Weak-coupling Calculations Research Articles

BCS-LIKE APPROXIMATION IN A TWO-BAND MODEL FOR SUPERCONDUCTIVITY IN MgB2

The BCS limit of a two-band model for superconductivity in MgB 2 is discussed and the temperature dependence of the gap functions is calculated together with their values at T = 0. We have studied the effect of interband coupling on the order parameters and critical temperature. The validity of the approximation was investigated by direct comparison with more accurate Eliashberg calculation and it was found that the BCS-like model is appropriate for temperatures up to T ~ 10 K . The two-band superconductivity in MgB 2 has been extensively studied in the literature, in Eliashberg or weak-coupling calculations, as well as in ab initio evaluations of electron–phonon interaction. Here we find from an analytical calculation the well known result that the ratio 2Δ/Tc is no longer universal in the multiband model, in contrast with the classical single-band BCS model.

Melting Pattern of Diquark Condensates in Quark Matter

Thermal color superconducting phase transitions in high density three-flavor quark matter are investigated in the Ginzburg-Landau approach. The effects of nonzero strange quark mass, electric and color charge neutrality, and direct instantons are considered. Weak coupling calculations show that an interplay between the mass and electric neutrality effects near the critical temperature gives rise to three successive second-order phase transitions as the temperature increases: a modified color-flavor locked (mCFL) phase (ud, ds, and us pairings) --> a d-quark superconducting (dSC) phase (ud and ds pairings) --> an isoscalar pairing phase (ud pairing) --> a normal phase (no pairing). The dSC phase is novel in the sense that while all eight gluons are Meissner screened as in the mCFL phase, three out of nine quark quasiparticles are always gapless.

Applicability of weak-coupling results in high density QCD

Quark matter at asymptotically high baryon chemical potential is in a color superconducting state characterized by a gap Delta. We demonstrate that although present weak-coupling calculations of Delta are formally correct for mu -> Infinity, the contributions which have to this point been neglected are large enough that present results can only be trusted for mu >> mu_c ~ 10^8 MeV. We make this argument by using the gauge dependence of the present calculation as a diagnostic tool. It is known that the present calculation yields a gauge invariant result for mu -> Infinity; we show, however, that the gauge dependence of this result only begins to decrease for mu > mu_c, and conclude that the result can certainly not be trusted for mu < mu_c. In an appendix, we set up the calculation of the influence of the Meissner effect on the magnitude of the gap. This contribution to Delta is, however, much smaller than the neglected contributions whose absence we detect via the resulting gauge dependence.

Frequency Shifts and Master Equations for a Quantum Oscillator Coupled to a Reservoir

For a quantum oscillator coupled to a reservoir, master equations obtained under the assumptions of weak coupling and use of a rotating-wave Hamiltonian (RWA) are known to give incorrect frequency shifts. Here, we show that a calculation which does not invoke the RWA gives results for the frequency shifts, which agree with exact results for Lamb-type (temperatureT=0) shifts. However, for non-zeroT, we point out that, in general, corresponding energy and free energy shifts for the system require exact treatments since off-resonant contributions (which are automatically excluded in weak coupling calculations) are important in the case of super-Ohmic reservoirs.

Ferromagnetic transition and phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping

We study the phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping using exact diagonalization, the density-matrix renormalization group, the Edwards variational ansatz, and an adaptation of weak-coupling calculations on the two-chain Hubbard model. We find that a substantial region of the strong-coupling phase diagram is ferromagnetic, and that three physically different limiting cases are connected in one ferromagnetic phase. At a point in the phase diagram at which there are two Fermi points at weak coupling, we study carefully the phase transition from the paramagnetic state to the fully polarized one as a function of the on-site Coulomb repulsion. We present evidence that the transition is second order and determine the critical exponents numerically. In this parameter regime, the system can be described as a Luttinger liquid at weak coupling. We extract the Luttinger-liquid parameters and show how their behavior differs from that of the nearest-neighbor Hubbard model. The general weak-coupling phase diagram can be mapped onto that of the two-chain Hubbard model. We exhibit explicitly the adapted phase diagram and determine its validity by numerically calculating spin and charge gaps using the density-matrix renormalization group.

Effectiveness ofD-branes in the description of near-extremal black holes

It is known that weak coupling calculations of absorption or emission by slightly nonextremal $D$-brane configurations are in exact agreement with semiclassical results for the black holes they describe at strong couplings. We investigate one open string loop corrections to processes involving single and parallel $D$-branes and show that a class of relevant terms vanish, indicating that these processes are not renormalized. Our results have implications for five-dimensional black holes and extremal 3-branes.

Nearly antiferromagnetic Fermi liquids are high temperature superconductors: Are the superconducting cuprates nearly antiferromagnetic liquids?

