## Search

## Probability and Statistics

The challenge of inserting wind power generation into the Brazilian hydrothermal optimal dispatch.

*Reinaldo Castro Souza*, Industrial Engineering Dept., PUC-Rio, Rio de Janeiro, Brazil.

## Abstract

Brazil has a total of 4.648 power generation projects in operation, totaling 161 GW of installed capacity, where 74% comes from hydroelectric power plants and about 7% from intermittent generation sources (wind power in particular). An addition of 25 GW is scheduled for the next few years in the country's generation capacity, where 43% of this increment will come from intermittent sources. Nowadays, planning the Brazilian energy sector means, basically, making decisions about the dispatch of hydroelectric and thermoelectric plants where the operation strategy minimizes the expected value of the operation cost during the planning period, which is composed of fuel costs plus penalties for failing to supply the projected expected load. Given the growing trend of wind power generation, basically in the Northeast region of the country, within the Brazilian energy matrix, it is necessary to include this type of generation into the optimal approach dispatch currently used, so that this type of generation is effectively considered in the long term planning. This talk aims to show the preliminary developments toward the implementation in a stochastic way of such kind of energy generation, in order to generate the optimal hydrothermal wind dispatch.

Keywords: Hydro, Thermal wind power generation, optimal dispatch, demand forecast, inflow and wind speed uncertainties

## Mathematical Relativity

Cosmic no-hair in spherically symmetric black hole spacetimes.

*Pedro Oliveira*, Instituto Superior Técnico.

## Abstract

We analyze in detail the geometry and dynamics of the cosmological region arising in spherically symmetric black hole solutions of the Einstein-Maxwell-scalar field system with a positive cosmological constant. More precisely, we solve, for such a system, a characteristic initial value problem with data emulating a dynamic cosmological horizon. Our assumptions are fairly weak, in that we only assume that the data approaches that of a subextremal Reissner-Nordström-de Sitter black hole, without imposing any rate of decay. We then show that the radius (of symmetry) blows up along any null ray parallel to the cosmological horizon ("near" $i^+$), in such a way that $r=+\infty$ is, in an appropriate sense, a spacelike hypersurface. We also prove a version of the Cosmic No-Hair Conjecture by showing that in the past of any causal curve reaching infinity both the metric and the Riemann curvature tensor asymptote those of a de Sitter spacetime. Finally, we discuss conditions under which all the previous results can be globalized.

## CEMAT’s Open Seminar

Central Results from Newton’s Principia Mathematica.

*Josef Bemelmans*, RWTH Aachen University, Germany.

## Abstract

### I. The Body of Least Resistance

Newton solves a variational problem about 10 years before the curve of quickest descent was found, a topic that is regarded to be the beginning of modern calculus of variations.

### II. The Force of Attraction of a Spherical Body** **

First the geometrical proof of this theorem is analyzed; then it is indicated that this result demonstrates the definitive role of mathematics in modern natural philosophy.

**See also**: Poster

Introduced by Hugo Beirão da Veiga, Università di Pisa.

## Functional Analysis, Linear Structures and Applications

Four concrete applications of Toeplitz operators.

*Albrecht Böttcher*, Technische Universität Chemnitz, Germany.

## Abstract

I present four concrete and very different applications of Toeplitz operators.

These applications are (1) a problem in optimal ell-one control, (2) Wiener-Hopf and spectral factorization of polynomials of degree 20000, (3) computation of the volume of the fundamental domains of some high-dimensional lattices, and (4) the determination of the Hausdorff limit of the zero set of polynomials of the Fibonacci type. The talk allows you to switch off four times and to re-enter the same number of times.

## Mathematical Relativity

Mass Ladder Operators.

*Masashi Kimura*, Instituto Superior Técnico.

## Abstract

We introduce a novel type of ladder operators, which map a solution to the massive Klein-Gordon equation into another solution with a different mass. It is shown that such operators are constructed from closed conformal Killing vector fields in arbitrary dimensions if the vector fields are eigenvectors of the Ricci tensor. As an example, we explicitly construct the ladder operators in AdS spacetime. It is shown that the ladder operators exist for masses above the Breitenlohner-Freedman bound. We also discuss their applications, ladder operator for spherical harmonics, the relation between supersymmetric quantum mechanics, and some phenomenon around extremal black holes whose near horizon geometry is AdS2.

## Mathematical Relativity

On the Cosmic No-Hair Conjecture in $\mathbb{T}^2$-symmetric non-linear scalar field spacetimes.

*Katharina Radermacher*, KTH Royal Institute of Technology.

## Abstract

At late times, cosmological spacetimes solving Einstein's field equations, at least when assuming a positive cosmological constant, are conjectured to isotropise and appear like the de Sitter spacetime to late time observers. This is the statement of the Cosmic No-Hair conjecture. In this talk, I consider Einstein's non-linear scalar field equations and spacetimes with $\mathbb{T}^2$-symmetry. I present results on future global existence of such solutions and discuss the conjecture in the setting of a constant potential.

This talk is based on arXiv:1712.01801.

## Quantum Computation and Information

Quantum and classical thermodynamic machines: work, power, cooling.

*Gershon Kurizki*, Weizmann Institute of Science.

