A Proposal for a Differential Calculus in Quantum Mechanics

In this paper, using the Weyl-Wigner-Moyal formalism for quantum mechanics, we develop a {\it quantum-deformed} exterior calculus on the phase-space of an arbitrary hamiltonian system. Introducing additional bosonic and fermionic coordinates we construct a super-manifold which is closely related to the tangent and cotangent bundle over phase-space. Scalar functions on the super-manifold become equivalent to differential forms on the standard phase-space. The algebra of these functions is equipped with a Moyal super-star product which deforms the pointwise product of the classical tensor calculus. We use the Moyal bracket algebra in order to derive a set of quantum-deformed rules for the exterior derivative, Lie derivative, contraction, and similar operations of the Cartan calculus.Comment: TeX file with phyzzx macro, 43 pages, no figure

The place of space technology in economic development: Reflections on present and future aspects

The effects of the development of satellite applications on the orientation of the space effort were examined. The gap between available and exploited technology, the impact of the current economic climate and future trends are discussed. Europe's low level of public funding for its space effort, in comparison to other space powers, and the dangers of complacency regarding Europe's competitiveness in the space market are illustrated. A proposal for the general direction which Europe's future strategy must take if European independence in this field is to be preserved is presented

Get the gist? The effects of processing depth on false recognition in short-term and long-term memory

Gist-based processing has been proposed to account for robust false memories in the converging-associates task. The deep-encoding processes known to enhance verbatim memory also strengthen gist memory and increase distortions of long-term memory (LTM). Recent research has demonstrated that compelling false memory illusions are relatively delay-invariant, also occurring under canonical short-term memory (STM) conditions. To investigate the contributions of gist to false memory at short and long delays, processing depth was manipulated as participants encoded lists of four semantically related words and were probed immediately, following a filled 3- to 4-s retention interval, or approximately 20 min later, in a surprise recognition test. In two experiments, the encoding manipulation dissociated STM and LTM on the frequency, but not the phenomenology, of false memory. Deep encoding at STM increases false recognition rates at LTM, but confidence ratings and remember/know judgments are similar across delays and do not differ as a function of processing depth. These results suggest that some shared and some unique processes underlie false memory illusions at short and long delays

Quantum Gravity Effects in the Kerr Spacetime

We analyze the impact of the leading quantum gravity effects on the properties of black holes with nonzero angular momentum by performing a suitable renormalization group improvement of the classical Kerr metric within Quantum Einstein Gravity (QEG). In particular we explore the structure of the horizons, the ergosphere, and the static limit surfaces as well as the phase space avilable for the Penrose process. The positivity properties of the effective vacuum energy momentum tensor are also discussed and the "dressing" of the black hole's mass and angular momentum are investigated by computing the corresponding Komar integrals. The pertinent Smarr formula turns out to retain its classical form. As for their thermodynamical properties, a modified first law of black hole thermodynamics is found to be satisfied by the improved black holes (to second order in the angular momentum); the corresponding Bekenstein-Hawking temperature is not proportional to the surface gravity.Comment: 57 pages, 30 figure

Geometric Phases and Critical Phenomena in a Chain of Interacting Spins

The geometric phase can act as a signature for critical regions of interacting spin chains in the limit where the corresponding circuit in parameter space is shrunk to a point and the number of spins is extended to infinity; for finite circuit radii or finite spin chain lengths, the geometric phase is always trivial (a multiple of 2pi). In this work, by contrast, two related signatures of criticality are proposed which obey finite-size scaling and which circumvent the need for assuming any unphysical limits. They are based on the notion of the Bargmann invariant whose phase may be regarded as a discretized version of Berry's phase. As circuits are considered which are composed of a discrete, finite set of vertices in parameter space, they are able to pass directly through a critical point, rather than having to circumnavigate it. The proposed mechanism is shown to provide a diagnostic tool for criticality in the case of a given non-solvable one-dimensional spin chain with nearest-neighbour interactions in the presence of an external magnetic field.Comment: 7 Figure

Running Gauge Coupling in Asymptotically Safe Quantum Gravity

We investigate the non-perturbative renormalization group behavior of the gauge coupling constant using a truncated form of the functional flow equation for the effective average action of the Yang-Mills-gravity system. We find a non-zero quantum gravity correction to the standard Yang-Mills beta function which has the same sign as the gauge boson contribution. Our results fit into the picture according to which Quantum Einstein Gravity (QEG) is asymptotically safe, with a vanishing gauge coupling constant at the non-trivial fixed point.Comment: 27 page

Fingerprints for spin-selection rules in the interaction dynamics of O2 at Al(111)

We performed mixed quantum-classical molecular dynamics simulations based on first-principles potential-energy surfaces to demonstrate that the scattering of a beam of singlet O2 molecules at Al(111) will enable an unambiguous assessment of the role of spin-selection rules for the adsorption dynamics. At thermal energies we predict a sticking probability that is substantially less than unity, with the repelled molecules exhibiting characteristic kinetic, vibrational and rotational signatures arising from the non-adiabatic spin transition.Comment: 4 pages including 3 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

Non-perturbative QEG Corrections to the Yang-Mills Beta Function

We discuss the non-perturbative renormalization group evolution of the gauge coupling constant by using a truncated form of the functional flow equation for the effective average action of the Yang-Mills-gravity system. Our result is consistent with the conjecture that Quantum Einstein Gravity (QEG) is asymptotically safe and has a vanishing gauge coupling constant at the non-trivial fixed point.Comment: To appear in the proceedings of CORFU 200