Following a brief review of the weak coupling calculations by Monthoux, Balatsky, and Pines, and the strong coupling calculations of Monthoux and Pines which demonstrate that the spin-fluctuation-induced interaction between planar quasiparticles in a nearly antiferromagnetic Fermi liquid produces a transition to a superconducting d x 2−y 2 pairing state at high temperatures, I review recent theoretical calculations and experiments which provide strong evidence for the physical and mathematical description of the normal state of YBa 2Cu 3O 7 as a nearly antiferromagnetic Fermi liquid, with commensurate nearly antiferromagnetic spin fluctuations providing the mechanism for high T c.

Phase separation, charge-transfer instability, and superconductivity in the three-band extended Hubbard model: Weak-coupling theory.

We study the interplay of charge-transfer instability and phase separation in the three-band model using the Hartree-Fock variational method for values of the interaction couplings comparable to the bandwidth. We establish that phase separation occurs near the region where previous weak-coupling calculations found {ital s}-wave superconductivity and a charge-transfer instability.

Monte Carlo calculation of density fluctuations on the superconductivity of a simple model for high T c oxide superconductors

Monte Carlo Calculations are performed on a trivial wave function with density fluctuation correlations for a simple model with anisotropic interactions for the oxide superconductors proposed recently by Chui and Ziman. In the trial wave function the density correlation at different momentum transfers can be different. Our results provide an explicit demonstration that density fluctuations do not destroy superconductivity. It suggests that density fluctuations cancel the superconducting fluctuation at small momentum transfers, consistent with earlier weak coupling calculations by Chui et al. We also found that there is an increased probability of finding electrons with opposite spins close to each other and thus a suppression of the spin susceptibility in the superconducting state, suggesting that recent Knight shift measurements, which were interpreted in terms of singlet pairing, can also be consistent with triplet pairing.

Cranked-deformed-shell model for neutron-proton systems. Weak-coupling calculations

Cranking calculations including neutron-proton interactions are presented for nucleons in a deformed g 9 2 shell. A weak-coupling approximation, which enormously reduces the size of the calculations, is shown to work well if the basis is chosen to be frequency dependent.

Investigation of the phase transition at H c1 in low- K superconductors

Abstract Several low- K superconductors (Nb, Ta, V, LaAl 2 ) were doped with small amounts of impurities in order to vary the Ginzburg-Landau parameter near its critical value K = 1 2 . The corresponding magnetization curves show type-I, type-II/1 and type-II/2 behavior depending on the magnitude of K at T c . The experimental results demonstrate that the phase boundaries separating the different types of phase transitions in the t- K plane are material independent, in remarkable contrast to theoretical results based on weak-coupling calculations. The anisotropic strong-coupling theory on the other hand agrees well with the bulk of the data.

11Ba( alpha,p)14C*(Ex=23.288 MeV) reaction and (p, pi +) production mechanisms.

A narrow, strongly excited state was observed in the $^{11}\mathrm{B}(\ensuremath{\alpha},p)^{14}\mathrm{C}$ reaction at 23.288 MeV. This excitation energy is in agreement with peaks seen in $^{13}\mathrm{C}(p,{\ensuremath{\pi}}^{+})^{14}\mathrm{C}$ and $^{14}\mathrm{C}(e,{e}^{\ensuremath{'}})^{14}\mathrm{C}$ reactions. However, the ($p,{\ensuremath{\pi}}^{+}$) work indicates that this state may be a ${3}^{\ensuremath{-}}$, $T=2$ state. The population of this level via the ($\ensuremath{\alpha},p$) reaction rules this out. Furthermore, weak coupling calculations suggest that the centroid of the $|^{11}\mathrm{B}\ensuremath{\bigotimes}\ensuremath{\nu}({p}_{\frac{1}{2}},{d}_{\frac{5}{2}}),\ensuremath{\pi}({d}_{\frac{5}{2}})〉$ configuration lies very close to this energy. It is therefore more probable that this state has a spin and parity of ${7}^{+}$, $T=1$ rather than a ${3}^{\ensuremath{-}}$, $T=2$ assignment.

( alpha,n) reaction to high spin states in 14N and 27Si.

The 0\ifmmode^\circ\else\textdegree\fi{} differential cross sections for the $^{11}\mathrm{B}$(\ensuremath{\alpha},n${)}^{14}$N, $^{12}\mathrm{C}$(\ensuremath{\alpha},n${)}^{15}$O, and $^{24}\mathrm{Mg}$ (\ensuremath{\alpha},n${)}^{27}$Si reactions were measured at ${E}_{\ensuremath{\alpha}}$=47.4 MeV. Well-known states of high spin in $^{15}\mathrm{O}$ were used to determine the excitation energy of states in $^{14}\mathrm{N}$ and $^{27}\mathrm{Si}$. Several states of high excitation energy in these nuclei are reported. The energies of these states are consistent with particle-hole weak coupling calculations for high spin states. Comparisons with previous experiments are made where possible.

