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This thesis describes the first demonstration of a cooperative optical non-linearity based on Rydberg excitation. Whereas in conventional non-linear optics the non-linearity arises directly from the interaction between light and matter, in a cooperative process it is mediated by dipole-dipole interactions between light-induced excitations. For excitation to high Rydberg states where the electron is only weakly bound, the dipole-dipole interactions are extremely large and long range, enabling an enormous enhancement of the non-linear effect. Consequently, cooperative non-linear optics using Rydberg excitations opens a new era for quantum optics enabling large single photon non-linearity to be accessible in free space for the first time. The thesis describes the theoretical underpinnings of the non- linear effect, the pioneering experimental results and implications for experiments in the single photon regime.
For Pestilence, the White Horseman, love becomes the most powerful cure. Having lost his wife and child during the Black Death, Pestilence accepts the fate destiny has given him as one of the Four Horsemen of the Apocalypse. For centuries, Pestilence did his job, spreading plagues and disease around the world. He does it to keep the balance between good and evil, yet he hates every minute of it. He longs to be left alone, but suddenly fate seems to have a different plan for him. When Bart Winston stumbles into an Amazon clearing, he's terribly ill and sure he's going to die. A tall white-haired man with unusual black eyes catches him in his arms and Bart's life takes a turn into the unbelievable. Blaming the whole situation on his illness might have worked, but as he gets better and learns about the strange man who heals him, Bart must accept there are more things in the world than he ever guessed. Pestilence and Bart heal each other, and begin to wonder if there can be a future for the White Horseman and the mortal he's fallen in love with.
Discrete subgroups have played a central role throughout the development of numerous mathematical disciplines. Discontinuous group actions and the study of fundamental regions are of utmost importance to modern geometry. Flows and dynamical systems on homogeneous spaces have found a wide range of applications, and of course number theory without discrete groups is unthinkable. This book, written by a master of the subject, is primarily devoted to discrete subgroups of finite covolume in semi-simple Lie groups. Since the notion of "Lie group" is sufficiently general, the author not only proves results in the classical geometry setting, but also obtains theorems of an algebraic nature, e.g. classification results on abstract homomorphisms of semi-simple algebraic groups over global fields. The treatise of course contains a presentation of the author's fundamental rigidity and arithmeticity theorems. The work in this monograph requires the language and basic results from fields such as algebraic groups, ergodic theory, the theory of unitary representatons, and the theory of amenable groups. The author develops the necessary material from these subjects; so that, while the book is of obvious importance for researchers working in related areas, it is essentially self-contained and therefore is also of great interest for advanced students.
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