Two-loop renormalization-group theory for the quasi-one-dimensional Hubbard model at half filling

We derive two-loop renormalization-group equations for the half-filled one-dimensional Hubbard chains coupled by the interchain hopping. Our renormalization-group scheme for the quasi-one-dimensional electron system is a natural extension of that for the purely one-dimensional systems in the sense that transverse-momentum dependences are introduced in the g-ological coupling constants and we regard the transverse momentum as a patch index. We develop symmetry arguments for the particle-hole symmetric half-filled Hubbard model and obtain constraints on the g-ological coupling constants by which resultant renormalization equations are given in a compact form. By solving the renormalization-group equations numerically, we estimate the magnitude of excitation gaps and clarify that the charge gap is suppressed due to the interchain hopping but is always finite even for the relevant interchain hopping. To show the validity of the present analysis, we also apply this to the two-leg ladder system. By utilizing the field-theoretical bosonization and fermionization method, we derive low-energy effective theory and analyze the magnitude of all the excitation gaps in detail. It is shown that the low-energy excitations in the two-leg Hubbard ladder have SO(3) x SO(3) x U(1) symmetry when the interchain hopping exceeds the magnitude of the charge gap.Comment: 18 pages, 9 figures; Two appendices and one figure adde

Solar Oscillations and Convection: II. Excitation of Radial Oscillations

Solar p-mode oscillations are excited by the work of stochastic, non-adiabatic, pressure fluctuations on the compressive modes. We evaluate the expression for the radial mode excitation rate derived by Nordlund and Stein (Paper I) using numerical simulations of near surface solar convection. We first apply this expression to the three radial modes of the simulation and obtain good agreement between the predicted excitation rate and the actual mode damping rates as determined from their energies and the widths of their resolved spectral profiles. We then apply this expression for the mode excitation rate to the solar modes and obtain excellent agreement with the low l damping rates determined from GOLF data. Excitation occurs close to the surface, mainly in the intergranular lanes and near the boundaries of granules (where turbulence and radiative cooling are large). The non-adiabatic pressure fluctuations near the surface are produced by small instantaneous local imbalances between the divergence of the radiative and convective fluxes near the solar surface. Below the surface, the non-adiabatic pressure fluctuations are produced primarily by turbulent pressure fluctuations (Reynolds stresses). The frequency dependence of the mode excitation is due to effects of the mode structure and the pressure fluctuation spectrum. Excitation is small at low frequencies due to mode properties -- the mode compression decreases and the mode mass increases at low frequency. Excitation is small at high frequencies due to the pressure fluctuation spectrum -- pressure fluctuations become small at high frequencies because they are due to convection which is a long time scale phenomena compared to the dominant p-mode periods.Comment: Accepted for publication in ApJ (scheduled for Dec 10, 2000 issue). 17 pages, 27 figures, some with reduced resolution -- high resolution versions available at http://www.astro.ku.dk/~aake/astro-ph/0008048

Contact Discontinuities in Models of Contact Binaries Undergoing Thermal Relaxation Oscillations

In this paper we pursue the suggestion by Shu, Lubow & Anderson (1979) and Wang (1995) that contact discontinuity (DSC) may exist in the secondary in the expansion TRO (thermal relaxation oscillation) state. It is demonstrated that there is a mass exchange instability in some range of mass ratio for the two components. We show that the assumption of {\it constant} volume of the secondary should be relaxed in DSC model. For {\it all} mass ratio the secondary alway satisfies the condition that no mass flow returns to the primary through the inner Lagrangian point. The secondary will expand in order to equilibrate the interaction between the common convective envelope and the secondary. The contact discontinuity in contact binary undergoing thermal relaxation does not violate the second law of thermodynamics. The maintaining condition of contact discontinuity is derived in the time-dependent model. It is desired to improve the TRO model with the advanced contact discontinuity layer in future detailed calculations.Comment: 5 pages in emulateapj, 1 figur

Power laws in a 2-leg ladder of interacting spinless fermions

We use the Density-Matrix Renormalization Group to study the single-particle and two-particle correlation functions of spinless fermions in the ground state of a quarter-filled ladder. This ladder consists of two chains having an in-chain extended Coulomb interaction reaching to third neighbor and coupled by inter-chain hopping. Within our short numerical coherence lengths, typically reaching ten to twenty sites, we find a strong renormalization of the interchain hopping and the existence of a dimensional crossover at smaller interactions. We also find power exponents for single-particle hopping and interchain polarization consistent with the single chain. The total charge correlation function has a larger power exponent and shows signs of a crossover from incoherent fermion hopping to coherent particle-hole pair motion between chains. There are no significant excitation energies.Comment: RevTex 4 file, 10 pages, 10 eps figure