Location of multiparticle-multihole strength in 16N via the 3-particle transfer reaction 13C(α, p) 16N at 118 MeV

Differential cross sections were measured for the 13C(α, p) 16N reaction at E α = 118 MeV for an excitation energy range up to 14.5 MeV. Zero-range distorted wave Born approximation (DWBA) calculations were performed using microscopic form factors. Spin-parity assignments are suggested for states at 11.21 MeV (6 −) and 11.81 MeV (7 −) on the basis of Bansal-French-Zamick weak coupling calculations and DWBA calculations. Arguments from 16O(e, e'), 16O(p, p') and the present experiment are given relating to the location of J π = 4 −, T = 1 strength in 16N.

Magnetic moments of the (3/2)1- and (5/2)1- states in 107,109Ag.

The ratios of g factors of the first excited states of the $^{107}$,109Ag isotopes, g((3/2))/g((5/2))=1.5(3) and 2.3(5), respectively, have been measured by the perturbed angular correlation transient field technique. The absolute magnitudes of the g factors have been obtained through a calibration procedure that makes use of the magnetic dipole moments of the first ${2}^{+}$ states of $^{106}\mathrm{Pd}$ and $^{110}\mathrm{Cd}$ and are $^{107}\mathrm{Ag}$: g${((3/2)}_{1}^{\mathrm{\ensuremath{-}}}$)=0.61(12), g${((5/2)}_{1}^{\mathrm{\ensuremath{-}}}$)=0.41(7) and $^{109}\mathrm{Ag}$: g${((3/2)}_{1}^{\mathrm{\ensuremath{-}}}$)=0.66(10), g${((5/2)}_{1}^{\mathrm{\ensuremath{-}}}$)=0.29(6). These results are compared with weak coupling calculations as well as with Nilsson models with symmetric or triaxial cores. The latter reveal a sensitive dependence of the g factors on the deformation parameter \ensuremath{\gamma}. .AE

Far-infrared absorption and transmission of ultrathin superconducting aluminium films

The FIR absorption and transmission have been measured of ultrathin superconducting Al films. The absorption of films with a thickness of the order of 10 mm is in excellent agreement with weak-coupling calculations. Ultrathin films with a thickness less than 5 nm show interesting deviations from the weak-coupling theory which are interpreted in terms of an enhanced electron-phonon coupling induced by a softening of the lattice.

Transition from weak to strong coupling in QCD and in grand unified models at high temperature

We investigate the weak-coupling expansion at high temperature for relativistic quantum field theories. Boson self-energies generally acquire a non-analytic dependence on the coupling due to the infrared plasmon effect. We show how to sum loops within loops for such thermodynamic quantities as pressure and energy density. Recent high-precision Monte Carlo simulations of quarkless SU(3) gauge theory are compared to the weak-coupling expansion and an excellent agreement is obtained for the high-temperature phase. Weak-coupling calculations are also carried out for supersymmetric grand unified models. We find indications that such models are often strongly coupled already at the unification temperature. This may have a significant effect on models of the early universe.

Gyromagnetic ratios of excited states in 107, 109Ag

Abstract The gyromagnetic ratios of the lowest excited 3 2 − and 5 2 − states in 107, 109Ag were simultaneously measured relative to that of the 21+ level in 108Pd. The thin-foil, perturbed γ-ray angular distribution technique was employed utilizing the transient hyperfine magnetic field present at the nuclei of these ions as they swiftly recoiled through a thin magnetized Co foil. The states of interest were Coulomb-excited using beams of 100 MeV 32S ions. The present measurements yielded g( 3 2 − ; 107 Ag ) = +0.63 ± 0.09, g( 5 2 − ; 107 Ag ) = + 0.37±0.06, g( 3 2 − ; 109 Ag ) = +0.77 ± 0.10, and g( 5 2 − ; 109 Ag ) = +0.36 ± 0.05 . These findings are compared with weak-coupling and other appropriate model calculations.

Optical absorption weak coupling theory of polarons bound to defects

We calculate the infrared absorption of large polarons bound to defects in the weak coupling limit. Polar crystals with more than one longitudinal optical phonon branch coupled to the electrons are considered. Oscillator strengths corresponding to defect transitions without phonons and to transitions with emission of phonons are calculated using the Larsen wave-functions. The results are applied to infrared data in strontium titanate and it is found that weak coupling calculations are in better agreement than strong coupling ones.

High-spin states in 40K and 42Ca

High spin states in 40K and 42Ca have been investigated using the 27 Al( 19 F, xyzγ) 40 K, 42 Ca reaction. In-beam measurements of γ- γ coincidences. γ-ray excitation functions and angular distributions were performed with Ge(Li) detectors, one of which had a Nal Compton suppression shield. Level schemes for 40K and 42Ca have been constructed up to spin I π = 11. The structures of the yrast lines are discussed in terms of weak-coupling calculations,