A Parallel Section Functor for 2-Vector Bundles

We associate to a 2-vector bundle over an essentially finite groupoid a 2-vector space of parallel sections, or, in representation theoretic terms, of higher invariants, which can be described as homotopy fixed points. Our main result is the extension of this assignment to a symmetric monoidal 2-functor $\operatorname{Par} : \mathbf{2VecBunGrpd} \to \mathbf{2Vect}$. It is defined on the symmetric monoidal bicategory $\mathbf{2VecBunGrpd}$ whose morphisms arise from spans of groupoids in such a way that the functor $\operatorname{Par}$ provides pull-push maps between 2-vector spaces of parallel sections of 2-vector bundles. The direct motivation for our construction comes from the orbifoldization of extended equivariant topological field theories.Comment: 32 page

Non-equilibrium steady state of a driven levitated particle with feedback cooling

Laser trapped nanoparticles have been recently used as model systems to study fundamental relations holding far from equilibrium. Here we study, both experimentally and theoretically, a nanoscale silica sphere levitated by a laser in a low density gas. The center of mass motion of the particle is subjected, at the same time, to feedback cooling and a parametric modulation driving the system into a non-equilibrium steady state. Based on the Langevin equation of motion of the particle, we derive an analytical expression for the energy distribution of this steady state showing that the average and variance of the energy distribution can be controlled separately by appropriate choice of the friction, cooling and modulation parameters. Energy distributions determined in computer simulations and measured in a laboratory experiment agree well with the analytical predictions. We analyse the particle motion also in terms of the quadratures and find thermal squeezing depending on the degree of detuning.Comment: Submitted to the New Journal of Physic