The Born-Oppenheimer Approach to the Matter-Gravity System and Unitarity

The Born-Oppenheimer approach to the matter-gravity system is illustrated and the unitary evolution for matter, in the absence of phenomena such as tunnelling or other instabilities, verified. The Born-Oppenheimer approach to the matter-gravity system is illustrated in a simple minisuperspace model and the corrections to quantum field theory on a semiclassical background exhibited. Within such a context the unitary evolution for matter, in the absence of phenomena such as tunnelling or other instabilities, is verified and compared with the results of other approaches. Lastly the simplifications associated with the use of adiabatic invariants to obtain the solution of the explicitly time dependent evolution equation for matter are evidenced.Comment: Latex, 12 pages. Revised version as accepted for publication by Class. and Quant. Grav. Some points explained and misprints correcte

128-bit multicomparator

A 128-bit multicomparator was designed to perform the search-sort function on arbitrary length data strings. Devices can be cascaded for longer block lengths or paralleled for bit-parallel, word-serial applications. The circuit utilizes a 3-phase static-dynamic shift register cell for data handling and a unique gated EXCLUSIVE-NOR circuit to accomplish the compare function. The compare operation is performed bit parallel between a `data' register and a `key' register with a third `mask' register containing DON'T CARE bits that disable the comparator. The multicomparator was fabricated using p-channel silicon-gate metal-oxide-semiconductor (MOS) technology on a 107/spl times/150 mil chip containing 3350 devices. With transistor-transistor logic (TTL) input, data rates in excess of 2 MHz have been attained. The average power dissipation was 250 mW in the dynamic mode and 300 mW in the static mode

Phenotypic heterogeneity and genetic modification of P102L inherited prion disease in an international series

The largest kindred with inherited prion disease P102L, historically Gerstmann-Sträussler-Scheinker syndrome, originates from central England, with émigrés now resident in various parts of the English-speaking world. We have collected data from 84 patients in the large UK kindred and numerous small unrelated pedigrees to investigate phenotypic heterogeneity and modifying factors. This collection represents by far the largest series of P102L patients so far reported. Microsatellite and genealogical analyses of eight separate European kindreds support multiple distinct mutational events at a cytosine-phosphate diester-guanidine dinucleotide mutation hot spot. All of the smaller P102L kindreds were linked to polymorphic human prion protein gene codon 129M and were not connected by genealogy or microsatellite haplotype background to the large kindred or each other. While many present with classical Gerstmann-Sträussler-Scheinker syndrome, a slowly progressive cerebellar ataxia with later onset cognitive impairment, there is remarkable heterogeneity. A subset of patients present with prominent cognitive and psychiatric features and some have met diagnostic criteria for sporadic Creutzfeldt-Jakob disease. We show that polymorphic human prion protein gene codon 129 modifies age at onset: the earliest eight clinical onsets were all MM homozygotes and overall age at onset was 7 years earlier for MM compared with MV heterozygotes (P = 0.02). Unexpectedly, apolipoprotein E4 carriers have a delayed age of onset by 10 years (P = 0.02). We found a preponderance of female patients compared with males (54 females versus 30 males, P = 0.01), which probably relates to ascertainment bias. However, these modifiers had no impact on a semi-quantitative pathological phenotype in 10 autopsied patients. These data allow an appreciation of the range of clinical phenotype, modern imaging and molecular investigation and should inform genetic counselling of at-risk individuals, with the identification of two genetic modifiers

Born-Oppenheimer Approximation near Level Crossing

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anomalous Zeeman shift of vibrational levels near a crossing.Comment: 8 pages, 1 figure, Lette

Berry's Phase in the Presence of a Stochastically Evolving Environment: A Geometric Mechanism for Energy-Level Broadening

The generic Berry phase scenario in which a two-level system is coupled to a second system whose dynamical coordinate is slowly-varying is generalized to allow for stochastic evolution of the slow system. The stochastic behavior is produced by coupling the slow system to a heat resevoir which is modeled by a bath of harmonic oscillators initially in equilibrium at temperature T, and whose spectral density has a bandwidth which is small compared to the energy-level spacing of the fast system. The well-known energy-level shifts produced by Berry's phase in the fast system, in conjunction with the stochastic motion of the slow system, leads to a broadening of the fast system energy-levels. In the limit of strong damping and sufficiently low temperature, we determine the degree of level-broadening analytically, and show that the slow system dynamics satisfies a Langevin equation in which Lorentz-like and electric-like forces appear as a consequence of geometrical effects. We also determine the average energy-level shift produced in the fast system by this mechanism.Comment: 29 pages, RevTex, submitted to Phys. Rev.

The regulated four parameter one dimensional point interaction

The general four parameter point interaction in one dimensional quantum mechanics is regulated. It allows the exact solution, but not the perturbative one. We conjecture that this is due to the interaction not being asymptotically free. We then propose a different breakup of unperturbed theory and interaction, which now is asymptotically free but leads to the same physics. The corresponding regulated potential can be solved both exactly and perturbatively, in agreement with the conjecture.Comment: 17 pages, no figures, Tex fil

Optical and Radio monitoring of S5 1803+74

The optical (BVRI) and radio (8.4 GHz) light curves of S5 1803+784 on a time span of nearly 6 years are presented and discussed. The optical light curve showed an overall variation greater than 3 mag, and the largest changes occured in three strong flares. No periodicity was found in the light curve on time scales up to a year. The variability in the radio band is very different, and shows moderate oscillations around an average constant flux density rather than relevant flares, with a maximum amplitude of $\sim$30%, without a simultaneous correspondence between optical and radio luminosity. The optical spectral energy distribution was always well fitted by a power law. The spectral index shows small variations and there is indication of a positive correlation with the source luminosity. Possible explanations of the source behaviour are discussed in the framework of current models.Comment: 25 pages, 12 figure