example of the biosphere as a recycling machine. Requiring the elimination of the concept of residues, the system can be summarised by the following continuous cycle: recycling-manufacturing-use-recycling. The hypothesis posed is as follows: using technology presently available, represented by the lightweight modular construction that is commercialised by renting (making it possible to return the modules to the factory once their useful life is over, therefore recuperating resources), a management system capable to close the material cycle at least to 90% can be developed. (conventional building construction currently manages a recycling value of 10% of used resources).La condición de sostenibilidad, desde el punto de vista físico, puede ser definida como el cierre de los ciclos materiales, alcanzándose éste en un sistema determinado cuando no existen flujos de residuos sino que los recursos se reciclan constantemente. Tal condición encuentra un fuerte obstáculo en el modelo productivo que caracteriza a la mayor parte de la industria contemporánea, nacido en la revolución industrial, que puede sintetizarse en la secuencia lineal extracción > fabricación > uso > residuo. En oposición a ello, el modelo productivo en el que se centra la investigación que aquí se presenta es la ecología industrial y se basa en el ejemplo de la biosfera como máquina de reciclar. Supone la eliminación del concepto de residuo y puede resumirse en el ciclo continuo de reciclaje-fabricación-uso-reciclaje. La hipótesis planteada consiste en que, a partir de los sistemas de construcción modular ligera que se comercializan bajo el sistema de alquiler (que hace posible que los módulos regresen a la fábrica una vez cumplida su vida útil, recuperándose sus componentes) se puede desarrollar un sistema de gestión de los recursos empleados en el ciclo de vida de los edificios capaz de cerrar los ciclos materiales hasta en un 90% (en la construcción convencional se alcanza un 10%)

A general framework for quantum splines

Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert projective space, which generalize the notion of Riemannian cubic splines to the quantum domain. In this paper, we present a generalization of this concept to general density matrices with a Hamiltonian approach and using a geometrical formulation of quantum mechanics. Our main goal is to formulate an optimal control problem for a nonlinear system on u∗(n) which corresponds to the variational problem of quantum splines. The corresponding Hamiltonian equations and interpolation conditions are derived. The results are illustrated with some examples and the corresponding quantum splines are computed with the implementation of a suitable iterative algorithm.The work of L. Abrunheiro was supported by Portuguese funds through the Center for Research and Development in Mathematics and Applications (CIDMA) and the Portuguese Foundation for Science and Technology (“FCT–Fundaçao para a Ciência e a Tecnologia”), within project UID/MAT/04106/2013. The work of M. Camarinha and P. Santos was partially supported by the Centre for Mathematics of the University of Coimbra – UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020. The work of J. Clemente-Gallardo and J. C. Cuchí was partially covered by MICINN grants FIS2013-46159-C3-2-P and MTM2012-33575 and by DGA Grant 2016-24/1

Statistics and Nos\'e formalism for Ehrenfest dynamics

Quantum dynamics (i.e., the Schr\"odinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. Once we know the canonical distribution of a Ehrenfest system, it is straightforward to extend the formalism of Nos\'e (invented to do constant temperature Molecular Dynamics by a non-stochastic method) to our Ehrenfest formalism. This work also provides the basis for extending stochastic methods to Ehrenfest dynamics.Comment: 28 pages, 1 figure. Published version. arXiv admin note: substantial text overlap with arXiv:1010.149

Recent tectonic and morphostructural evolution of Byers Peninsula (Antarctica): insight into the development of the South Shetland Islands and Bransfield Basin

