Approximate Decoherence of Histories and 't Hooft's Deterministic Quantum Theory

This paper explores the possibility that an exactly decoherent set of histories may be constructed from an approximately decoherent set by small distortions of the operators characterizing the histories. In particular, for the case of histories of positions and momenta, this is achieved by doubling the set of operators and then finding, amongst this enlarged set, new position and momentum operators which commute, so decohere exactly, and which are ``close'' to the original operators. The enlarged, exactly decoherent, theory has the same classical dynamics as the original one, and coincides with the so-called deterministic quantum theories of the type recently studied by 't Hooft. These results suggest that the comparison of standard and deterministic quantum theories may provide an alternative method of characterizing emergent classicality. A side-product is the surprising result that histories of momenta in the quantum Brownian motion model (for the free particle in the high-temperature limit) are exactly decoherent.Comment: 41 pages, plain Te

A Closed Contour of Integration in Regge Calculus

The analytic structure of the Regge action on a cone in $d$ dimensions over a boundary of arbitrary topology is determined in simplicial minisuperspace. The minisuperspace is defined by the assignment of a single internal edge length to all 1-simplices emanating from the cone vertex, and a single boundary edge length to all 1-simplices lying on the boundary. The Regge action is analyzed in the space of complex edge lengths, and it is shown that there are three finite branch points in this complex plane. A closed contour of integration encircling the branch points is shown to yield a convergent real wave function. This closed contour can be deformed to a steepest descent contour for all sizes of the bounding universe. In general, the contour yields an oscillating wave function for universes of size greater than a critical value which depends on the topology of the bounding universe. For values less than the critical value the wave function exhibits exponential behaviour. It is shown that the critical value is positive for spherical topology in arbitrary dimensions. In three dimensions we compute the critical value for a boundary universe of arbitrary genus, while in four and five dimensions we study examples of product manifolds and connected sums.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra

Ions in solution: Density Corrected Density Functional Theory (DC-DFT)

Standard density functional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected density functional theory (DC-DFT), certain classes of density functional theory calculations are significantly improved by using densities more accurate than the self-consistent densities. We discuss how to identify such cases, and how DC-DFT applies more generally. To illustrate, we calculate potential energy surfaces of HO$\cdot$Cl$^-$ and HO$\cdot$H$_2$O complexes using various common approximate functionals, with and without this density correction. Commonly used approximations yield wrongly shaped surfaces and/or incorrect minima when calculated self consistently, while yielding almost identical shapes and minima when density corrected. This improvement is retained even in the presence of implicit solvent

Time-asymmetry of probabilities versus relativistic causal structure: an arrow of time

There is an incompatibility between the symmetries of causal structure in relativity theory and the signaling abilities of probabilistic devices with inputs and outputs: while time-reversal in relativity will not introduce the ability to signal between spacelike separated regions, this is not the case for probabilistic devices with space-like separated input-output pairs. We explicitly describe a non-signaling device which becomes a perfect signaling device under time-reversal, where time-reversal can be conceptualized as playing backwards a videotape of an agent manipulating the device. This leads to an arrow of time that is identifiable when studying the correlations of events for spacelike separated regions. Somewhat surprisingly, although time-reversal of Popuscu-Roerlich boxes also allows agents to signal, it does not yield a perfect signaling device. Finally, we realize time-reversal using post-selection, which could lead experimental implementation.Comment: 4 pages, some figures; replaces arXiv:1010.4572 [quant-ph

Sum-over-histories origin of the composition laws of relativistic quantum mechanics and quantum cosmology

The scope of the paper has been broadened to include a more complete discussion of the following topics: The derivation of composition laws in quantum cosmology. The connection between the existence of a composition law in the sum over histories approach to relativistic quantum mechanics and quantum cosmology, and the existence of a canonical formulation.Comment: 36 page

Quantum-Mechanical Histories and the Uncertainty Principle. II. Fluctuations About Classical Predictability

This paper is concerned with two questions in the decoherent histories approach to quantum mechanics: the emergence of approximate classical predictability, and the fluctuations about it necessitated by the uncertainty principle. We consider histories characterized by position samplings at $n$ moments of time. We use this to construct a probability distribution on the value of (discrete approximations to) the field equations, $F = m \ddot x + V'(x)$, at $n-2$ times. We find that it is peaked around $F=0$; thus classical correlations are exhibited. We show that the width of the peak $\Delta F$ is largely independent of the initial state and the uncertainty principle takes the form $2 \sigma^2 \ (\Delta F)^2 \ge { \hbar^2 / t^2 }$, where $\sigma$ is the width of the position samplings, and $t$ is the timescale between projections. We determine the modifications to this result when the system is coupled to a thermal environment. We show that the thermal fluctuations become comparable with the quantum fluctuations under the same conditions that decoherence effects come into play. We also study an alternative measure of classical correlations, namely the conditional probability of finding a sequence of position samplings, given that particular initial phase space data have occurred. We use these results to address the issue of the formal interpretation of the probabilities for sequences of position samplings in the decoherent histories approach to quantum mechanics. The decoherence of the histories is also briefly discussed.Comment: 40 pages (plain Tex), Imperial College Preprin

