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.

Geometric Phase, Curvature, and Extrapotentials in Constrained Quantum Systems

We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian depends on quantities which are external to the constraint manifold, such as the external curvature of the constraint manifold, the (Riemannian) curvature of the ambient space, and the constraining potential. In particular, we find the remarkable fact that the twisting of the constraining potential appears as a gauge potential in the constrained Hamiltonian. This gauge potential is an example of geometric phase, closely related to that originally discussed by Berry. The constrained Hamiltonian also contains an effective potential depending on the external curvature of the constraint manifold, the curvature of the ambient space, and the twisting of the constraining potential. The general nature of our analysis allows applications to a wide variety of problems, such as rigid molecules, the evolution of molecular systems along reaction paths, and quantum strip waveguides.Comment: 27 pages with 1 figure, submitted to Phys. Rev.

Renormalization of the Inverse Square Potential

The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization. In the renormalized version of the theory, there is a strong-coupling regime where quantum-mechanical breaking of scale symmetry takes place through dimensional transmutation, with the creation of a single bound state and of an energy-dependent s-wave scattering matrix element.Comment: 5 page

Optical Holonomic Quantum Computer

In this paper the idea of holonomic quantum computation is realized within quantum optics. In a non-linear Kerr medium the degenerate states of laser beams are interpreted as qubits. Displacing devices, squeezing devices and interferometers provide the classical control parameter space where the adiabatic loops are performed. This results into logical gates acting on the states of the combined degenerate subspaces of the lasers, producing any one qubit rotations and interactions between any two qubits. Issues such as universality, complexity and scalability are addressed and several steps are taken towards the physical implementation of this model.Comment: 16 pages, 3 figures, REVTE

Collinge et al. reply

REPLYING TO C. Feeney et al. Nature 535, 10.1038/nature18602 (2016)

A clinical study of kuru patients with long incubation periods at the end of the epidemic in Papua New Guinea

Kuru is so far the principal human epidemic prion disease. While its incidence has steadily declined since the cessation of its route of transmission, endocannibalism, in Papua New Guinea in the 1950s, the arrival of variant Creutzfeldt–Jakob disease (vCJD), also thought to be transmitted by dietary prion exposure, has given kuru a new global relevance. We investigated all suspected cases of kuru from July 1996 to June 2004 and identified 11 kuru patients. There were four females and seven males, with an age range of 46–63 years at the onset of disease, in marked contrast to the age and sex distribution when kuru was first investigated 50 years ago. We obtained detailed histories of residence and exposure to mortuary feasts and performed serial neurological examination and genetic studies where possible. All patients were born a significant period before the mortuary practice of transumption ceased and their estimated incubation periods in some cases exceeded 50 years. The principal clinical features of kuru in the studied patients showed the same progressive cerebellar syndrome that had been previously described. Two patients showed marked cognitive impairment well before preterminal stages, in contrast to earlier clinical descriptions. In these patients, the mean clinical duration of 17 months was longer than the overall average in kuru but similar to that previously reported for the same age group, and this may relate to the effects of both patient age and PRNP codon 129 genotype. Importantly, no evidence for lymphoreticular colonization with prions, seen uniformly in vCJD, was observed in a patient with kuru at tonsil biopsy

KiDS+VIKING+GAMA:Testing semi-analytic models of galaxy evolution with galaxy-galaxy-galaxy lensing

Several semi-analytic models (SAMs) try to explain how galaxies form, evolve and interact inside the dark matter large-scale structure. These SAMs can be tested by comparing their predictions for galaxy-galaxy-galaxy-lensing (G3L), which is weak gravitational lensing around galaxy pairs, with observations. We evaluate the SAMs by Henriques et al. (2015; H15) and by Lagos et al. (2012; L12), implemented in the Millennium Run, by comparing their predictions for G3L to observations at smaller scales than previous studies and also for pairs of lens galaxies from different populations. We compare the G3L signal predicted by the SAMs to measurements in the overlap of the Galaxy And Mass Assembly survey (GAMA), the Kilo-Degree Survey (KiDS), and the VISTA Kilo-degree Infrared Galaxy survey (VIKING), splitting lens galaxies into two colour and five stellar-mass samples. Using an improved G3L estimator, we measure the three-point correlation of the matter distribution for mixed lens pairs with galaxies from different samples, and unmixed lens pairs with galaxies from the same sample. Predictions by the H15 SAM agree with the observations for all colour-selected and all but one stellar-mass-selected sample with 95% confidence. Deviations occur for lenses with stellar masses below $9.5h^{-2}\mathrm{M}_\odot$ at scales below $0.2h^{-1}\mathrm{Mpc}$. Predictions by the L12 SAM for stellar-mass selected samples and red galaxies are significantly higher than observed, while the predicted signal for blue galaxy pairs is too low. The L12 SAM predicts more pairs of small stellar-mass and red galaxies than the H15 SAM and the observations, as well as fewer pairs of blue galaxies. Likely explanations are different treatments of environmental effects by the SAMs and different models of the initial mass function. We conclude that G3L provides a stringent test for models of galaxy formation and evolution.Comment: 14 pages, 8 figures, replaced with version accepted to Astronomy & Astrophysics after considering referees comment

Generalised network architectures for environmental sensing: case studies for a digitally enabled environment

A digitally enabled environment is a setting which incorporates sensors coupled with reporting and analytics tools for understanding, observing or managing that environment. Large scale data collection and analysis are a part of the emerging digitally enabled approach for the characterisation and understanding of our environment. It is recognised as offering an effective methodology for addressing a range of complex and interrelated social, economic and environmental concerns. The development and construction of the approach requires advances in analytics control linked with a clear definition of the issues pertaining to the interaction between elements of these systems. This paper presents an analysis of selected issues in the field of analytics control. It also discusses areas of progress, and areas in need of further investigation as sensing networks evolve. Three case studies are described to illustrate these points. The first is a physical analytics test kit developed as a part of the “Reinvent the Toilet Challenge” (RTTC) for process control in a range of environments. The second case study is the Cranfield Urban Observatory that builds on elements of the RTTC and is designed to allow users to develop user interfaces to monitor, characterise and compare a variety of environmental and infrastructure systems plus behaviours (e.g., water distribution, power grids). The third is the Data and Analytics Facility for National Infrastructure, a cloud-based high-performance computing cluster, developed to receive, store and present such data to advanced analytical and visualisation tools.Engineering and Physical Sciences Research Council (EPSRC): EP/P016782/1, EP/R013411/1, EP/R012202/1 and EP/R017727/1. Bill & Melinda Gates Foundatio

"Meaning" as a sociological concept: A review of the modeling, mapping, and simulation of the communication of knowledge and meaning

The development of discursive knowledge presumes the communication of meaning as analytically different from the communication of information. Knowledge can then be considered as a meaning which makes a difference. Whereas the communication of information is studied in the information sciences and scientometrics, the communication of meaning has been central to Luhmann's attempts to make the theory of autopoiesis relevant for sociology. Analytical techniques such as semantic maps and the simulation of anticipatory systems enable us to operationalize the distinctions which Luhmann proposed as relevant to the elaboration of Husserl's "horizons of meaning" in empirical research: interactions among communications, the organization of meaning in instantiations, and the self-organization of interhuman communication in terms of symbolically generalized media such as truth, love, and power. Horizons of meaning, however, remain uncertain orders of expectations, and one should caution against reification from the meta-biological perspective of systems theory