119348416
Generalized quantum theory of recollapsing homogeneous cosmologies
A sum-over-histories generalized quantum theory is developed for homogeneous minisuperspace type A Bianchi cosmological models, focussing on the particular example of the classically recollapsing Bianchi IX universe. The decoherence functional for such universes is exhibited. We show how the probabilities of decoherent sets of alternative, coarse-grained histories of these model universes can be calculated. We consider in particular the probabilities for classical evolution defined by a suitable coarse-graining. For a restricted class of initial conditions and coarse grainings we exhibit the approximate decoherence of alternative histories in which the universe behaves classically and those in which it does not. For these situations we show that the probability is near unity for the universe to recontract classically if it expands classically. We also determine the relative probabilities of quasi-classical trajectories for initial states of WKB form, recovering for such states a precise form of the familiar heuristic "J d\Sigma" rule of quantum cosmology, as well as a generalization of this rule to generic initial states.
8706909
A Bell inequality analog in quantum measure theory
One obtains Bell's inequalities if one posits a hypothetical joint probability distribution, or measure, whose marginals yield the probabilities produced by the spin measurements in question. The existence of a joint measure is in turn equivalent to a certain causality condition known as 'screening off'. We show that if one assumes, more generally, a joint quantal measure, or 'decoherence functional', one obtains instead an analogous inequality weaker by a factor of . The proof of this 'Tsirel'son inequality' is geometrical and rests on the possibility of associating a Hilbert space to any strongly positive quantal measure. These results lead both to a question: 'Does a joint measure follow from some quantal analog of 'screening off'?', and to the observation that non-contextual hidden variables are viable in histories-based quantum mechanics, even if they are excluded classically.
118432031
Dynamical eigenfunctions and critical density in loop quantum cosmology
We offer a new, physically transparent argument for the existence of the critical, universal maximum matter density in loop quantum cosmology for the case of a flat Friedmann?Lema?tre?Robertson?Walker cosmology with scalar matter. The argument is based on the existence of a sharp exponential ultraviolet cutoff in momentum space on the eigenfunctions of the quantum cosmological dynamical evolution operator (the gravitational part of the Hamiltonian constraint), attributable to the fundamental discreteness of spatial volume in loop quantum cosmology. The existence of the cutoff is proved directly from recently found exact solutions for the eigenfunctions for this model. As a consequence, the operators corresponding to the momentum of the scalar field and the spatial volume approximately commute. The ultraviolet cutoff then implies that the scalar momentum, though not a bounded operator, is in effect bounded on subspaces of constant volume, leading to the upper bound on the expectation value of the matter density. The maximum matter density is universal (i.e. independent of the quantum state) because of the?linear scaling of the cutoff with volume. These heuristic arguments are supplemented by a new proof in the volume representation of the existence of the maximum matter density. The techniques employed to demonstrate the existence of the cutoff also allow us to extract the large-volume limit of the exact eigenfunctions, confirming earlier numerical and analytical work showing that the eigenfunctions approach superpositions of the eigenfunctions of the Wheeler?DeWitt quantization of the same model. We argue that generic (not just semiclassical) quantum states approach symmetric superpositions of expanding and contracting universes.
121169692
A Consistent Histories Formulation of Wheeler‐DeWitt Quantum Cosmology
We summarize a fully worked‐out consistent histories formulation of a quantum cosmological model, and illustrate with an example calculation of the probability that the quantum universe becomes singular. Specifically, we take a complete Wheeler‐DeWitt canonical quantization of a flat Friedmann‐Robertson‐Walker cosmological model sourced with a free massless scalar field, and construct the decoherence functional which determines which quantum histories may be consistently assigned probabilities. As an example, we exhibit the probability that the quantum universe is singular in the sense that it assumes zero volume. The classical solutions of this model are all singular; we show that the quantum solutions are as well. We comment on the crucial role played by quantum decoherence in arriving at this conclusion.
120866757
Generalized Quantum Mechanics for Fermionic Systems
118728323
Consistent Histories in Quantum Cosmology
We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmological model sourced with a free massless scalar field, we calculate the probability that the universe is singular in the sense that it assumes zero volume. Classical solutions of this model are a disjoint set of expanding and contracting singular branches. A naive assessment of the behavior of quantum states which are superpositions of expanding and contracting universes suggests that a “quantum bounce” is possible i.e. that the wave function of the universe may remain peaked on a non-singular classical solution throughout its history. However, a more careful consistent histories analysis shows that for arbitrary states in the physical Hilbert space the probability of this Wheeler-DeWitt quantum universe encountering the big bang/crunch singularity is equal to unity. A quantum Wheeler-DeWitt universe is inevitably singular, and a “quantum bounce” is thus not possible in these models.
182462112
Deadtime of SDC Straw Detectors
120610624
Sensitivity of Small-Angle Correlations of Light Charged Particles to Reaction Mechanisms in the 16O+27A1 Reaction at 40MeV/Nucleon
Small-angle $p$-$p$, $p$-$d$, $d$-$\ensuremath{\alpha}$, and $\ensuremath{\alpha}$-$\ensuremath{\alpha}$ correlation functions were measured following the reaction ${}^{16}$O+${}^{27}$Al at 40 MeV/nucleon ${}^{16}$O. These light charged particles (LCP's) were measured with a closely packed hexagonal array of CsI detectors, located at $35\ifmmode^\circ\else\textdegree\fi{}$, with a center to center opening angle of 2.35$\ifmmode^\circ\else\textdegree\fi{}$ for adjacent detectors. Coincident particles were simultaneously detected in the NSCL $4\ensuremath{\pi}$ detector. This measurement was intended to be a complement to earlier results from the same system. Based on studies of this system at lower energies and other published correlation measurements, it was expected that at 40 MeV/nucleon there would be significant positive correlations from the nuclear force and deep anticorrelations from Coulomb repulsion. However, correlation functions from this higher energy are remarkably similar to those previously measured at $\ensuremath{\approx}$15 MeV/nucleon. Correlation functions formed from events with a high multiplicity or high total detected energy (central collisions) are not significantly different from the inclusive measurements. As a possible explanation we suggest that significant correlations are most readily seen in experiments sensitive to LCP's from fast preequilibrium processes and that measurements at more backward angles are primarily sensitive to LCP's from a longer-lived source formed after preequilibrium processes are done. This idea is supported by trends of $p$-$p$ correlation functions from a wide range of systems. A schematic calculation based on a Boltzmann-Ueling-Uhlenbeck (BUU) model and statistical emission qualitatively reproduces the results from this work.