Approximation in quantale-enriched categories

Our work is a fundamental study of the notion of approximation in V-categories and in (U,V)-categories, for a quantale V and the ultrafilter monad U. We introduce auxiliary, approximating and Scott-continuous distributors, the way-below distributor, and continuity of V- and (U,V)-categories. We fully characterize continuous V-categories (resp. (U,V)-categories) among all cocomplete V-categories (resp. (U,V)-categories) in the same ways as continuous domains are characterized among all dcpos. By varying the choice of the quantale V and the notion of ideals, and by further allowing the ultrafilter monad to act on the quantale, we obtain a flexible theory of continuity that applies to partial orders and to metric and topological spaces. We demonstrate on examples that our theory unifies some major approaches to quantitative domain theory.Comment: 17 page

Dynamics in the Ising field theory after a quantum quench

We study the real-time dynamics of the order parameter $$in the Ising field theory after a quench in the fermion mass, which corresponds to a quench in the transverse field of the corresponding transverse field Ising chain. We focus on quenches within the ordered phase. The long-time behaviour is obtained analytically by a resummation of the leading divergent terms in a form-factor expansion for$$. Our main result is the development of a method for treating divergences associated with working directly in the field theory limit. We recover the scaling limit of the corresponding result by Calabrese et al. [Phys. Rev. Lett. \textbf{106}, 227203 (2011)], which was obtained for the lattice model. Our formalism generalizes to integrable quantum quenches in other integrable models

Symmetries in the Lorenz-96 model

The Lorenz-96 model is widely used as a test model for various applications, such as data assimilation methods. This symmetric model has the forcing $F\in\mathbb{R}$ and the dimension $n\in\mathbb{N}$ as parameters and is $\mathbb{Z}_n$ equivariant. In this paper, we unravel its dynamics for $F<0$ using equivariant bifurcation theory. Symmetry gives rise to invariant subspaces, that play an important role in this model. We exploit them in order to generalise results from a low dimension to all multiples of that dimension. We discuss symmetry for periodic orbits as well. Our analysis leads to proofs of the existence of pitchfork bifurcations for $F<0$ in specific dimensions $n$: In all even dimensions, the equilibrium $(F,\ldots,F)$ exhibits a supercritical pitchfork bifurcation. In dimensions $n=4k$, $k\in\mathbb{N}$, a second supercritical pitchfork bifurcation occurs simultaneously for both equilibria originating from the previous one. Furthermore, numerical observations reveal that in dimension $n=2^qp$, where $q\in\mathbb{N}\cup\{0\}$ and $p$ is odd, there is a finite cascade of exactly $q$ subsequent pitchfork bifurcations, whose bifurcation values are independent of $n$. This structure is discussed and interpreted in light of the symmetries of the model.Comment: 31 pages, 9 figures and 3 table

Are Local Milieus the Key to Innovation Performance?

This study investigates how local milieus foster innovation success in firms. We complement the common practice of linking firm performance indicators to regional characteristics with survey evidence on the perceived importance of locational factors. While the former approach assumes that location characteristics affect all firms in the same way, the survey allows us to model how firms judge the attractiveness of locations using a heterogeneous set of criteria. It turns out that the availability of highly skilled labor and the proximity to suppliers matter for firms' innovation performance. Interestingly, location factors obtained from the survey provide a more accurate explanation of how local milieus facilitate innovation. --Innovation performance,R&D,location factors,Flanders

Financial Constraints: Routine Versus Cutting Edge R&D Investment

We analyze financial constraints for R&D, where we account for heterogeneity among investments which has been neglected in previous literature. According to economic theory, investments should be distinguished by their degree of uncertainty, e.g. routine R&D versus cutting-edge R&D. Financial constraints should be more binding for cutting-edge R&D than for routine R&D. Using panel data we find that R&D spending of firms devoting a significant fraction of R&D to cutting-edge projects is curtailed by credit constraints while routine R&D investments are not. This has important policy implications with respect to the distribution of R&D subsidies in the economy. --R&D,Financial Constraints,Panel Data

Are Local Milieus the Key to Innovation Performance?

This study investigates how local milieus foster innovation success of firms. We complement the common practice of linking firm performance indicators to regional characteristics with survey evidence on the perceived importance of locational factors. While the former approach assumes that location characteristics affect all firms in the same way, the survey allows us to model firms judging the attractiveness of locations by a heterogeneous set of criteria. It turns out that the availability of highly skilled labor and the proximity to suppliers matters for firms? innovation performance. Interestingly, location factors obtained from the survey provide a more accurate explanation on how local milieus facilitate innovation. --Innovation performance,R&D,location factors,Flanders

Quantum quench in the sine-Gordon model

We consider the time evolution in the repulsive sine-Gordon quantum field theory after the system is prepared in a particular class of initial states. We focus on the time dependence of the one-point function of the semi-local operator $\exp\big(i\ \beta \ \Phi(x)/2\big)$. By using two different methods based on form-factor expansions, we show that this expectation value decays to zero exponentially, and we determine the decay rate by analytical means. Our methods generalise to other correlation functions and integrable models.Comment: 41 pages, 1 figure, some typos correcte

Transverse momentum distribution of vector mesons produced in ultraperipheral relativistic heavy ion collisions

We study the transverse momentum distribution of vector mesons produced in ultraperipheral relativistic heavy ion collisions (UPCs). In UPCs there is no strong interaction between the nuclei and the vector mesons are produced in photon-nucleus collisions where the (quasireal) photon is emitted from the other nucleus. Exchanging the role of both ions leads to interference effects. A detailed study of the transverse momentum distribution which is determined by the transverse momentum of the emitted photon, the production process on the target and the interference effect is done. We study the total unrestricted cross section and those, where an additional electromagnetic excitation of one or both of the ions takes place in addition to the vector meson production, in the latter case small impact parameters are emphasized.Comment: 12 pages, REVTeX manuscrip