A Berger type normal holonomy theorem for complex submanifolds

We prove a kind of Berger-Simons' Theorem for the normal holonomy group of a complex submanifold of the projective spac

Holonomy and submanifold geometry

We survey applications of holonomic methods to the study of submanifold geometry, showing the consequences of some sort of extrinsic version of de Rham decomposition and Berger's Theorem, the so-called Normal Holonomy Theorem. At the same time, from geometric methods in submanifold theory we sketch very strong applications to the holonomy of Lorentzian manifolds. Moreover we give a conceptual modern proof of a result of Kostant for homogeneous space

Dissipative Binding of Lattice Bosons through Distance-Selective Pair Loss

We show that in a gas of ultra cold atoms distance selective two-body loss can be engineered via the resonant laser excitation of atom pairs to interacting electronic states. In an optical lattice this leads to a dissipative Master equation dynamics with Lindblad jump operators that annihilate atom pairs with a specific interparticle distance. In conjunction with coherent hopping between lattice sites this unusual dissipation mechanism leads to the formation of coherent long-lived complexes that can even exhibit an internal level structure which is strongly coupled to their external motion. We analyze this counterintuitive phenomenon in detail in a system of hard-core bosons. While current research has established that dissipation in general can lead to the emergence of coherent features in many-body systems our work shows that strong non-local dissipation can effectuate a binding mechanism for particles

Facilitated spin models of dissipative quantum glasses

We introduce a class of dissipative quantum spin models with local interactions and without quenched disorder that show glassy behaviour. These models are the quantum analogs of the classical facilitated spin models. Just like their classical counterparts, quantum facilitated models display complex glassy dynamics despite the fact that their stationary state is essentially trivial. In these systems, dynamical arrest is a consequence of kinetic constraints and not of static ordering. These models display a quantum version of dynamic heterogeneity: the dynamics towards relaxation is spatially correlated despite the absence of static correlations. Associated dynamical fluctuation phenomena such as decoupling of timescales is also observed. Moreover, we find that close to the classical limit quantum fluctuations can enhance glassiness, as recently reported for quantum liquids.Comment: 7 pages, 6 figure

Universal time-evolution of a Rydberg lattice gas with perfect blockade

We investigate the dynamics of a strongly interacting spin system that is motivated by current experimental realizations of strongly interacting Rydberg gases in lattices. In particular we are interested in the temporal evolution of quantities such as the density of Rydberg atoms and density-density correlations when the system is initialized in a fully polarized state without Rydberg excitations. We show that in the thermodynamic limit the expectation values of these observables converge at least logarithmically to universal functions and outline a method to obtain these functions. We prove that a finite one-dimensional system follows this universal behavior up to a given time. The length of this universal time period depends on the actual system size. This shows that already the study of small systems allows to make precise predictions about the thermodynamic limit provided that the observation time is sufficiently short. We discuss this for various observables and for systems with different dimensions, interaction ranges and boundary conditions.Comment: 16 pages, 3 figure