Cut-off Lengths Research Articles

Jordan-Fock type uncertainty relations and cut-off lengths in quantum general relativity

It is demonstrated that in quantized general relativity one is led to Jordan-Fock type uncertainty relations implying the occurrence of cut-off lengths. We argue that these lengths (i) represent limitations on the measurability of quantum effects of general relativity and (ii) provide a cut-off length of quantum divergences.

Cut-off lengths and uncertainty relations in quantum general relativity

The object of this paper is to discuss the status of the inaccuracy relations arising in quantum general relativity and to give a short review of some of their physical implications.

Quantum General Relativity and the Meaning of (R + R2) Theories

It is argued that, due to the cut-off lengths arising in Quantum General Relativity, R2 corrections of Einstein's theory cannot be interpreted as quantum corrections. Quantisierte Allgemeine Relativitätstheorie und die Bedeutung von (R + R2)-Theorien Es wird gezeigt, daß infolge der in der quantisierten Allgemeinen Relativitätstheorie auftretenden Abschneidlängen R2-Korrekturen der Einsteinschen Theorie nicht als Quantenkorrekturen interpretiert werden können.

Theory of geminate recombination on a lattice. IV. Results using large Coulomb radii on the simple cubic and square lattices

We have expanded the molecular theory of geminate recombination of charge-carrier pairs to the consideration of arbitrary Coulomb cutoff lengths. The results on the simple cubic and square lattices exhibit behavior typical of that observed experimentally. This behavior is controlled by a set of molecular parameters as well as the initial distribution of the electron about the hole. It is shown also that the temperature dependence in the infinite-sink limit is qualitatively Onsager-like, but does not quantitatively match the predictions of the Onsager formulation, reflecting previously noted deficiencies in the continuum approximation. It is also shown that the two parameters φ0 and r0 of the Onsager model cannot, in general, be regarded as giving the actual, physical initial quantum efficiency and initial separation of the charge carriers, respectively. In the course of these calculations, methods are developed for calculating two- and three-dimensional lattice Green’s functions in the presence of an external electric field. Analytical and numerical methods are established, as well as recursion relations useful in calculation. A relationship is exhibited and utilized between two- and three-dimensional field-dependent Green’s functions.

Southeast Hoover Field: Model of Foreland Tectonics of Arbuckle Region, Southern Oklahoma: ABSTRACT

The Southwest Hoover field, located on the northern side of the Arbuckel Mountains, typifies the structural style common to the foreland of southern Oklahoma. This oil field, which produces primarily from the upper Arbuckle Group carbonates, was created in response to the Late Pennsylvanian Arbuckle orogeny. Various interpretations of the mode of deformation have been proposed such as wrench faulting, gravity sliding, and overthrusting. This research supports the idea of moderately dipping thrust faults created by northeast-southwest compression. Paleozoic rocks, originally deposited on the northern edge of the Southern Oklahoma aulacogen, have been transported to the northeast on southwest-dipping thrust faults, and now comprise the leading edge of the Arbuckle Mountains. In a detailed study, the Southeast Hoover field was reinterpreted in light of the compressional thrust-fault theory. Large-scale structural closure controls the location of hydrocarbon accumulation in the Arbuckle Group. Structures in the shallower horizons are characterized by detached anticlines that were created as a response to volume adjustments in adjacent upward-tightening synclines. Fault cutoff lengths and hanging-wall cutoff angles provide clues to predeformation fault-plane geometry. Comparison of the Southeast Hoover field with other structures in the Arbuckle region indicates a close similarity of style, which suggests this studymore » can be used as a geologic model for interpreting foreland oil fields throughout southern Oklahoma.« less

An interacting instanton and anti-instanton system under external color magnetic fields

The equilibrium configurations for the instanton and anti-instanton system of the SU(2) gauge field under constant external color magnetic fields are studied by applying the statistical mechanics method. The vacuum has a stable equilibrium state in the case where the interaction between pseudoparticles is partly considered through the local gauge field in determining the mean dipole moment of instantons. It is shown, however, that there exists no equilibrium state, either stable or unstable, when the dipolar interaction with a particular instanton-size-dependent cutoff is taken into account directly by the second virial coefficient. To analyze this discrepancy a more general cutoff is introduced and the density of instantons is determined for equilibrium states with vanishing external fields, when the cutoff parameter is varied. Above a certain cutoff length there exist two branches of equilibrium configurations with high or low instanton densities, while below it no equilibrium state is obtained. It is shown that we have a critical cutoff length near but slightly larger than the above value and that the equilibrium states on the lower density branch corresponding to cutoff lengths larger than this critical value are stable, while all remaining equilibrium states are unstable.

Magnetoelastic YIG Delay Lines with Linear Dispersion

The internal magnetic field in YIG cones and pyramids has been calculated. With a ratio of the height to the base diameter between 0.7 and 1, constant slopes of the axial fields and hence linear dispersion curves for the magnetoelastic echoes are obtained. The useful frequency range is estimated in terms of the focusing condition for spin waves which requires H(off axis) > H(on axis). Experimentally a nearly linear dispersion curve was obtained with a cone of 4.5-mm height and equal base diameter over a frequency range from 1 to 2 GHz; the dispersion rate was 1.7 nsec/MHz. When the turning surface approaches the region in the crystal where the focusing condition is violated, the echoes are cut off. Measured cutoff lengths and demagnetizing fields agree well with calculations. Similar results have been obtained for pyramids and truncated cones.