Killings, Duality and Characteristic Polynomials

In this paper the complete geometrical setting of (lowest order) abelian T-duality is explored with the help of some new geometrical tools (the reduced formalism). In particular, all invariant polynomials (the integrands of the characteristic classes) can be explicitly computed for the dual model in terms of quantities pertaining to the original one and with the help of the canonical connection whose intrinsic characterization is given. Using our formalism the physically, and T-duality invariant, relevant result that top forms are zero when there is an isometry without fixed points is easily proved.Comment: 14 pages, Late

Unified formalism for higher-order non-autonomous dynamical systems

This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems, generalizing previous developments for higher-order autonomous mechanical systems and first-order non-autonomous mechanical systems. Then, we use this unified formulation to derive the standard Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map and the Euler-Lagrange and the Hamilton equations, both for regular and singular systems. As applications of our model, two examples of regular and singular physical systems are studied.Comment: 43 pp. We have corrected and clarified the statement of Propositions 2 and 3. A remark is added after Proposition

Time-dependent Mechanics and Lagrangian submanifolds of Dirac manifolds

A description of time-dependent Mechanics in terms of Lagrangian submanifolds of Dirac manifolds (in particular, presymplectic and Poisson manifolds) is presented. Two new Tulczyjew triples are discussed. The first one is adapted to the restricted Hamiltonian formalism and the second one is adapted to the extended Hamiltonian formalism

Highly-efficient noise-assisted energy transport in classical oscillator systems

Photosynthesis is a biological process that involves the highly-efficient transport of energy captured from the sun to a reaction center, where conversion into useful biochemical energy takes place. Even though one can always use a quantum perspective to describe any physical process, since everything follows the laws of Quantum Mechanics, is the use of quantum theory imperative to explain this high efficiency? Making use of the quantum-classical correspondence of electronic energy transfer recently introduced by Eisfeld and Briggs [Phys. Rev. E 85, 046118 (2012)], we show here that the highly-efficient noise-assisted energy transport described by Rebentrost et al. [New J. Phys. 11, 033003 (2009)], and Plenio and Huelga [New J. Phys. 10, 113019 (2008)], as the result of the interplay between the quantum coherent evolution of the photosynthetic system and noise introduced by its surrounding environment, it can be found as well in purely classical systems. The wider scope of applicability of the enhancement of energy transfer assisted by noise might open new ways for developing new technologies aimed at enhancing the efficiency of a myriad of energy transfer systems, from information channels in micro-electronic circuits to long-distance high-voltage electrical lines.Comment: 4 pages, 3 figure

Inflation including collapse of the wave function: The quasi-de Sitter case

The precise physical mechanism describing the emergence of the seeds of cosmic structure from a perfect isotropic and homogeneous universe has not been fully explained by the standard version of inflationary models. To handle this shortcoming, D. Sudarsky and collaborators have developed a proposal: the self-induced collapse hypothesis. In this scheme, the objective collapse of the inflaton wave function is responsible for the emergence of inhomogeneity and anisotropy at all scales. In previous papers, the proposal was developed with an almost exact de Sitter space-time approximation for the background that led to a perfect scale-invariant power spectrum. In the present article, we consider a full quasi-de Sitter expansion and calculate the primordial power spectrum for three different choices of the self-induced collapse. The consideration of a quasi-de Sitter background allow us to distinguish departures from an exact scale-invariant power spectrum that are due to the inclusion of the collapse hypothesis. These deviations are also different from the prediction of standard inflationary models with running spectral index. Comparison with the primordial power spectrum and the CMB temperature fluctuation spectrum preferred by the latest observational data is also discussed. From the analysis performed in this work, it follows that most of the collapse schemes analysed in this paper are viable candidates to explain present observations of the CMB fluctuation spectrum.Comment: 24 pages, 12 figures. Replaced to match published versio