Quantum cosmology with a curvature squared action

The correct quantum description for a curvature squared term in the action can be obtained by casting the action in the canonical form with the introduction of a variable which is the negative of the first derivative of the field variable appearing in the action, only after removing the total derivative terms from the action. We present the Wheeler-DeWitt equation and obtain the expression for the probability density and current density from the equation of continuity. Furthermore, in the weak energy limit we obtain the classical Einstein equation. Finally we present a solution of the wave equation.Comment: 8 pages, revte

An Information-Theoretic Measure of Uncertainty due to Quantum and Thermal Fluctuations

We study an information-theoretic measure of uncertainty for quantum systems. It is the Shannon information $I$ of the phase space probability distribution \la z | \rho | z \ra , where |z \ra are coherent states, and $\rho$ is the density matrix. The uncertainty principle is expressed in this measure as $I \ge 1$. For a harmonic oscillator in a thermal state, $I$ coincides with von Neumann entropy, - \Tr(\rho \ln \rho), in the high-temperature regime, but unlike entropy, it is non-zero at zero temperature. It therefore supplies a non-trivial measure of uncertainty due to both quantum and thermal fluctuations. We study $I$ as a function of time for a class of non-equilibrium quantum systems consisting of a distinguished system coupled to a heat bath. We derive an evolution equation for $I$. For the harmonic oscillator, in the Fokker-Planck regime, we show that $I$ increases monotonically. For more general Hamiltonians, $I$ settles down to monotonic increase in the long run, but may suffer an initial decrease for certain initial states that undergo ``reassembly'' (the opposite of quantum spreading). Our main result is to prove, for linear systems, that $I$ at each moment of time has a lower bound $I_t^{min}$, over all possible initial states. This bound is a generalization of the uncertainty principle to include thermal fluctuations in non-equilibrium systems, and represents the least amount of uncertainty the system must suffer after evolution in the presence of an environment for time $t$.Comment: 36 pages (revised uncorrupted version), Report IC 92-93/2

La collaboration scientifique et technologique en Amérique du Nord : un point de vue Canadien

Canada, as a country with a small, open economy, faces the immediate challenge of learning to shape dynamic comparative advantage in the emerging international economy. About 75 % of Canada's trade linkages are with the United States, and a very large component of the Canadian experience of « globalization » is driven by North American economic integration. This integration is taking place in the absence of institutions and policy mechanisms to promote and manage science, technology, and innovation relations on a continental scale. Bilateral s & T arrangements centered on the United States presently characterize the North American innovation System. Circumstances in North America pose three sets of challenges to Canadian s & T policy. 1) Science and technology are increasing in importance in international trade, environmental, and social/cultural matters. This means that Canada must learn to improve its management of an increasingly internationalized domestic s & T System. 2) Canada must cultivate mutually beneficial bilateral s & T relationships with its two partners in NAFTA, Mexico and the United States. 3) Canada must identify where its interests lie in the development and governance of trilateral and international rules and arrangements for science, technology, and innovation

The mutualistic fungus Piriformospora indica protects barley roots from a loss of antioxidant capacity caused by the necrotrophic pathogen Fusarium culmorum

Fusarium culmorum causes root rot in barley (Hordeum vulgare), resulting in severely reduced plant growth and yield. Pretreatment of roots with chlamydospores of the mutualistic root-colonizing basidiomycete Piriformospora indica (Agaricomycotina) prevented necrotization of root tissues and plant growth retardation commonly associated with Fusarium root rot. Quantification of Fusarium infections with a real-time PCR assay revealed a correlation between root rot symptoms and the relative amount of fungal DNA. Fusarium-infected roots showed reduced levels of ascorbate and glutathione (GSH), along with reduced activities of antioxidant enzymes such as superoxide dismutase (SOD), ascorbate peroxidase (APX), glutathione reductase (GR), dehydroascorbate reductase (DHAR), and monodehydroascorbate reductase (MDHAR). Consistent with this, Fusarium-infected roots showed elevated levels of lipid hydroperoxides and decreased ratios of reduced to oxidized forms of ascorbate and glutathione. In clear contrast, roots treated with P. indica prior to inoculation with F. culmorum showed levels of ascorbate and GSH that were similar to controls. Likewise, lipid peroxidation and the overall reduction in antioxidant enzyme activities were largely attenuated by P. indica in roots challenged by F. culmorum. These results suggest that P. indica protects roots from necrotrophic pathogens at least partly, through activating the plant’s antioxidant capacity