Ladder Contributions Research Articles

Weak-localization approach to a 2D electron gas with a spectral node

We study a weakly disordered 2D electron gas with two bands and a spectral node within the weak-localization approach and compare its results with those of Gaussian fluctuations around the self-consistent Born approximation. The appearance of diffusive modes depends on the type of disorder. In particular, we find for a random gap a diffusive mode only from ladder contributions, whereas for a random scalar potential the diffusive mode is created by ladder and by maximally crossed contributions. The ladder (maximally crossed) contributions correspond to fermionic (bosonic) Gaussian fluctuations. We calculate the conductivity corrections from the density–density Kubo formula and find a good agreement with the experimentally observed V-shape conductivity of graphene.

Alternative formulation of explicitly correlated third-order Møller–Plesset perturbation theory

The second-order wave operator in the explicitly correlated wave function theory has been newly defined as an extension of the conventional s- and p-wave (SP) ansatz (also referred to as the FIXED amplitude ansatz) based on the linked-diagram theorem. The newly defined second-order wave operator has been applied to the calculation of the F12 correction to the third-order many-body perturbation (MP3) energy. In addition to this new wave operator, the F12 correction with the conventional first-order wave operator has been derived and calculated. Among three components of the MP3 correlation energy, the particle ladder contribution, which has shown the slowest convergence with respect to the basis set size, is fairly ameliorated by employing these F12 corrections. Both the newly defined and conventional formalisms of the F12 corrections exhibit a similar recovery of over 90% of the complete basis set limit of the particle ladder contribution of the MP3 correlation energy with a triple-zeta quality basis set for the neon atom, while the amount is about 75% without the F12 correction. The corrections to the ring term are small but the corrected energy has shown similar recovery as the particle ladder term. The hole ladder term has shown a rapid convergence even without the F12 corrections. Owing to these balanced recoveries, the deviation of the total MP3 correlation energy from the complete basis set limit has been calculated to be about 1 kcal/mol with the triple-zeta quality basis set, which is more than five times smaller than the error without the F12 correction.

The role of three-nucleon forces and many-body processes in nuclear pairing

We present microscopic valence-shell calculations of pairing gaps in the calcium isotopes, focusing on the role of three-nucleon (3N) forces and many-body processes. In most cases, we find a reduction in pairing strength when the leading chiral 3N forces are included, compared to results with low-momentum two-nucleon (NN) interactions only. This is in agreement with a recent energy density functional study. At the NN level, calculations that include particle–particle and hole–hole ladder contributions lead to smaller pairing gaps compared with experiment. When particle–hole contributions as well as the normal-ordered one- and two-body parts of 3N forces are consistently included to third order, we find reasonable agreement with experimental three-point mass differences. This highlights the important role of 3N forces and many-body processes for pairing in nuclei. Finally, we relate pairing gaps to the evolution of nuclear structure in neutron-rich calcium isotopes and study the predictions for the 2+ excitation energies, in particular for 54Ca.

Hidden sector effects on double Higgs production near threshold at the LHC

In this Letter we study a novel effect of a hidden sector coupling to the standard model Higgs boson: an enhancement of the Higgs pair production cross section near threshold due to bound state effects. After summing the ladder contributions of the hidden sector to the effective ggHH coupling, we find the amplitude for gluon–gluon scattering via a Higgs loop. We relate this amplitude to the double Higgs production cross section via the optical theorem. We find that enhancements of the O(100) for the partonic cross section near the threshold region can be obtained for a hidden sector strongly coupled to the Higgs boson. The corresponding cross section at the LHC can be as large as O(10) times the SM result for extreme values of the coupling. The detection of such an effect could in principle lead to important information about the hidden sector.

SELF-CONSISTENT TREATMENT OF THE SELF-ENERGY IN NUCLEAR MATTER

The influence of hole–hole propagation in addition to the conventional particle–particle propagation on the energy per nucleon and the momentum distribution is investigated. The results are compared to the Brueckner–Hartree–Fock (BHF) calculations with a continuous choice and a conventional choice for the single-particle spectrum. Also, the structure of nucleon self-energy in nuclear matter is evaluated. All the off-shell self-energies are calculated self-consistently. Using the self-consistent self-energy, the hole and particle self-consistent spectral functions including the particle–particle and hole–hole ladder contributions in nuclear matter are calculated using realistic NN interactions. We found that the hole–hole ladder brought about non-negligible contributions to the nuclear matter binding energy per nucleon.

Particle–Hole Ladders

A self contained analysis demonstrates that the sum of all particle-hole ladder contributions for a two dimensional, weakly coupled fermion gas with a strictly convex Fermi curve at temperature zero is bounded. This is used in our construction of two dimensional Fermi liquids. This summary article contains the statements of the main results. The proofs are contained in the full, electronic, article. Electronic Supplementary Material: Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00220-004-1038-2.

Convergence of Perturbation Expansions in Fermionic Models. Part 2: Overlapping Loops

We improve on the abstract estimate obtained in Part 1 by assuming that there are constraints imposed by ‘overlapping momentum loops’. These constraints are active in a two dimensional, weakly coupled fermion gas with a strictly convex Fermi curve. The improved estimate is used in another paper to control everything but the sum of all ladder contributions to the thermodynamic Green’s functions.

