120866757
Generalized Quantum Mechanics for Fermionic Systems
120988952
BRANCH WAVE FUNCTIONS FOR QUASI-CLASSICAL HOMOGENEOUS UNIVERSES
119269617
Consistent Probabilities in Wheeler-DeWitt Quantum Cosmology
We give an explicit, rigorous framework for calculating quantum probabilities in a model theory of quantum gravity. Specifically, we construct the decoherence functional for the Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmology with a free, massless, minimally coupled scalar field, thus providing a complete decoherent histories formulation for this quantum cosmological model. The decoherence functional is applied to study predictions concerning the model's Dirac (relational) observables; the behavior of semiclassical states and superpositions of such states; and to study the singular behavior of quantum Wheeler-DeWitt universes. Within this framework, rigorous formulas are given for calculating the corresponding probabilities from the wave function when those probabilities may be consistently defined, thus replacing earlier heuristics for interpreting the wave function of the universe with explicit constructions. It is shown according to a rigorously formulated standard, and in a quantum-mechanically consistent way, that in this quantization these models are generically singular. Independent of the choice of state we show that the probability for these Wheeler-DeWitt quantum universes to ever encounter a singularity is unity. In addition, the relation between histories formulations of quantum theory and relational Dirac observables is clarified.
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.
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.