Doping dependence of the electron-doped cuprate superconductors from the antiferromagnetic properties of the Hubbard model

Within the Kotliar-Ruckenstein slave-boson approach, we have studied the antiferromagnetic (AF) properties for the $t$-$t'$-$t''$-$U$ model applied to electron-doped cuprate superconductors. Due to inclusion of spin fluctuations the AF order decreases with doping much faster than obtained in the Hartree-Fock theory. Under an intermediate {\it constant} $U$ the calculated doping evolution of the spectral intensity has satisfactorily reproduced the experimental results, without need of a strongly doping-dependent $U$ as argued earlier. This may reconcile a discrepancy suggested in recent studies on photoemission and optical conductivity.Comment: 5 pages, 4 eps figures, minor improvement, references added, to appear in Phys. Rev.

Generalized Background-Field Method

The graphical method discussed previously can be used to create new gauges not reachable by the path-integral formalism. By this means a new gauge is designed for more efficient two-loop QCD calculations. It is related to but simpler than the ordinary background-field gauge, in that even the triple-gluon vertices for internal lines contain only four terms, not the usual six. This reduction simplifies the calculation inspite of the necessity to include other vertices for compensation. Like the ordinary background-field gauge, this generalized background-field gauge also preserves gauge invariance of the external particles. As a check of the result and an illustration for the reduction in labour, an explicit calculation of the two-loop QCD $\beta$-function is carried out in this new gauge. It results in a saving of 45% of computation compared to the ordinary background-field gauge.Comment: 17 pages, Latex, 18 figures in Postscrip

Time-dependent universal conductance fluctuations in mesoscopic Au wires: implications

In cold, mesoscopic conductors, two-level fluctuators lead to time-dependent universal conductance fluctuations (TDUCF) manifested as $1/f$ noise. In Au nanowires, we measure the magnetic field dependence of TDUCF, weak localization (WL), and magnetic field-driven (MF) UCF before and after treatments that alter magnetic scattering and passivate surface fluctuators. Inconsistencies between $L_{\phi}^{\rm WL}$ and $L_{\phi}^{\rm TDUCF}$ strongly suggest either that the theory of these mesoscopic phenomena in weakly disordered, highly pure Au is incomplete, or that the assumption that the TDUCF frequency dependence remains $1/f$ to very high frequencies is incorrect. In the latter case, TDUCF in excess of $1/f$ expectations may have implications for decoherence in solid-state qubits.Comment: 8 pages, 9 figures, accepted to PR

Study of gossamer superconductivity and antiferromagnetism in the t-J-U model

The d-wave superconductivity (dSC) and antiferromagnetism are analytically studied in a renormalized mean field theory for a two dimensional t-J model plus an on-site repulsive Hubbard interaction $U$. The purpose of introducing the $U$ term is to partially impose the no double occupancy constraint by employing the Gutzwiller approximation. The phase diagrams as functions of doping $\delta$ and $U$ are studied. Using the standard value of $t/J=3.0$ and in the large $U$ limit, we show that the antiferromagnetic (AF) order emerges and coexists with the dSC in the underdoped region below the doping $\delta\sim0.1$. The dSC order parameter increases from zero as the doping increases and reaches a maximum near the optimal doping $\delta\sim0.15$. In the small $U$ limit, only the dSC order survives while the AF order disappears. As $U$ increased to a critical value, the AF order shows up and coexists with the dSC in the underdoped regime. At half filing, the system is in the dSC state for small $U$ and becomes an AF insulator for large $U$. Within the present mean field approach, We show that the ground state energy of the coexistent state is always lower than that of the pure dSC state.Comment: 7 pages, 8 figure

The induced representations of Brauer algebra and the Clebsch-Gordan coefficients of SO(n)

Induced representations of Brauer algebra $D_{f}(n)$ from $S_{f_{1}}\times S_{f_{2}}$ with $f_{1}+f_{2}=f$ are discussed. The induction coefficients (IDCs) or the outer-product reduction coefficients (ORCs) of $S_{f_{1}}\times S_{f_{2}}\uparrow D_{f}(n)$ with $f\leq 4$ up to a normalization factor are derived by using the linear equation method. Weyl tableaus for the corresponding Gel'fand basis of SO(n) are defined. The assimilation method for obtaining CG coefficients of SO(n) in the Gel'fand basis for no modification rule involved couplings from IDCs of Brauer algebra are proposed. Some isoscalar factors of $SO(n)\supset SO(n-1)$ for the resulting irrep $[\lambda_{1},~\lambda_{2},~ \lambda_{3},~\lambda_{4},\dot{0}]$ with $\sum\limits_{i=1}^{4}\lambda_{i}\leq .Comment: 48 pages latex, submitted to Journal of Phys.

Small-Recoil Approximation

In this review we discuss a technique to compute and to sum a class of Feynman diagrams, and some of its applications. These are diagrams containing one or more energetic particles that suffer very little recoil in their interactions. When recoil is completely neglected, a decomposition formula can be proven. This formula is a generalization of the well-known eikonal formula, to non-abelian interactions. It expresses the amplitude as a sum of products of irreducible amplitudes, with each irreducible amplitude being the amplitude to emit one, or several mutually interacting, quasi-particles. For abelian interaction a quasi-particle is nothing but the original boson, so this decomposition formula reduces to the eikonal formula. In non-abelian situations each quasi-particle can be made up of many bosons, though always with a total quantum number identical to that of a single boson. This decomposition enables certain amplitudes of all orders to be summed up into an exponential form, and it allows subleading contributions of a certain kind, which is difficult to reach in the usual way, to be computed. For bosonic emissions from a heavy source with many constituents, a quasi-particle amplitude turns out to be an amplitude in which all bosons are emitted from the same constituent. For high-energy parton-parton scattering in the near-forward direction, the quasi-particle turns out to be the Reggeon, and this formalism shows clearly why gluons reggeize but photons do not. The ablility to compute subleading terms in this formalism allows the BFKL-Pomeron amplitude to be extrapolated to asymptotic energies, in a unitary way preserving the Froissart bound. We also consider recoil corrections for abelian interactions in order to accommodate the Landau-Pomeranchuk-Migdal effect.Comment: 21 pages with 4 figure

On several families of elliptic curves with arbitrary large Selmer groups

In this paper, we calculate the $\phi (\hat{\phi})-$Selmer groups S^{(\phi)} (E / \Q) and S^{(\hat{\varphi})} (E^{\prime} / \Q) of elliptic curves $y^{2} = x (x + \epsilon p D) (x + \epsilon q D)$ via descent theory (see [S, Chapter X]), in particular, we obtain that the Selmer groups of several families of such elliptic curves can be arbitrary large.Comment: 22 page