A Contemporary View of Coronal Heating

Determining the heating mechanism (or mechanisms) that causes the outer atmosphere of the Sun, and many other stars, to reach temperatures orders of magnitude higher than their surface temperatures has long been a key problem. For decades the problem has been known as the coronal heating problem, but it is now clear that `coronal heating' cannot be treated or explained in isolation and that the heating of the whole solar atmosphere must be studied as a highly coupled system. The magnetic field of the star is known to play a key role, but, despite significant advancements in solar telescopes, computing power and much greater understanding of theoretical mechanisms, the question of which mechanism or mechanisms are the dominant supplier of energy to the chromosphere and corona is still open. Following substantial recent progress, we consider the most likely contenders and discuss the key factors that have made, and still make, determining the actual (coronal) heating mechanism (or mechanisms) so difficult

Cosmic Ray Protons and Magnetic Fields in Clusters of Galaxies and their Cosmological Consequences

The masses of clusters of galaxies estimated by gravitational lensing exceed in many cases the mass estimates based on hydrostatic equilibrium. This may suggest the existence of nonthermal pressure. We ask if radio galaxies can heat and support the cluster gas with injected cosmic ray protons and magnetic field densities, which are permitted by Faraday rotation and gamma ray observations of clusters of galaxies. We conclude that they are powerful enough to do this within a cluster radius of roughly 1 Mpc. If present, nonthermal pressures could lead to a revised estimate of the ratio of baryonic mass to total mass, and the apparent baryonic overdensity in clusters would disappear. In consequence, $\Omega_{\rm cold}$, the clumping part of the cosmological density $\Omega_{o}$, would be larger than $0.4\,h_{50}^{-1/2}$.Comment: Accepted by ApJ, 16 pages, LaTeX, 2 figures, epsfig.sty, aaspp4.st

Satellites and large doping- and temperature-dependence of electronic properties in hole-doped BaFe2As2

Over the last years, superconductivity has been discovered in several families of iron-based compounds. Despite intense research, even basic electronic properties of these materials, such as Fermi surfaces, effective electron masses, or orbital characters are still subject to debate. Here, we address an issue that has not been considered before, namely the consequences of dynamical screening of the Coulomb interactions among Fe-d electrons. We demonstrate its importance not only for correlation satellites seen in photoemission spectroscopy, but also for the low-energy electronic structure. From our analysis of the normal phase of BaFe2As2 emerges the picture of a strongly correlated compound with strongly doping- and temperature-dependent properties. In the hole overdoped regime, an incoherent metal is found, while Fermi-liquid behavior is recovered in the undoped compound. At optimal doping, the self-energy exhibits an unusual square-root energy dependence which leads to strong band renormalizations near the Fermi level

Oscillating axion bubbles as alternative to supermassive black holes at galactic centers

Recent observations of near-infrared and X-ray flares from Sagittarius A*, which is believed to be a supermassive black hole at the Galactic center, show that the source exhibits about 20-minute periodic variability. Here we provide arguments based on a quantitative analysis that supermassive objects at galactic centers may be bubbles of dark matter axions rather than black holes. An oscillating axion bubble can explain periodic variability of Sagittarius A* and yields the axion mass about 0.6 meV which fits in the open axion mass window. The bubble scenario with no other free parameters explains lack of supermassive "black holes" with mass M<10^6 M_{Sun}. Low-mass bubbles decay fast and as a result are very rare. We also found that the mass of an axion bubble can not exceed 1.5\times 10^9 M_{Sun}, in agreement with the upper limit on the supermassive "black hole" mass obtained from observations. Our finding, if confirmed, suggests that Einstein general relativity is invalid for strong gravity and the gravitational field for the bubble effectively becomes repulsive at large potential. Imaging a shadow of the "black hole" at the Galactic center with VLBI in the next decade can distinguish between the black hole and the oscillating axion bubble scenarios. In the case of axion bubble, a steady shadow will not be observed. Instead, the shadow will appear and disappear periodically with a period of about 20 min.Comment: 10 pages, 4 figures, added derivation of the exponential metric based on superposition principl

Some comments on "The Mathematical Universe"

I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of which lies in the acceptance that mathematics is (at least in part) a human construction, and discuss concrete consequences of this--at first sight purely philosophical--difference in point of view.Comment: 11 page