Wheeler-DeWitt Equation in 3 + 1 Dimensions

Physical properties of the quantum gravitational vacuum state are explored by solving a lattice version of the Wheeler-DeWitt equation. The constraint of diffeomorphism invariance is strong enough to uniquely determine the structure of the vacuum wave functional in the limit of infinitely fine triangulations of the three-sphere. In the large fluctuation regime the nature of the wave function solution is such that a physically acceptable ground state emerges, with a finite non-perturbative correlation length naturally cutting off any infrared divergences. The location of the critical point in Newton's constant $G_c$, separating the weak from the strong coupling phase, is obtained, and it is inferred from the structure of the wave functional that fluctuations in the curvatures become unbounded at this point. Investigations of the vacuum wave functional further suggest that for weak enough coupling, $G<G_c$, a pathological ground state with no continuum limit appears, where configurations with small curvature have vanishingly small probability. One is then lead to the conclusion that the weak coupling, perturbative ground state of quantum gravity is non-perturbatively unstable, and that gravitational screening cannot be physically realized in the lattice theory. The results we find are in general agreement with the Euclidean lattice gravity results, and lend further support to the claim that the Lorentzian and Euclidean lattice formulations for gravity describe the same underlying non-perturbative physics.Comment: 44 pages, 5 figures. arXiv admin note: text overlap with arXiv:1207.375

Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ∑s∣ps∣+μ\sum_{s}|p_s| + \mu

We consider the parametric representation of the amplitudes of Abelian models in the so-called framework of rank $d$ Tensorial Group Field Theory. These models are called Abelian because their fields live on $U(1)^D$. We concentrate on the case when these models are endowed with particular kinetic terms involving a linear power in momenta. New dimensional regularization and renormalization schemes are introduced for particular models in this class: a rank 3 tensor model, an infinite tower of matrix models $\phi^{2n}$ over $U(1)$, and a matrix model over $U(1)^2$. For all divergent amplitudes, we identify a domain of meromorphicity in a strip determined by the real part of the group dimension $D$. From this point, the ordinary subtraction program is applied and leads to convergent and analytic renormalized integrals. Furthermore, we identify and study in depth the Symanzik polynomials provided by the parametric amplitudes of generic rank $d$ Abelian models. We find that these polynomials do not satisfy the ordinary Tutte's rules (contraction/deletion). By scrutinizing the "face"-structure of these polynomials, we find a generalized polynomial which turns out to be stable only under contraction.Comment: 69 pages, 35 figure

The Great Space Weather Event during February 1872 Recorded in East Asia

The study of historical great geomagnetic storms is crucial for assessing the possible risks to the technological infrastructure of a modern society, caused by extreme space-weather events. The normal benchmark has been the great geomagnetic storm of September 1859, the so-called "Carrington Event". However, there are numerous records of another great geomagnetic storm in February 1872. This storm, about 12 years after the Carrington Event, resulted in comparable magnetic disturbances and auroral displays over large areas of the Earth. We have revisited this great geomagnetic storm in terms of the auroral and sunspot records in the historical documents from East Asia. In particular, we have surveyed the auroral records from East Asia and estimated the equatorward boundary of the auroral oval to be near 24.3 deg invariant latitude (ILAT), on the basis that the aurora was seen near the zenith at Shanghai (20 deg magnetic latitude, MLAT). These results confirm that this geomagnetic storm of February 1872 was as extreme as the Carrington Event, at least in terms of the equatorward motion of the auroral oval. Indeed, our results support the interpretation of the simultaneous auroral observations made at Bombay (10 deg MLAT). The East Asian auroral records have indicated extreme brightness, suggesting unusual precipitation of high-intensity, low-energy electrons during this geomagnetic storm. We have compared the duration of the East Asian auroral displays with magnetic observations in Bombay and found that the auroral displays occurred in the initial phase, main phase, and early recovery phase of the magnetic storm.Comment: 28 pages, 5 figures, accepted for publication in the Astrophysical Journal on 31 May 201

Competing Ground States of the New Class of Halogen-Bridged Metal Complexes

Based on a symmetry argument, we study the ground-state properties of halogen-bridged binuclear metal chain complexes. We systematically derive commensurate density-wave solutions from a relevant two-band Peierls-Hubbard model and numerically draw the the ground-state phase diagram as a function of electron-electron correlations, electron-phonon interactions, and doping concentration within the Hartree-Fock approximation. The competition between two types of charge-density-wave states, which has recently been reported experimentally, is indeed demonstrated.Comment: 4 pages, 5 figures embedded, to appear in J. Phys. Soc. Jp

Quantum and Thermal Phase Transitions of Halogen-Bridged Binuclear Transition-Metal Complexes

