Momentum maps for mixed states in quantum and classical mechanics

This paper presents the momentum map structures which emerge in the dynamics of mixed states. Both quantum and classical mechanics are shown to possess analogous momentum map pairs. In the quantum setting, the right leg of the pair identifies the Berry curvature, while its left leg is shown to lead to more general realizations of the density operator which have recently appeared in quantum molecular dynamics. Finally, the paper shows how alternative representations of both the density matrix and the classical density are equivariant momentum maps generating new Clebsch representations for both quantum and classical dynamics. Uhlmann's density matrix and Koopman-von Neumann wavefunctions are shown to be special cases of this construction.Comment: 20 pages; no figures. To appear in J. Geom. Mec

Illiberal regimes in the perspective of comparative constitutionalism

Illiberal regimes are generally de ned as regimes in which neither democracy nor fundamental rights are granted, and in which rule of law is substantially disregarded. Instead of attempting a taxonomy, the article gives an account of their origins and of the problems raised by their emergence in the perspective of comparative constitutionalism

A note on an Umayyad carved ivory plaque kept at the Walters Art Gallery

This paper proposes an iconographical and stylistic analysis of a carved ivory plaque kept at the Walters Art Gallery in Baltimore (acc. no. 71.62). It will show that it is not a Coptic artefact featuring a Sasanian king, as assumed until now, but an Umayyad artefact which must be contextualised within a specific tradition of imagery related to the expression of the Umayyad concept of Caliphal authority

Reconstruction of mimetic gravity in a non-singular bouncing universe from quantum gravity

We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function $f(\Box\phi)$ implementing the limiting curvature hypothesis. We show how relevant physical information can be extracted from power law expansions of $f$ in different regimes, corresponding e.g. to the very early universe or to late times. Our results are then applied to two specific models reproducing the cosmological background dynamics obtained in group field theory and in loop quantum cosmology, and we discuss the possibility of using this framework as providing an effective field theory description of quantum gravity. We study the evolution of anisotropies near the bounce, and discuss instabilities of scalar perturbations. Furthermore, we discuss two equivalent formulations of mimetic gravity: one in terms of an effective fluid with exotic properties, the other featuring two distinct time-varying gravitational "constants" in the cosmological equations.Comment: Invited article for the special issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms" of the journal "Universe"; 21 pages, 2 figures; v2: matches published versio

Hellenistic Gymnasia in the Heart of Athens: Change and Continuity

Während die alten Gymnasia (Akademie, Lykaion, Kynosarges) außerhalb der Stadtmauern Athens lagen, wurden kurz nach 229 v. Chr. zwei neue Gymnasia im Zentrum der Stadt errichtet: das Diogeneion und das Ptolemaion. In diesem Beitrag werden die Geschichte, Architektur und Funktion dieser beiden Gymnasia untersucht, auf Basis einer systematischen Analyse aller relevanten literarischen, epigraphischen und archäologischen Quellen. Die Komplexe waren wichtig für das Stadtbild, weil sie dem chaotischen, altmodischen Zentrum einen Hauch von Modernität verliehen. Ihre exakte Lage bleibt zwar umstritten, aber sie waren topographisch und ideologisch fest mit dem alten Stadtzentrum verbunden und dienten als Zentren für die Ausbildung der Epheben in der gesamten hellenistischen und römischen Zeit