Studies in a Random Noise Model of Decoherence

We study the effects of noise and decoherence for a double-potential well system, suitable for the fabrication of qubits and quantum logic elements. A random noise term is added to the hamiltonian, the resulting wavefunction found numerically and the density matrix obtained by averaging over noise signals. Analytic solutions using the two-state model are obtained and found to be generally in agreement. In particular, a simple formula for the decoherence rate in terms of the noise parameters in the two-state model is reviewed and verified for the full simulation with the multi-level system. The formalism is extended to describe multiple sources of noise or different "dephasing" axes at the same time. Furthermore, the old formula for the "Turing-Watched Pot" effect is generalized to the case where the environmental interactions do not conserve the "quality" in question. Various forms for the noise signal are investigated. An interesting result is the importance of the noise power at low frequency. If it vanishes there is, in leading order, no decoherence. This is verified in a numerical simulation where two apparently similar noise signals, but differing in the power at zero frequency, give strikingly different decoherence effects. A short discussion of situations dominated by low frequency noise is given.Comment: 27 pages, 10 figures. New section added on Very Low Frequency Noise, with two additional figures. Conclusions, Abstract modified accordingly. Various other small editorial changes and clarification

Quantum inequalities and `quantum interest' as eigenvalue problems

Quantum inequalities (QI's) provide lower bounds on the averaged energy density of a quantum field. We show how the QI's for massless scalar fields in even dimensional Minkowski space may be reformulated in terms of the positivity of a certain self-adjoint operator - a generalised Schroedinger operator with the energy density as the potential - and hence as an eigenvalue problem. We use this idea to verify that the energy density produced by a moving mirror in two dimensions is compatible with the QI's for a large class of mirror trajectories. In addition, we apply this viewpoint to the `quantum interest conjecture' of Ford and Roman, which asserts that the positive part of an energy density always overcompensates for any negative components. For various simple models in two and four dimensions we obtain the best possible bounds on the `quantum interest rate' and on the maximum delay between a negative pulse and a compensating positive pulse. Perhaps surprisingly, we find that - in four dimensions - it is impossible for a positive delta-function pulse of any magnitude to compensate for a negative delta-function pulse, no matter how close together they occur.Comment: 18 pages, RevTeX. One new result added; typos fixed. To appear in Phys. Rev.

A geological model of London and the Thames Valley, southeast England

Many geological survey organisations have started delivering digital geological models as part of their role. This article describes the British Geological Survey (BGS) model for London and the Thames Valley in southeast England. The model covers 4800 km2 and extends to several hundred metres depth. It includes extensive spreads of Quaternary river terraces and alluvium of the Thames drainage system resting on faulted and folded Palaeogene and Cretaceous bedrock strata. The model extends to the base of the Jurassic sedimentary rocks. The baseline datasets used and the uses and limitations of the model are given. The model has been used to generate grids for the elevation of the base of the Quaternary, the thickness of Quaternary deposits, and enabled a reassessment of the subcrop distribution and faulting of the Palaeogene and Cretaceous bedrock units especially beneath the Quaternary deposits. Digital outputs from the model include representations of geological surfaces, which can be used in GIS, CAD and geological modelling software, and also graphic depictions such as a fence diagram of cross-sections through the model. The model can be viewed as a whole, and be dissected, in the BGS Lithoframe Viewer. Spatial queries of this and other BGS models, at specific points, along defined lines or at a specified depth, can be performed with the new BGS Groundhog application, which delivers template-based reports. The model should be viewed as a first version that should be improved further, and kept up to date, as new data and understanding emerges

Recurrence of fidelity in near integrable systems

Within the framework of simple perturbation theory, recurrence time of quantum fidelity is related to the period of the classical motion. This indicates the possibility of recurrence in near integrable systems. We have studied such possibility in detail with the kicked rotor as an example. In accordance with the correspondence principle, recurrence is observed when the underlying classical dynamics is well approximated by the harmonic oscillator. Quantum revivals of fidelity is noted in the interior of resonances, while classical-quantum correspondence of fidelity is seen to be very short for states initially in the rotational KAM region.Comment: 13 pages, 6 figure

On the ratio of consecutive gaps between primes

In the present work we prove a common generalization of Maynard-Tao's recent result about consecutive bounded gaps between primes and on the Erd\H{o}s-Rankin bound about large gaps between consecutive primes. The work answers in a strong form a 60 years old problem of Erd\"os, which asked whether the ratio of two consecutive primegaps can be infinitely often arbitrarily small, and arbitrarily large, respectively

