Nonequilibrium many-body quantum dynamics: from full random matrices to real systems

We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full random matrices can guide and support our studies of realistic systems. We show that features of the dynamics can be anticipated from a detailed analysis of the spectrum and the structure of the initial state projected onto the energy eigenbasis. On the other way round, if we only have access to the dynamics, we can use it to infer the properties of the spectrum of the system. Our focus is on the survival probability, but results for other observables, such as the spin density imbalance and Shannon entropy are also mentioned.Comment: 14 pages, 7 figures, chapter for the book "Thermodynamics in the Quantum Regime - Recent Progress and Outlook

Boundary Conditions for Kerr-AdS Perturbations

The Teukolsky master equation and its associated spin-weighted spheroidal harmonic decomposition simplify considerably the study of linear gravitational perturbations of the Kerr(-AdS) black hole. However, the formulation of the problem is not complete before we assign the physically relevant boundary conditions. We find a set of two Robin boundary conditions (BCs) that must be imposed on the Teukolsky master variables to get perturbations that are asymptotically global AdS, i.e. that asymptotes to the Einstein Static Universe. In the context of the AdS/CFT correspondence, these BCs allow a non-zero expectation value for the CFT stress-energy tensor while keeping fixed the boundary metric. When the rotation vanishes, we also find the gauge invariant differential map between the Teukolsky and the Kodama-Ishisbashi (Regge-Wheeler-Zerilli) formalisms. One of our Robin BCs maps to the scalar sector and the other to the vector sector of the Kodama-Ishisbashi decomposition. The Robin BCs on the Teukolsky variables will allow for a quantitative study of instability timescales and quasinormal mode spectrum of the Kerr-AdS black hole. As a warm-up for this programme, we use the Teukolsky formalism to recover the quasinormal mode spectrum of global AdS-Schwarzschild, complementing previous analysis in the literature.Comment: 33 pages, 6 figure

Ages and metallicities of star clusters: new calibrations and diagnostic diagrams from visible integrated spectra

We present homogeneous scales of ages and metallicities for star clusters from very young objects, through intermediate-age ones up to the oldest known clusters. All the selected clusters have integrated spectra in the visible range, as well as reliable determinations of their ages and metallicities. From these spectra equivalent widths (EWs) of KCaII, Gband(CH) and MgI metallic, and Hdelta, Hgamma and Hbeta Balmer lines have been measured homogeneously. The analysis of these EWs shows that the EW sums of the metallic and Balmer H lines, separately, are good indicators of cluster age for objects younger than 10 Gyr, and that the former is also sensitive to cluster metallicity for ages greater than 10 Gyr. We propose an iterative procedure for estimating cluster ages by employing two new diagnostic diagrams and age calibrations based on the above EW sums. For clusters older than 10 Gyr, we also provide a calibration to derive their overall metal contents.Comment: 9 pages, 4 figures, accepted by A&

Negative modes and the thermodynamics of Reissner-Nordstr\"om black holes

We analyse the problem of negative modes of the Euclidean section of the Reissner-Nordstr\"om black hole in four dimensions. We find analytically that a negative mode disappears when the specific heat at constant charge becomes positive. The sector of perturbations analysed here is included in the canonical partition function of the magnetically charged black hole. The result obeys the usual rule that the partition function is only well-defined when there is local thermodynamical equilibrium. We point out the difficulty in quantising Einstein-Maxwell theory, where the so-called conformal factor problem is considerably more intricate. Our method, inspired by hep-th/0608001, allows us to decouple the divergent gauge volume and treat the metric perturbations sector in a gauge-invariant way.Comment: 24 pages, 1 figure; v2 minor changes to fit published versio