Summation of an infinite series of ladder diagrams

The recent result of Ussyukina and Davydychev, relating L-loop 3-point and 4-point ladder diagrams in 4-dimensional massless λφ 3 3! theory, is derived from a conformal transformation. An expansion of the underlying integral is given in terms of Chebyshev polynomials. For the sum of ladder contributions to the derivative of the self-energy, Euler-Maclaurin and Abel-Plana methods yield the strong-coupling expansion Σ′ lad (ω 2) ∼ 1 24 − e − λ ω ( λ 2πω ) 5 2 [ 1 2 π + O( ω λ )] , with a constant term − 1 2 ζ(−1) = 1 24 , at infinite coupling and time-like momenta, which reflects the black of a zero-loop perturbative contribution. The exponentially suppressed corrections are obtained exactly, as a simple contour integral that yields an asymptotic series.

Binding energy and momentum distribution of nuclear matter using Green's function methods.

The influence of hole-hole (h-h) propagation in addition to the conventional particle-particle (p-p) propagation, on the energy per particle and the momentum distribution is investigated for the {ital v}{sub 2} central interaction which is derived from Reid's soft-core potential. The results are compared to Brueckner-Hartree-Fock calculations with a continuous choice for the single-particle (SP) spectrum. Calculation of the energy from a self-consistently determined SP spectrum leads to a lower saturation density. This result is not corroborated by calculating the energy from the hole spectral function, which is, however, not self-consistent. A generalization of previous calculations of the momentum distribution, based on a Goldstone diagram expansion, is introduced that allows the inclusion of h-h contributions to all orders. From this result an alternative calculation of the kinetic energy is obtained. In addition, a direct calculation of the potential energy is presented which is obtained from a solution of the ladder equation containing p-p and h-h propagation to all orders. These results can be considered as the contributions of selected Goldstone diagrams (including p-p and h-h terms on the same footing) to the kinetic and potential energy in which the SP energy is given by the quasiparticle energy. The results for themore » summation of Goldstone diagrams leads to a different momentum distribution than the one obtained from integrating the hole spectral function which in general gives less depletion of the Fermi sea. Various arguments, based partly on the results that are obtained, are put forward that a self-consistent determination of the spectral functions including the p-p and h-h ladder contributions (using a realistic interaction) will shed light on the question of nuclear saturation at a nonrelativistic level that is consistent with the observed depletion of SP orbitals in finite nuclei.« less

Finite velocity meson exchange in nuclei.

Many-body techniques are used to develop a practical formalism for including an energy-transfer dependence in the nucleon-nucleon interaction used in nuclear linear response models. An energy-transfer dependence is naturally expected from the exchange of finite mass, finite velocity mesons. The formalism is applied in a Tamm-Dancoff approximation model structure calculation for $^{16}\mathrm{O}$. The importance of meson retardation effects on the structure calculation is studied as a function of the magnitude of unperturbed particle-hole energies. The relative importance of ring and ladder contributions is also investigated. It is found that retardation effects can become qualitatively important when particle-hole energies are comparable to the mass of the exchanged meson as would be the case for ${\mathit{N}}^{\mathrm{*}}$ particle-nucleon hole configurations. While ladder kernels exhibit a significant energy-transfer dependence, the actual results obtained including retardation when solving for the ladder polarization propagator follow closely the results obtained using an instantaneous ladder kernel. This result suggests a simple procedure for including retardation effects.

Hole-hole propagation and saturation

Ladder contributions to the effective interaction are calculated with inclusion of hole-hole (hh) propagation to all orders. For a correct calculation of the self-energy resulting from the ladder-summed effective interaction, ΓL, dispersion relations are used numerically. The single-particle (sp) energy is calculated self-consistently from the real on-shell self-energy. The contribution of the hh terms leads to a repulsive contribution to the energy per particle which increases with density. This saturation mechanism has not been identified previously and results are presented for the ν2 homework potential.

Pion form factor in a scalar model

Using as an example the simple scalar modelρ (6) 3 ; we describe our method of analysing the bound-state form factors based on the systematic use of the alpha-representation for Feynman diagrams. The nature of «nonrenormalization group» logarithms specific for the form-factor-type problems is investigated. The summation of ladder contributions is performed in the leading-logarithm approximation.

Paramagnon exchange and quasiparticle interaction in3He

The effective interaction, fp1p2ss' between two quasiparticles in normal 3He with spins s,s' and momenta p1,p2 on the Fermi surface is calculated for a repulsive interaction between antiparallel spins which has a delta -function space dependence and decays exponentially in time. The simplest ladder and bubble diagrams are summed to all orders, with the aid of an approach to solution of the Bethe-Salpeter equation for the ladder contribution which converts it to a differential equation. For a sufficiently large finite value of the damping constant beta , the ladder sum is independent of p1 and p2, which implies that the Landau parameters Fjs and Fja for j>or=1 should be nearly equal. For the latter case, the remaining interaction parameter has been adjusted to make the calculated F12 fit experimental data at six pressures between 0 and 30 bar and then Fjs for 2<or=j<or=8 is computed at each pressure. It is concluded that the sequence of Landau parameters probably cannot be truncated after j=2.

Contribution to the nucleon-nucleus optical potential due to a pick-up reaction

In terms of diagrams the essential contribution to the self-energy, which is due to a pick-up reaction, comes from the particle-particle ladder. This ladder contribution is calculated in an approximative way. An absorptive part of the optical potential is obtained which acts essentially as a surface absorptive. For each partial wave of the elastic channel it is a finite sum of separable terms. A strong angular momentum dependence of the imaginary part of the potential at pick-up threshold is found. This dependence is governed by the angular momentum of the bound orbitals, from which pick-up occurs.

Analytic 4th order crossed ladder contribution to the lamb shift

A systematic investigation is made of the wotk of Soto. The algebra is redone entirely. The integrals are tested numerically. Each dubious or litigious integral is recomputed analytically. The contribution to the 4th order slope zero momentum transfer is found to be ▪ in the Feynman gauge.