ANNUAL REPORT 2011 - Instituto de Estructura de la Materia

2B.1 THEORETICAL PHYSICS AND CHEMISTRY DEPARTMENTRESEARCH LINES:‣ Gravitation and Cosmology.‣ Condensed Matter Theory.‣ Theoretical Nuclear Physics: Structure and Reactions.‣ Theoretical Physical-Chemistry applied to Astrophysics.RESEARCH SUBLINES:Classical and Quantum General Relativity.Quantum Cosmology.Loop Quantum Gravity.Black hole physics.Computational methods in gravitational physics.Strongly correlated and mesoscopic systems.Electroweak processes in nuclei.Nuclear Structure from a selfconsistent correlated mean field approach.Three-body techniques in Nuclear Physics.Reactions of relevance in Nuclear Astrophysics.Inelastic non-reactive collisions at low temperatures.Theoretical spectroscopy of molecular species relevant for astrophysics and atmosphere.EMPLOYED TECHNIQUES:oooooooTheoretical and mathematical physics.Computational methods.Renormalization group.Selfconsistent mean field calculation techniques.Numerical methods to solve the Faddeev equations in coordinate space.Hyperspherical Adiabatic Expansion Method.High level ab initio calculations.RESEARCH ACTIVITY:QUANTUM GRAVITY& QUANTUM COSMOLOGYDuring the year 2011 we have carried to completion the work that we had been developing in the last years on thestudy of black hole entropy in loop quantum gravity (LQG). Specifically we have been able to finish the study of theasymptotic behavior of the entropy as a function of the horizon area. The most important open problem in thisregard was to determine if the intriguing structure observed for low areas was also present in the asymptotic regime.To accomplish this goal, during 2010 we developed a number of statistical methods that led to an efficientapproximation procedure for the statistical entropy that clearly explained why the low area substructure had todisappear at large scales. The result that we have just described can be understood, from a completely differentperspective, if we rely on the formalism of statistical mechanics and, in particular, on some aspects related to itsmathematical foundations. In this context it is of basic importance to understand the mathematical properties of theentropy as a function of the energy (the relevant variable in standard statistical mechanics). It is very important, forexample, to determine under which conditions the entropy is a sufficiently smooth function of the energy and itsconvexity properties. The first point is relevant because thermodynamical properties (such as the temperature of agiven system) are defined as derivatives of the entropy, whereas the second is central to the understanding of thestability of physical systems. The classical theorems on these issues prove that in the so called thermodynamic limitthe entropy satisfies reasonable smoothness and convexity properties.During the last year we have devoted a considerable effort to understand the thermodynamic limit for black holes byusing the combinatorial methods that we have developed in the preceding years. As in the case of interest for us it ispossible to effectively build both the microcanonical and the canonical (area) ensembles, we have been able to studythe behavior of black holes in the thermodynamic limit (not to be confused with the large area limit). The mostimportant conclusion of our work is that, in this limit, the entropy is indeed a smooth and concave function of thearea and it also satisfies the Bekenstein-Hawking law. It is important to highlight, nonetheless, the fact that48