Byers Peninsula forms the western extremity of the Livingston Island (Antarctica) in the continental South Shetland Block. This tectonic block is bounded by the South Shetland Trench to the north, the Bransfield back-arc basin to the south, and extends to the South Scotia Ridge on the east. Westwards it is connected to the Antarctic Plate by a broad deformation zone located at the southern end of the Hero Fracture Zone. In Byers Peninsula we analyzed more than 1,200 lineaments, and 359 fault planes from 16 sites, both in sedimentary and intrusive igneous rocks. Statistical analysis of lineaments and mesoscopic fractures, with a length varying between 31 and 1,555 m, shows a NW-SE maximum trend, with two NE-SW and ENE-WSW secondary maximums. Fault orientation analysis shows similar trends suggesting that most of the lineaments correspond to fractures. Due to the absence of striated faults and the lack of kinematic evidence on the regime in most of the analyzed faults we have used the Search Grid paleostress determination method. The results obtained allow us to improve and complete the data on the recent evolution of the South Shetland Block. In this complex geodynamic setting, Byers Peninsula has been subjected to NNW-SSE to NNE-SSW extension related to Bransfield Basin opening and NE-SW and NW-SE local compressions respectively associated to Scotia-Antarctic plate convergence and the South Shetland Trench subduction.La Península Byers se localiza en el extremo occidental de la Isla Livingston (Antártida) que pertenece al bloque continental de las Shetland del Sur. Este bloque tectónico está limitado al norte por la Fosa de las Shetland del Sur, al sur por la cuenca de trasarco de Bransfield, y hacia el este se extiende por la Dorsal Sur de Scotia. Hacia el oeste conecta con la placa Antártica a través de una amplia zona de deformación localizada en la prolongación meridional de la Zona de Fractura Hero. En este trabajo se han analizado conjuntamente más de 1.200 lineamientos, así como 359 planos de fallas en 16 estaciones en rocas sedimentarias e ígneas de la Península Byers. El análisis estadístico de los lineamientos y las fracturas a escala mesoscópica, con una longitud que oscila entre 31 y 1.555 m, muestran una orientación máxima NO-SE, con dos máximos secundarios de dirección NE-SO y ENE-OSO. El análisis de las fracturas muestra orientaciones similares que sugieren que gran parte de estos lineamientos están relacionados con fracturas. La ausencia de indicadores cinemáticos de calidad en la mayor parte de las fracturas sólo nos ha permitido aplicar el método de Redes de Búsqueda para el cálculo de paleoesfuerzos. Los resultados obtenidos son compatibles con los obtenidos en otros sectores del Bloque de las Shetland del Sur. En este complejo contexto geodinámico, la Península Byers ha estado sometida a extensión NNW-SSE/ NNE-SSW ligada a la apertura de la cuenca de Bransfield, así como a compresión local NE-SO y NO-SE asociada respectivamente a la convergencia entre las placas Scotia y Antártica, y a la subducción en la Fosa de las Shetland del Sur

Evolución tectónica y morfoestructural reciente de la Península Byers (Antártida): evidencias sobre el desarrollo de las Islas Shetland del Sur y la Cuenca de Bransfield

[EN] Byers Peninsula forms the western extremity of the Livingston Island (Antarctica) in the continental South Shetland Block. This tectonic block is bounded by the South Shetland Trench to the north, the Bransfield back-arc basin to the south, and extends to the South Scotia Ridge on the east. Westwards it is connected to the Antarctic Plate by a broad deformation zone located at the southern end of the Hero Fracture Zone. In Byers Peninsula we analyzed more than 1,200 lineaments, and 359 fault planes from 16 sites, both in sedimentary and intrusive igneous rocks. Statistical analysis of lineaments and mesoscopic fractures, with a length varying between 31 and 1,555 m, shows a NW-SE maximum trend, with two NE-SW and ENE-WSW secondary maximums. Fault orientation analysis shows similar trends suggesting that most of the lineaments correspond to fractures. Due to the absence of striated faults and the lack of kinematic evidence on the regime in most of the analyzed faults we have used the Search Grid paleostress determination method. The results obtained allow us to improve and complete the data on the recent evolution of the South Shetland Block. In this complex geodynamic setting, Byers Peninsula has been subjected to NNW-SSE to NNE-SSW extension related to Bransfield Basine Antarcopening and NE-SW and NW-SE local compressions respectively associated to Scotia-Antarctic plate convergence and the South Shetland Trench subduction.[ES] La Península Byers se localiza en el extremo occidental de la Isla Livingston (Antártida) que pertenece al bloque continental de las Shetland del Sur. Este bloque tectónico está limitado al norte por la Fosa de las Shetland del Sur, al sur por la cuenca de trasarco de Bransfield, y hacia el este se extiende por la Dorsal Sur de Scotia. Hacia el oeste conecta con la placa Antártica a través de una amplia zona de deformación localizada en la prolongación meridional de la Zona de Fractura Hero. En este trabajo se han analizado conjuntamente más de 1.200 lineamientos, así como 359 planos de fallas en 16 estaciones en rocas sedimentarias e ígneas de la Península Byers. El análisis estadístico de los lineamientos y las fracturas a escala mesoscópica, con una longitud que oscila entre 31 y 1.555 m, muestran una orientación máxima NO-SE, con dos máximos secundarios de dirección NE-SO y ENE-OSO. El análisis de las fracturas muestra orientaciones similares que sugieren que gran parte de estos lineamientos están relacionados con fracturas. La ausencia de indicadores cinemáticos de calidad en la mayor parte de las fracturas sólo nos ha permitido aplicar el método de Redes de Búsqueda para el cálculo de paleoesfuerzos. Los resultados obtenidos son compatibles con los obtenidos en otros sectores del Bloque de las Shetland del Sur. En este complejo contexto geodinámico, la Península Byers ha estado sometida a extensión NNW-SSE/ NNE-SSW ligada a la apertura de la cuenca de Bransfield, así como a compresión local NE-SO y NO-SE asociada respectivamente a la convergencia entre las placas Scotia y Antártica, y a la subducción en la Fosa de las Shetland del Sur.Financial support for this work was provided by the research projects REN2001-0643, CGL2005-03256 and CGL2007-28812-E/ANT of the Spanish R & D National Plan.Peer reviewe