Electronic theory for superconductivity in Sr2_2RuO4_4: triplet pairing due to spin-fluctuation exchange

Using a two-dimensional Hubbard Hamiltonian for the three electronic bands crossing the Fermi level in Sr$_2$RuO$_4$ we calculate the band structure and spin susceptibility $\chi({\bf q}, \omega)$ in quantitative agreement with nuclear magnetic resonance (NMR) and inelastic neutron scattering (INS) experiments. The susceptibility has two peaks at {\bf Q}$_i = (2\pi/3, 2\pi/3)$ due to the nesting Fermi surface properties and at {\bf q}$_i = (0.6\pi, 0)$ due to the tendency towards ferromagnetism. Applying spin-fluctuation exchange theory as in layered cuprates we determine from $\chi({\bf q}, \omega)$, electronic dispersions, and Fermi surface topology that superconductivity in Sr$_2$RuO$_4$ consists of triplet pairing. Combining the Fermi surface topology and the results for $\chi({\bf q}, \omega)$ we can exclude $s-$ and $d-$wave symmetry for the superconducting order parameter. Furthermore, within our analysis and approximations we find that $f$-wave symmetry is slightly favored over p-wave symmetry due to the nesting properties of the Fermi surface.Comment: 5 pages, 5 figures, misprints correcte

Spin-triplet superconductivity due to antiferromagnetic spin-fluctuation in Sr_2RuO_4

A mechanism leading to the spin-triplet superconductivity is proposed based on the antiferromagnetic spin fluctuation. The effects of anisotropy in spin fluctuation on the Cooper pairing and on the direction of d vector are examined in the one-band Hubbard model with RPA approximation. The gap equations for the anisotropic case are derived and applied to Sr_2RuO_4. It is found that a nesting property of the Fermi surface together with the anisotropy leads to the triplet superconductivity with the d=z(sin{k_x}\pm isin{k_y}), which is consistent with experiments.Comment: 4 pages, 3 eps figures, revte

NEW CORRECTIONS OF ORDER α3(Zα)4\alpha^3(Z\alpha)^4 AND α2(Zα)6\alpha^2(Z\alpha)^6 TO THE LAMB SHIFT

Two corrections to the Lamb shift, induced by the polarization operator insertions in the external photon lines are calculated.Comment: 4 pages, revtex, no figure

Ionization Potential of the Helium Atom

Ground state ionization potential of the He^4 atom is evaluated to be 5 945 204 221 (42) MHz. Along with lower order contributions, this result includes all effects of the relative orders alpha^4, alpha^3*m_e/m_alpha and alpha^5*ln^2(alpha).Comment: 4 page

Calculation of the Electron Self Energy for Low Nuclear Charge

We present a nonperturbative numerical evaluation of the one-photon electron self energy for hydrogenlike ions with low nuclear charge numbers Z=1 to 5. Our calculation for the 1S state has a numerical uncertainty of 0.8 Hz for hydrogen and 13 Hz for singly-ionized helium. Resummation and convergence acceleration techniques that reduce the computer time by about three orders of magnitude were employed in the calculation. The numerical results are compared to results based on known terms in the expansion of the self energy in powers of (Z alpha).Comment: 10 pages, RevTeX, 2 figure

The Cold Big-Bang Cosmology as a Counter-example to Several Anthropic Arguments

A general Friedmann big-bang cosmology can be specified by fixing a half-dozen cosmological parameters such as the photon-to-baryon ratio Eta, the cosmological constant Lambda, the curvature scale R, and the amplitude Q of (assumed scale-invariant) primordial density fluctuations. There is currently no established theory as to why these parameters take the particular values we deduce from observations. This has led to proposed `anthropic' explanations for the observed value of each parameter, as the only value capable of generating a universe that can host intelligent life. In this paper, I explicitly show that the requirement that the universe generates sun-like stars with planets does not fix these parameters, by developing a class of cosmologies (based on the classical `cold big-bang' model) in which some or all of the cosmological parameters differ by orders of magnitude from the values they assume in the standard hot big-bang cosmology, without precluding in any obvious way the existence of intelligent life. I also give a careful discussion of the structure and context of anthropic arguments in cosmology, and point out some implications of the cold big-bang model's existence for anthropic arguments concerning specific parameters.Comment: 13 PRD-style pages, 2 postscript figures. Reference 26 corrected. Accepted to Phys. Rev.

Scale-dependent Galaxy Bias

We present a simple heuristic model to demonstrate how feedback related to the galaxy formation process can result in a scale-dependent bias of mass versus light, even on very large scales. The model invokes the idea that galaxies form initially in locations determined by the local density field, but the subsequent formation of galaxies is also influenced by the presence of nearby galaxies that have already formed. The form of bias that results possesses some features that are usually described in terms of stochastic effects, but our model is entirely deterministic once the density field is specified. Features in the large-scale galaxy power spectrum (such as wiggles that might in an extreme case mimic the effect of baryons on the primordial transfer function) could, at least in principle, arise from spatial modulations of the galaxy formation process that arise naturally in our model. We also show how this fully deterministic model gives rise to apparently stochasticity in the galaxy distribution.Comment: 14 pages, 2 figures, typos corrected, discussion added and references corrected; matches version accepted by JCA

Electron Self Energy for the K and L Shell at Low Nuclear Charge

A nonperturbative numerical evaluation of the one-photon electron self energy for the K- and L-shell states of hydrogenlike ions with nuclear charge numbers Z=1 to 5 is described. Our calculation for the 1S state has a numerical uncertainty of 0.8 Hz in atomic hydrogen, and for the L-shell states (2S and 2P) the numerical uncertainty is 1.0 Hz. The method of evaluation for the ground state and for the excited states is described in detail. The numerical results are compared to results based on known terms in the expansion of the self energy in powers of (Z alpha).Comment: 21 pages, RevTeX, 5 Tables, 6 figure

Arbitrary Choice of Basic Variables in Density Functional Theory. II. Illustrative Applications

Our recent theory (Ref. 1) enables us to choose arbitrary quantities as the basic variables of the density functional theory. In this paper we apply it to several cases. In the case where the occupation matrix of localized orbitals is chosen as a basic variable, we can obtain the single-particle equation which is equivalent to that of the LDA+U method. The theory also leads to the Hartree-Fock-Kohn-Sham equation by letting the exchange energy be a basic variable. Furthermore, if the quantity associated with the density of states near the Fermi level is chosen as a basic variable, the resulting single-particle equation includes the additional potential which could mainly modify the energy-band structures near the Fermi level.Comment: 27 page

The dynamical Green's function and an exact optical potential for electron-molecule scattering including nuclear dynamics

We derive a rigorous optical potential for electron-molecule scattering including the effects of nuclear dynamics by extending the common many-body Green's function approach to optical potentials beyond the fixed-nuclei limit for molecular targets. Our formalism treats the projectile electron and the nuclear motion of the target molecule on the same footing whereby the dynamical optical potential rigorously accounts for the complex many-body nature of the scattering target. One central result of the present work is that the common fixed-nuclei optical potential is a valid adiabatic approximation to the dynamical optical potential even when projectile and nuclear motion are (nonadiabatically) coupled as long as the scattering energy is well below the electronic excitation thresholds of the target. For extremely low projectile velocities, however, when the cross sections are most sensitive to the scattering potential, we expect the influences of the nuclear dynamics on the optical potential to become relevant. For these cases, a systematic way to improve the adiabatic approximation to the dynamical optical potential is presented that yields non-local operators with respect to the nuclear coordinates.Comment: 22 pages, no figures, accepted for publ., Phys. Rev.