## Abstract

Heat engine efficiency is limited by the Carnot bound. However, Scully et al. [Science 299, 862(2003)] bypassed this bound by allowing for extra heat input, and hence a higher hot-bath temperature, via coherence in the working fluid. In recent years, squeezed thermal baths have been claimed to yield extra heat input and hence surpass the Carnot bound [Rossnagel et al., PRL 112, 030602 (2014)]. However, the latter claim is unfounded, since squeezed baths transfer not just heat but also work to the working fluid, as shown by us [Gelbwaser-Klimovsky et al., NJP 18, 083012 (2016)]. Consequently, such engines are no longer heat engines but more like mechanical engines, and hence the Carnot bound is irrelevant to them. We have recently formulated a universal theory of any quantum or classical machines, fueled by arbitrary heat and work reservoirs [W. Niedenzu et al., Nature Commun. (2017)], which shows that what counts for maximal efficiency is the minimal loss of energy to the cold bath, which may be completely different from a Carnot bound if the baths are non-thermal. The crucial feature that allows for maximal work and power is maximized non-passivity (ergotropy) of the working fluid and/or the piston, as shown by us lately for a heat engine whose piston is squeezed by a pump [A. Ghosh et al., PNAS 2017]. Analogous considerations apply to cooling / refrigeration performance.

## Quantum Computation and Information

Quantum Baths Under Control: More Friends than Foes?

*Gershon Kurizki*, Weizmann Institute of Science.

## Abstract

We wish to “make out a case” for quantum reservoirs (baths), typically thermal, as potentially useful resources in quantum technologies: quantum information processing, quantum sensing and metrology, as well as quantum thermodynamics. In general, there is little we can do to avoid the ubiquitous presence of environments described as thermal baths in contact with quantum systems: with very few exceptions, all quantum systems are open. One may try to reduce the bath effects on the quantum system of interest by means of dynamical control, originally developed to suppress bath-induced decoherence or dissipation.Yet such control does not always yield the desired results, hence we advocate a different strategy that may be colloquially summarized as follows: “If you can’t fight the bath – join it”, namely, take advantage of its effects, particularly those that do not obliterate “quantumness” in the system-bath compound. To this end, three possible approaches may be pursued:

- Control a quantum system within the memory time of the bath to which it couples: Dynamical control allows us to reveal quasi-reversible / coherent dynamical phenomena of quantum open systems, manifest by the quantum Zeno or anti-Zeno effects (QZE or AZE, respectively). Dynamical control methods based on the QZE are aimed at protecting the quantumness of the system, diagnosing the bath spectra and transferring quantum information via noisy media. By contrast, AZE-based control is useful for fast cooling of thermalized quantum systems.
- Engineer the coupling of quantum systems to selected bath modes: This approach allows to drastically modify bath-mediated exchange of vritual quanta between quantum systems and thereby enhance their coupling.More dramatically, such engineering allows us to achieve bath-induced entanglement or persistent coherence that may appear paradoxical if one takes the conventional view that coupling to baths destroys quantumness.
- Select or engineer baths with appropriate spectra: This approach is a prerequisite for the construction of the simplest and most efficient quantum heat machines (engines and refrigerators) and investigating their ability to attain the absolute zero.

## Mathematical Relativity

An introduction to the quantized Dirac field on a curved spacetime I.

*Moritz Reintjes*, Instituto Superior Técnico.

## Mathematical Relativity

An introduction to the quantized Dirac field on a curved spacetime II.

*Moritz Reintjes*, Instituto Superior Técnico.

## String Theory

Matrix quantum mechanics and black holes.

*Olga Papadoulaki*, University of Southampton.

## Geometria em Lisboa

To be announced.

*Alessandro Ghigi*, Università di Pavia.

## Mathematical Relativity

Test fields cannot destroy extremal black holes.

*Rodrigo Vicente*, Instituto Superior Tecnico.

## Abstract

We prove that (possibly charged) test fields satisfying the null energy condition at the event horizon cannot overspin/overcharge extremal Kerr-Newman or Kerr-Newman-anti de Sitter black holes, that is, the weak cosmic censorship conjecture cannot be violated in the test field approximation. The argument relies on black hole thermodynamics (without assuming cosmic censorship), and does not depend on the precise nature of the fields. We also discuss generalizations of this result to other extremal black holes.

This seminar is joint with CENTRA.

## Mathematical Relativity

Perturbations of the asymptotic region of the Schwarzschild-de Sitter spacetime.

*Edgar Gasperin*, Queen Mary, University of London.

## Abstract

Although the study of the Cauchy problem in General Relativity started in the decade of 1950 with the work of Foures-Bruhat, addressing the problem of global non-linear stability of solutions to the Einstein field equations is in general a hard problem. The first non-linear global non-linear stability result in General Relativity was obtained for the de-Sitter spacetime by H. Friedrich in the decade of 1980. In this talk the main tool used in the above result is introduced: a conformal (regular) representation of the Einstein field equations ---the so-called conformal Einstein field equations (CEFE). Then, the conformal structure of the Schwarzschild–de Sitter spacetime is analysed using the extended conformal Einstein field equations (XCEFE). To this end, initial data for an asymptotic initial value problem for the Schwarzschild–de Sitter spacetime are obtained. This initial data allow to understand the singular behaviour of the conformal structure at the asymptotic points where the horizons of the Schwarzschild–de Sitter spacetime meet the conformal boundary. Using the insights gained from the analysis of the Schwarzschild–de Sitter spacetime in a conformal Gaussian gauge, we consider nonlinear perturbations close to the Schwarzschild–de Sitter spacetime in the asymptotic region. Finally, we'll show that small enough perturbations of asymptotic initial data for the Schwarzschild–de Sitter spacetime give rise to a solution to the Einstein field equations which exists to the future and has an asymptotic structure similar to that of the Schwarzschild–de Sitter spacetime.

This seminar is joint with CENTRA, and will take place on the Physics Department (seminar room, 2nd floor).