Observation of Quantum Asymmetry in an Aharonov-Bohm Ring

We have investigated the Aharonov-Bohm effect in a one-dimensional GaAs/GaAlAs ring at low magnetic fields. The oscillatory magnetoconductance of these systems are for the first time systematically studied as a function of density. We observe phase-shifts of $\pi$ in the magnetoconductance oscillations, and halving of the fundamental $h/e$ period, as the density is varied. Theoretically we find agreement with the experiment, by introducing an asymmetry between the two arms of the ring.Comment: 4 pages RevTex including 3 figures, submitted to Phys. Rev.

Evaluation of human and non-human primate antibody binding to pig cells lacking GGTA1/CMAH/β4GalNT2 genes

Background Simultaneous inactivation of pig GGTA1 and CMAH genes eliminates carbohydrate xenoantigens recognized by human antibodies. The β4GalNT2 glycosyltransferase may also synthesize xenoantigens. To further characterize glycan-based species incompatibilities, we examined human and non-human primate antibody binding to cells derived from genetically modified pigs lacking these carbohydrate-modifying genes. Methods The Cas9 endonuclease and gRNA were used to create pigs lacking GGTA1, GGTA1/CMAH, or GGTA1/CMAH/β4GalNT2 genes. Peripheral blood mononuclear cells were isolated from these animals and examined for binding to IgM and IgG from humans, rhesus macaques, and baboons. Results Cells from GGTA1/CMAH/β4GalNT2 deficient pigs exhibited reduced human IgM and IgG binding compared to cells lacking both GGTA1 and CMAH. Nonhuman primate antibody reactivity with cells from the various pigs exhibited a slightly different pattern of reactivity than that seen in humans. Simultaneous inactivation of the GGTA1 and CMAH genes increased nonhuman primate antibody binding compared to cells lacking either GGTA1 only or to those deficient in GGTA1/CMAH/β4GalNT2. Conclusions Inactivation of the β4GalNT2 gene reduces human and nonhuman primate antibody binding resulting in diminished porcine xenoantigenicity. The increased humoral immunity of nonhuman primates towards GGTA1/CMAH-deficient cells compared to pigs lacking either GGTA1 or GGTA1/CMAH/β4GalNT2 highlights the complexities of carbohydrate xenoantigens and suggests potential limitations of the nonhuman primate model for examining some genetic modifications. The progressive reduction of swine xenoantigens recognized by human immunoglobulin through inactivation of pig GGTA1/CMAH/β4GalNT2 genes demonstrates that the antibody barrier to xenotransplantation can be minimized by genetic engineering

Nonlinear Differential Equations Satisfied by Certain Classical Modular Forms

A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, which yields a single nonlinear third-order equation, called a generalized Chazy equation. As byproducts, a table of divisor function and theta identities is generated by means of q-expansions, and a transformation law under \Gamma_0(4) for the second complete elliptic integral is derived. More generally, it is shown how Picard-Fuchs equations of triangle subgroups of PSL(2,R) which are hypergeometric equations, yield systems of nonlinear equations for weight-1 forms, and generalized Chazy equations. Each triangle group commensurable with \Gamma(1) is treated.Comment: 40 pages, final version, accepted by Manuscripta Mathematic

Characterizing Multi-planet Systems with Classical Secular Theory

Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help identify tidal effects, early planet-planet scattering, and dynamical coupling among the planets, for systems in which mean-motion resonances do not play a role. Although tidal damping can result in aligned major axes after all but one eigenmode have damped away, such alignment may simply be fortuitous. An example of this is 55 Cancri (orbital solution of Fischer et al., 2008) where multiple eigenmodes remain undamped. Various solutions for 55 Cancri are compared, showing differing dynamical groupings, with implications for the coupling of eccentricities and for the partitioning of damping among the planets. Solutions for orbits that include expectations of past tidal evolution with observational data, must take into account which eigenmodes should be damped, rather than expecting particular eccentricities to be near zero. Classical secular theory is only accurate for low eccentricity values, but comparison with other results suggests that it can yield useful qualitative descriptions of behavior even for moderately large eccentricity values, and may have advantages for revealing underlying physical processes and, as large numbers of new systems are discovered, for triage to identify where more comprehensive dynamical studies should have priority.Comment: Published in Celestial Mechanics and Dynamical Astronomy, 25 pages, 10 figure