Applications of a New Proposal for Solving the "Problem of Time" to Some Simple Quantum Cosmological Models

We apply a recent proposal for defining states and observables in quantum gravity to simple models. First, we consider a Klein-Gordon particle in an ex- ternal potential in Minkowski space and compare our proposal to the theory ob- tained by deparametrizing with respect to a time slicing prior to quantiza- tion. We show explicitly that the dynamics of the deparametrization approach depends on the time slicing. Our proposal yields a dynamics independent of the choice of time slicing at intermediate times but after the potential is turned off, the dynamics does not return to the free particle dynamics. Next we apply our proposal to the closed Robertson-Walker quantum cosmology with a massless scalar field with the size of the universe as our time variable, so the only dynamical variable is the scalar field. We show that the resulting theory has the semi-classical behavior up to the classical turning point from expansion to contraction, i.e., given a classical solution which expands for much longer than the Planck time, there is a quantum state whose dynamical evolution closely approximates this classical solution during the expansion. However, when the "time" gets larger than the classical maximum, the scalar field be- comes "frozen" at its value at the maximum expansion. We also obtain similar results in the Taub model. In an Appendix we derive the form of the Wheeler- DeWitt equation for the Bianchi models by performing a proper quantum reduc- tion of the momentum constraints; this equation differs from the usual one ob- tained by solving the momentum constraints classically, prior to quantization.Comment: 30 pages, LaTeX 3 figures (postscript file or hard copy) available upon request, BUTP-94/1

The Tevatron Higgs exclusion limits and theoretical uncertainties: a critical appraisal

We examine the exclusion limits set by the CDF and D0 experiments on the Standard Model Higgs boson mass from their searches at the Tevatron in the light of large theoretical uncertainties on the signal and background cross sections. We show that when these uncertainties are consistently taken into account, the sensitivity of the experiments becomes significantly lower and the currently excluded mass range $M_H=158$-175 GeV would be entirely reopened. The necessary luminosity required to recover the current sensitivity is found to be a factor of two higher than the present one.Comment: 11 pages, 5 Figures. Version published in Physics Letter B, including an erratu

Trapping in the random conductance model

We consider random walks on $\Z^d$ among nearest-neighbor random conductances which are i.i.d., positive, bounded uniformly from above but whose support extends all the way to zero. Our focus is on the detailed properties of the paths of the random walk conditioned to return back to the starting point at time $2n$. We show that in the situations when the heat kernel exhibits subdiffusive decay --- which is known to occur in dimensions $d\ge4$ --- the walk gets trapped for a time of order $n$ in a small spatial region. This shows that the strategy used earlier to infer subdiffusive lower bounds on the heat kernel in specific examples is in fact dominant. In addition, we settle a conjecture concerning the worst possible subdiffusive decay in four dimensions.Comment: 21 pages, version to appear in J. Statist. Phy

Constraints on the Charged Higgs Sector from the Tevatron Collider Data on Top Quark Decay

The top quark data in the lepton plus $\tau$ channel offers a viable probe for the charged Higgs boson signal. We analyse the recent Tevatron collider data in this channel to obtain a significant limit on the $H^\pm$ mass in the large $\tan\beta$ region.Comment: 8 pages, LaTeX file; 2 figures included (PS files

Quasi-Local Density Functional Theory and its Application within Extended Thomas-Fermi Approximation

A generalization of the Density Functional Theory is proposed. The theory developed leads to single-particle equations of motion with a quasi-local mean-field operator, which contains a quasi-particle position-dependent effective mass and a spin-orbit potential. The energy density functional is constructed using the Extended Thomas-Fermi approximation. Within the framework of this approach the ground-state properties of the doubly magic nuclei are considered. The calculations have been performed using the finite-range Gogny D1S force. The results are compared with the exact Hartree-Fock calculations

Vortex states in superconducting rings

The superconducting state of a thin superconducting disk with a hole is studied within the non-linear Ginzburg-Landau theory in which the demagnetization effect is accurately taken into account. We find that the flux through the hole is not quantized, the superconducting state is stabilized with increasing size of the hole for fixed radius of the disk, and a transition to a multi-vortex state is found if the disk is sufficiently large. Breaking the circular summetry through a non central location of the hole in the disk enhances the multi-vortex state.Comment: 11 pages, 23 figures (postscript). To appear in Physical Review B, Vol. 61 (2000

Quasi-Isotropization of the Inhomogeneous Mixmaster Universe Induced by an Inflationary Process

We derive a ``generic'' inhomogeneous ``bridge'' solution for a cosmological model in the presence of a real self-interacting scalar field. This solution connects a Kasner-like regime to an inflationary stage of evolution and therefore provides a dynamical mechanism for the quasi-isotropization of the universe. In the framework of a standard Arnowitt-Deser-Misner Hamiltonian formulation of the dynamics and by adopting Misner-Chitr\`e-like variables, we integrate the Einstein-Hamilton-Jacobi equation corresponding to a ``generic'' inhomogeneous cosmological model whose evolution is influenced by the coupling with a bosonic field, expected to be responsible for a spontaneous symmetry breaking configuration. The dependence of the detailed evolution of the universe on the initial conditions is then appropriately characterized.Comment: 17 pages, no figure, to appear on PR

Localized Random Lasing Modes and a New Path for Observing Localization

We demonstrate that a knowledge of the density-of-states and the eigenstates of a random system without gain, in conjunction with the frequency profile of the gain, can accurately predict the mode that will lase first. Its critical pumping rate can be also obtained. It is found that the shape of the wavefunction of the random system remains unchanged as gain is introduced. These results were obtained by the time-independent transfer matrix method and finite-difference-time-domain (FDTD) methods. They can be also analytically understood by generalizing the semi-classical Lamb theory of lasing in random systems. These findings provide a new path for observing the localization of light, such as looking for mobility edge and studying the localized states. %inside the random systems..Comment: Sent to PRL. 3 figure

The Flare-energy Distributions Generated by Kink-unstable Ensembles of Zero-net-current Coronal Loops

It has been proposed that the million degree temperature of the corona is due to the combined effect of barely-detectable energy releases, so called nanoflares, that occur throughout the solar atmosphere. Alas, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabilities is captured by an instability threshold for linear kink modes. Each point on the threshold is associated with a unique energy release and so we can predict a distribution of nanoflare energies. When the linear instability threshold is crossed, the instability enters a nonlinear phase as it is driven by current sheet reconnection. As the ensuing flare erupts and declines, the field transitions to a lower energy state, which is modelled by relaxation theory, i.e., helicity is conserved and the ratio of current to field becomes invariant within the loop. We apply the model so that all the loops within an ensemble achieve instability followed by energy-releasing relaxation. The result is a nanoflare energy distribution. Furthermore, we produce different distributions by varying the loop aspect ratio, the nature of the path to instability taken by each loop and also the level of radial expansion that may accompany loop relaxation. The heating rate obtained is just sufficient for coronal heating. In addition, we also show that kink instability cannot be associated with a critical magnetic twist value for every point along the instability threshold