Aiming to settle the controversial observations for halogen-bridged binuclear transition-metal (MMX) complexes, finite-temperature Hartree-Fock calculations are performed for a relevant two-band Peierls-Hubbard model. Thermal, as well as quantum, phase transitions are investigated with particular emphasis on the competition between electron itinerancy, electron-phonon interaction and electron-electron correlation. Recently observed distinct thermal behaviors of two typical MMX compounds Pt_2(CH_3CS_2)_4I and (NH_4)_4[Pt_2(P_2O_5H_2)_4I]2H_2O are supported and further tuning of their electronic states is predicted.Comment: 5 pages, 3 figures embedded, to be published in J. Phys. Soc. Jpn. Vol.70, No.5 (2001

Simulation of the Formation of a Solar Active Region

We present a radiative magnetohydrodynamics simulation of the formation of an Active Region on the solar surface. The simulation models the rise of a buoyant magnetic flux bundle from a depth of 7.5 Mm in the convection zone up into the solar photosphere. The rise of the magnetic plasma in the convection zone is accompanied by predominantly horizontal expansion. Such an expansion leads to a scaling relation between the plasma density and the magnetic field strength such that $B\propto\varrho^{1/2}$. The emergence of magnetic flux into the photosphere appears as a complex magnetic pattern, which results from the interaction of the rising magnetic field with the turbulent convective flows. Small-scale magnetic elements at the surface first appear, followed by their gradual coalescence into larger magnetic concentrations, which eventually results in the formation of a pair of opposite polarity spots. Although the mean flow pattern in the vicinity of the developing spots is directed radially outward, correlations between the magnetic field and velocity field fluctuations allow the spots to accumulate flux. Such correlations result from the Lorentz-force driven, counter-streaming motion of opposite-polarity fragments. The formation of the simulated Active Region is accompanied by transient light bridges between umbrae and umbral dots. Together with recent sunspot modeling, this work highlights the common magnetoconvective origin of umbral dots, light bridges and penumbral filaments.Comment: Accepted for publication in Ap

Photoinduced charge separation in Q1D heterojunction materials: Evidence for electron-hole pair separation in mixed-halide MXMX solids

Resonance Raman experiments on doped and photoexcited single crystals of mixed-halide $MX$ complexes ($M$=Pt; $X$=Cl,Br) clearly indicate charge separation: electron polarons preferentially locate on PtBr segments while hole polarons are trapped within PtCl segments. This polaron selectivity, potentially very useful for device applications, is demonstrated theoretically using a discrete, 3/4-filled, two-band, tight-binding, extended Peierls-Hubbard model. Strong hybridization of the PtCl and PtBr electronic bands is the driving force for separation.Comment: n LaTeX, figures available by mail from JTG ([email protected]

The Horizontal Component of Photospheric Plasma Flows During the Emergence of Active Regions on the Sun

The dynamics of horizontal plasma flows during the first hours of the emergence of active region magnetic flux in the solar photosphere have been analyzed using SOHO/MDI data. Four active regions emerging near the solar limb have been considered. It has been found that extended regions of Doppler velocities with different signs are formed in the first hours of the magnetic flux emergence in the horizontal velocity field. The flows observed are directly connected with the emerging magnetic flux; they form at the beginning of the emergence of active regions and are present for a few hours. The Doppler velocities of flows observed increase gradually and reach their peak values 4-12 hours after the start of the magnetic flux emergence. The peak values of the mean (inside the +/-500 m/s isolines) and maximum Doppler velocities are 800-970 m/s and 1410-1700 m/s, respectively. The Doppler velocities observed substantially exceed the separation velocities of the photospheric magnetic flux outer boundaries. The asymmetry was detected between velocity structures of leading and following polarities. Doppler velocity structures located in a region of leading magnetic polarity are more powerful and exist longer than those in regions of following polarity. The Doppler velocity asymmetry between the velocity structures of opposite sign reaches its peak values soon after the emergence begins and then gradually drops within 7-12 hours. The peak values of asymmetry for the mean and maximal Doppler velocities reach 240-460 m/s and 710-940 m/s, respectively. An interpretation of the observable flow of photospheric plasma is given.Comment: 20 pages, 10 figures, 3 tables. The results of article were presented at the ESPM-13 (12-16 September 2011, Rhodes, Greece, Abstract Book p. 102, P.4.12, http://astro.academyofathens.gr/espm13/documents/ESPM13_abstract_programme_book.pdf

Holographic Dark Energy Like in f(R)f(R) Gravity

We investigate the corresponding relation between $f(R)$ gravity and holographic dark energy. We introduce a kind of energy density from $f(R)$ which has role of the same as holographic dark energy. We obtain the differential equation that specify the evolution of the introduced energy density parameter based on varying gravitational constant. We find out a relation for the equation of state parameter to low redshifts which containing varying $G$ correction.Comment: 10 page