On a coalgebraic view on Logic

In this paper we present methods of transition from one perspective on logic to others, and apply this in particular to obtain a coalgebraic presentation of logic. The central ingredient in this process is to view consequence relations as morphisms in a category

Simulation of interaction Hamiltonians by quantum feedback: a comment on the dynamics of information exchange between coupled systems

Since quantum feedback is based on classically accessible measurement results, it can provide fundamental insights into the dynamics of quantum systems by making available classical information on the evolution of system properties and on the conditional forces acting on the system. In this paper, the feedback-induced interaction dynamics between a pair of quantum systems is analyzed. It is pointed out that any interaction Hamiltonian can be simulated by local feedback if the levels of decoherence are sufficiently high. The boundary between genuine entanglement generating quantum interactions and non-entangling classical interactions is identified and the nature of the information exchange between two quantum systems during an interaction is discussed.Comment: 14 pages, 4 figures; invited paper for the special issue of J. Opt. B on quantum contro

Sharp rate of average decay of the Fourier transform of a bounded set

We prove that the spherical mean of the Fourier transform of the characteristic function of a bounded convex set (without any additional assumptions) or a bounded set with a C^{3/2} boundary decays at infinity at the same rate as the Fourier transform of the characteristic function of the ball.Comment: 10 pages. GAFA (to appear

Pro-Lie Groups: A survey with Open Problems

A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and forms a complete category. It includes each finite-dimensional Lie group, each locally compact group which has a compact quotient group modulo its identity component and thus, in particular, each compact and each connected locally compact group; it also includes all locally compact abelian groups. This paper provides an overview of the structure theory and Lie theory of pro-Lie groups including results more recent than those in the authors' reference book on pro-Lie groups. Significantly, it also includes a review of the recent insight that weakly complete unital algebras provide a natural habitat for both pro-Lie algebras and pro-Lie groups, indeed for the exponential function which links the two. (A topological vector space is weakly complete if it is isomorphic to a power $\R^X$ of an arbitrary set of copies of $\R$. This class of real vector spaces is at the basis of the Lie theory of pro-Lie groups.) The article also lists 12 open questions connected with pro-Lie groups.Comment: 19 page

The response of Southern Ocean eddies to increased midlatitude westerlies: a non-eddy resolving model study

The midlatitude westerlies of the southern hemisphere have intensified since the 1970s. Non-eddy resolving general circulation models respond to such wind intensification with steeper isopycnals, a faster Antarctic Circumpolar Current (ACC), and a stronger Atlantic Meridional Overturning Circulation (AMOC). However, hydrographic observations show little change in the slope of the Southern Ocean isopycnals over the past 40 years. This insensitivity seems to result from a compensating mechanism whereby an initial increase in the slope of the isopycnals causes eddy activity to intensify and forces the isopycnal slopes down. Climate models do not yet resolve ocean eddies, and the eddy parameterizations included in them do not capture well the compensation mechanism mentioned above. We present simulations with a non-eddy resolving model incorporating an eddy parameterization in which eddy compensation is greatly enhanced by the use of a non-constant, spatially varying thickness diffusivity. The sensitivity of the simulated ACC and AMOC to increased southern hemisphere westerlies is greatly reduced compared to simulations using constant and uniform diffusivitie

Intensity dependence of Rydberg states

We investigate numerically and analytically the intensity dependence of the fraction of electrons that end up in a Rydberg state after strong-field ionization with linearly polarized light. We find that including the intensity dependent distribution of ionization times and non-adiabatic effects leads to a better understanding of experimental results. Furthermore, we observe using Classical Trajectory Monte Carlo simulations that the intensity dependence of the Rydberg yield changes with wavelength and that the previously observed power-law dependence breaks down at longer wavelengths. Our work suggests that Rydberg yield measurements can be used as an independent test for non-adiabaticity in strong field ionization

Proton irradiation of simple gas mixtures: Influence of irradiation parameters

In order to get information about the influence of irradiation parameters on radiolysis processes of astrophysical interest, methane gas targets were irradiated with 6.5 MeV protons at a pressure of 1 bar and room temperature. Yields of higher hydrocarbons like ethane or propane were found by analysis of irradiated gas samples using gas chromatography. The handling of the proton beam was of great experimental importance for determining the irradiation parameters. In a series of experiments current density of the proton beam and total absorbed energy were shown to have a large influence on the yields of produced hydrocarbons. Mechanistic interpretations of the results are given and conclusions are drawn with regard to the chemistry and the simulation of various astrophysical systems

FCIs and economic activity: Some international evidence

A Monetary Conditions Index (MCI), a weighted average of the short-term real interest rate and the real exchange rate, is a commonly used indicator of aggregate demand conditions. In-sample evidence for the US, the euro area, Japan and the UK suggests that a Financial Conditions Index (FCI), also comprising property prices and share prices, would be a better indicator for economic activity than the standard MCI. Out-of sample the FCI also performs better than the MCI, but its overall performance is mixed. An FCI would have predicted the recent economic downturn in Japan and the UK, but not in the US and the euro area. --