On the strongly damped wave equation with constraint

A weak formulation for the so-called "semilinear strongly damped wave equation with constraint" is introduced and a corresponding notion of solution is defined. The main idea in this approach consists in the use of duality techniques in Sobolev-Bochner spaces, aimed at providing a suitable "relaxation" of the constraint term. A global in time existence result is proved under the natural condition that the initial data have finite "physical" energy.Comment: 21 page

Detectores cuánticos y correlaciones de vacío en espacio y tiempo: resultados teóricos y propuestas de simulación

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Física Teórica I, leída el 27/11/2014Depto. de Física TeóricaFac. de Ciencias FísicasTRUEunpu

Numerical methods for finding stationary gravitational solutions

The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory-Laflamme zero modes of small rotating black holes in AdS. We also include several tools and tricks that have been useful throughout the literature

Shape & cutoff in superconducting qubits, work fluctuations in correlation creation, & critical commentary

Part I We apply the Unruh-DeWitt model for a qubit interacting with a quantum field to a superconducting qubit. We use the flexibility of this model, as compared to the spin-boson model used widely in the literature, to investigate the effect of an ultraviolet cutoff in the field and the finite size of a qubit on the dynamics of a qubit. In studying these features in the setup of a qubit coupled to an infinite transmission line, we find that both the shape and scale of the ultraviolet cutoff have a significant effect on the qubit’s dynamics. For experimentally reasonable parameters, we estimate that using an inaccurate model for the ultraviolet cutoff present in the line could introduce errors in calculation of probability of spontaneous emission of the qubit of around 10%. This is particularly interesting in light of the fact that superconducting lines have natural ultraviolet cutoffs due to the breakdown of superconductivity for high frequency electromagnetic waves. Part II We investigate a unitary protocol to create correlations in a bipartite quantum me- chanical system. The protocol was initially motivated by its optimal average work cost. We calculate the fluctuations in the work cost and show that for maximal generation of correlations, the fluctuations in the work cost are of the order of the average work cost, making the protocol energetically rather unreliable. We additionally explore some of the nuances of the discussion around work in quantum systems with discussion of the current literature as well as some philosophical motivations of the most widely used definitions of work. Throughout the thesis, we comment on the motivations for this research and its effect on our world. In doing so, we find multiple ways that supporting the project of developing quantum technology supports injustice. We also model a methodology for engaging with societal and ethical implications of work in theoretical physics

Classical Systems in Quantum Mechanics

If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of kinematics and dynamics of classical systems emerges from the mathematical formalism of QM. The first of these ways is to obtain an equivalent description of QM (with finite number of degrees of freedom) as a classical Hamiltonian field theory and afterwards restrict it in dependence of specific classical system to obtain the classical Hamiltonian mechanics of that finite system. The second way is transition to QM of systems with infinite number of degrees of freedom - i.e. of macroscopic systems - and extract from it classical mechanics (with finite number of degrees of freedom) of macroscopic variables of this quantum system. The last chapter contains some considerations concerning the "measurement problem in QM", in which a measured quantum "microsystem" has to be dynamically connected with changes of classical states of a macroscopic quantum (sub-)system - the measuring device. Several models of this process are presented.Comment: book format, 230 pages, extensive bibliography and index, hypertext; alternative versions appear on the author`s home page: davinci.fmph.uniba.sk/~bona1/CSinQM/CSinQM-June7.pd

Mathematical foundations of elasticity

[Preface] This book treats parts of the mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is intended for mathematicians, engineers, and physicists who wish to see this classical subject in a modern setting and to see some examples of what newer mathematical tools have to contribute

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity