Extraction of bound-state parameters from dispersive sum rules

The procedure of extracting the ground-state parameters from vacuum-to-vacuum and vacuum-to-hadron correlators within the method of sum rules is considered. The emphasis is laid on the crucial ingredient of this method—the effective continuum threshold. A new algorithm to fix this quantity is proposed and tested. First, a quantum-mechanical potential model which provides the only possibility to probe the reliability and the actual accuracy of this method is used as a study case. In this model, our algorithm is shown to lead to a remarkable improvement of the accuracy of the extracted ground-state parameters compared to the standard procedures adopted in the method and used in all previous applications of dispersive sum rules in QCD. As a next step, it is demonstrated that the procedures of extracting the ground-state decay constant in the potential model and in QCD are quantitatively very close to each other. Therefore, the application of the proposed algorithm in QCD promises a considerable increase of the accuracy of the extracted hadron parameters.     

Landau parameters and pairing-on the shores of the nuclear Fermi sea

We present a systematic scheme for calculating the ground-state energy, single-particle energies and the effective mass, Fermi-liquid parameters, and pairing matrix elements for nuclear and neutron matter with realistic state-dependent interactions. The method retains much of the clarity of more conventional treatments while permitting reliable numerical calculations. Deficiencies in the central Jastrow correlation operator ansatz are largely overcome by low-order perturbation theory in the correlated basis generated by the Jastrow operator. Calculations of these quantities are presented for the Reid and Bethe-Johnson interactions. An analysis of the results emphasizes the importance of state-dependent correlations arising directly from the interaction or indirectly through many-body effects. The numerical results provide insight into the actual structure of the self-energy operator in nuclear and neutron matter and into the usefulness of sum rules for the quasiparticle interaction and the Landau parameters.     

Transverse spin relaxation of spin carriers diffusing in spatially periodic magnetic fields

An exact solution of the Bloch–Torrey equation that covers the entire range of relative diffusivities D between the spin carriers and the magnetic structure (due to, e.g., spin‐density waves) is given for the transverse relaxation of an initally uniformly polarized spin system under the influence of a magnetic field varying sinusoidally in space. Explicit closed‐form results for the short‐time relaxation are obtained making use of Laplace transforms, the three‐term recurrence relations associated with Mathieu’s equation, and novel sum rules. At intermediate diffusivities the transverse polarization exhibits a novel long‐time behaviour as a function of D. This revised version was published online in August 2006 with corrections to the Cover Date.     

Quasilocal density functional theory in nuclei and its extension to include pairing correlations

We propose first a generalization of the Density Functional Theory. This theory leads to single-particle equations of motion with a quasilocal mean-field operator, which contains a quasiparticle position-dependent effective mass and a spin—orbit potential. The energy density functional is constructed using the extended Thomas—Fermi approximation. Some ground-state properties of doubly magic nuclei are considered within the framework of this approach. Calculations are performed using the finite-range Gogny D1S forces, and the results are compared with the exact Hartree—Fock calculations. Next, we present an extension of the density functional theory to include pairing correlations without formal violation of the particle-number condition. This problem, which is nonlocal, can be simplified by a suitable quasilocal reduction, which is also briefly discussed in this paper. The text was submitted by the authors in English.     

An alternative definition of the electron propagator in the superoperator form and its relation to linear response theory in a coupled-cluster framework

In this paper it is shown that (i) there exists an alternative definition of the superoperator resolvent for calculation of difference energy satisfying linked cluster theorem for a coupled-cluster choice of the ground-state function which may even be approximate; (ii) the pole-structure of this propagator-like function in superoperator form is shown to contain information similar to that contained in the conventional propagator. (iii) It is demonstrated that suitable “Killer conditions” and completeness of the “operator manifold”—essential for understanding the pole-structure of the propagator—can be established both for an exact and an approximate ground state function in a coupled-cluster form. (iv) It is also demonstrated that difference energies calculated with these propagator-like functions are identical to those obtained from a linear response theory in a coupled-cluster form put forward recently by Mukherjeeet al and Monkhorst.     

Parity Projected QCD Sum Rule of the Nucleon with MEM

The nucleon and its negative-parity excited states are examined in a maximum entropy method analysis of QCD sum rules. We derive the parity projected nucleon sum rules with all known first order α _s corrections to the Wilson coefficients of the operator product expansion (OPE). As these corrections have turned out to be large, we suppress them by using a phase-rotated Gaussian kernel. This phase rotation strongly suppresses the continuum contribution and improves the convergence of the OPE. The resulting sum rule has the interesting feature that it is dominated by the term containing the chiral condensate of dimension 3. Analyzing this sum rule by the maximum entropy method, we are able to extract information of both the positive and negative parity states.     

Bound-state perturbation method via SVZ sum rules in quantum mechanics

The perturbation method for bound states within the framework of the Shifman-Vainshtein-Zakharov sum rule method is studied on simple systems (linear harmonic oscillator, hydrogen atom) in external electric fields. It is pointed out that for stronger fields reasonable results for the ground-state energy can only be achieved when sum rules are written for the correction to the Euclidean Green function caused by the external field. Moreover, if the system is bound by a singular (Coulomb) potential, one needs to sum higher perturbative corrections to the Green function and to find a realistic approximation of the continuum contribution to the sum rules. The results are of relevance e.g. for calculations of nucleon magnetic moments and toponium properties via SVZ sum rules in QCD.     

Extraction of ground-state decay constant from dispersive sum rules: QCD vs potential models

We compare the extraction of the ground-state decay constant from the two-point correlator in QCD and in potential models and show that the results obtained at each step of the extraction procedure follow a very similar pattern. We prove that allowing for a Borel-parameter-dependent effective continuum threshold yields two essential improvements compared to employing a Borel-parameter-independent quantity: (i) It reduces considerably the (unphysical) dependence of the extracted bound-state mass and the decay constant on the Borel parameter. (ii) In a potential model, where the actual value of the decay constant is known from the Schrödinger equation, a Borel-parameter-dependent threshold leads to an improvement of the accuracy of the extraction procedure. Our findings suggest that in QCD a Borel-parameter-dependent threshold leads to a more reliable and accurate determination of bound-state characteristics by the method of sum rules.     

A Bayesian analysis of the nucleon QCD sum rules

QCD sum rules of the nucleon channel are reanalyzed, using the maximum-entropy method (MEM). This new approach, based on the Bayesian probability theory, does not restrict the spectral function to the usual “pole + continuum” form, allowing a more flexible investigation of the nucleon spectral function. Making use of this flexibility, we are able to investigate the spectral functions of various interpolating fields, finding that the nucleon ground state mainly couples to an operator containing a scalar diquark. Moreover, we formulate the Gaussian sum rule for the nucleon channel and find that it is more suitable for the MEM analysis to extract the nucleon pole in the region of its experimental value, while the Borel sum rule does not contain enough information to clearly separate the nucleon pole from the continuum.     

A Generalized Plasma and Interpolation Between Classical Random Matrix Ensembles

The eigenvalue probability density functions of the classical random matrix ensembles have a well known analogy with the one component log-gas at the special couplings β=1,2 and 4. It has been known for some time that there is an exactly solvable two-component log-potential plasma which interpolates between the β=1 and 4 circular ensemble, and an exactly solvable two-component generalized plasma which interpolates between β=2 and 4 circular ensemble. We extend known exact results relating to the latter—for the free energy and one and two-point correlations—by giving the general (k ₁+k ₂)-point correlation function in a Pfaffian form. Crucial to our working is an identity which expresses the Vandermonde determinant in terms of a Pfaffian. The exact evaluation of the general correlation is used to exhibit a perfect screening sum rule.     

Exact quantum Monte Carlo process for the statistics of discrete systems

We propose an exact Monte Carlo approach for the statistics of discrete quantum systems that does not employ the standard partition of the imaginary time into a mesh and does not contain small parameters. The method operates with discrete objects — kinks, describing virtual transitions at different moments in time. The global statistics of the kinks is reproduced by exact local procedures, the main one being based on the known solution for an asymmetric two-level system. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 12, 853–858 (25 December 1996)     

Kardar—Parisi—Zhang equation in one dimension and line ensembles

For suitably discretized versions of the Kardar—Parisi—Zhang equation in one space dimension, exact scaling functions are available, amongst them the stationary two-point function. We explain one central piece from the technology through which such results are obtained, namely the method of line ensembles with purely entropic repulsion.     

Radiative recoil corrections to hyperfine splitting: Polarization insertions in the electron factor

We consider three-loop radiative recoil corrections to hyperfine splitting in muonium due to insertions of the one-loop polarization operator in the electron factor. The contribution generated by electron polarization insertions is a cubic polynomial in the large logarithm of the electron—muon mass ratio. The leading logarithm cubed and logarithm squared terms are well known for some time. We calculate all single-logarithmic and nonlogarithmic radiative recoil corrections of the order α³ (m/M)E_F generated by diagrams with the electron and muon polarization insertions.     

Contribution of higher gluon condensates to light-quark vacuum polarization

A method of classifying quark operators in QCD sum rules is suggested. The expansion coefficients of all thed≦8 bilinear quark condensates in gluon condensates are calculated. The coefficient functions at the gluon operators withd≦8 in the polarization operator ∏(q ²) of the light-quark vector current are obtained. A comparison is performed with the calculations in the covariantly constant fields and self-dual fields. The results obtained can be used in the sum rules for the ρ, ω and ? families.     

Quarkonia at Finite T: An Approach Based On QCD Sum Rules and the Maximum Entropy Method

Quarkonium spectral functions at finite temperature are studied, making use of a recently developed method of analyzing QCD sum rules by the maximum entropy method. This approach enables us to directly obtain the spectral function from the sum rules, without having to introduce any specific assumption about its functional form. QCD sum rules for heavy quarkonia incorporate finite temperature effects in form of changing values of the various gluonic condensates that appear in the operator product expansion. These changes depend on the energy density and pressure at finite temperature, which we extract from quenched lattice QCD calculations. As a result, it is found that the charmonium ground states of both S-wave and P-wave channels dissolve into the continuum already at temperatures around or slightly above the critical temperature T _c , while the bottomonium states are less influenced by temperature effects, surviving up to about 2.5 T _c or higher for S-wave and about 2.0 T _c for P-wave states.     

Energy-weighted sum rules for spin operators and ground-state correlations

Energy-weighted sum rules are obtained for the spin part, both isoscalar and isovector, of the magnetic dipole operator. The same interaction is used to evaluate the relevant double commutator as is used to induce ground-state correlations. First a spin-dependent delta interaction is used; then a tensor interaction is considered. The main point of this work is that there is a lot of energy-weighted strength at high energies.     

A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules

We improve the Monte-Carlo based QCD sum rules by introducing the rigorous H¨older-inequalitydetermined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function.In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum. Therefore, an unbiased prediction can be obtained for the phenomenological parameters(the hadronic mass and width etc.). We test the new approach in the ρ meson channel with re-examination and inclusion of α_s corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels.     

The Girardeau's fermion-boson procedure in the light of the composite-boson many-body theory

We reconsider the procedure developed for atoms a few decades ago by Girardeau, in the light of the composite-boson many-body theory we recently proposed. The Girardeau's procedure makes use of a so called “unitary Fock-Tani operator” which in an exact way transforms one composite bound atom into one bosonic “ideal” atom. When used to transform the Hamiltonian of interacting atoms, this operator generates an extremely complex set of effective scatterings between ideal bosonic atoms and free fermions which makes the transformed Hamiltonian impossible to write explicitly, in this way forcing to some truncation. The scatterings restricted to the ideal-atom subspace are shown to read rather simply in terms of the two elementary scatterings of the composite-boson many-body theory, namely, the energy-like direct interaction scatterings — which describe fermion interactions without fermion exchange — and the dimensionless Pauli scatterings — which describe fermion exchanges without fermion interaction. We here show that, due to a fundamental difference in the scalar products of elementary and composite bosons, the Hamiltonian expectation value for N ground state atoms obtained by staying in the ideal-atom subspace and working with boson operators only, differ from the exact ones even for N = 2 and a mapping to the ideal-atom subspace performed, as advocated, from the fully antisymmetrical atomic state, i.e., the state which obeys the so-called “subsidiary condition”. This shows that, within this Girardeau's procedure too, we cannot completely forget the underlying fermionic components of the particles if we want to correctly describe their interactions.     

Magnetoplasma oscillations in a 2D electron system with spin-orbit interaction

The magnetoplasmon spectrum in a 2D electron plasma is investigated theoretically taking into account the spin—orbit interaction in the Rashba model. The expression is derived for the polarization operator in the semiclassical range of magnetic fields (in which the Fermi energy eF is much larger than the Landau quantum). Approximate analytic formulas are obtained for spin—plasmon branches. The dependences of plasma wave frequencies on the wavevector and magnetic field are calculated from a numerical solution of the dispersion equation. In addition, the magnetic field and frequency dependences of the plasmon absorption intensity are constructed. The absorption intensity at the peak is found to be sensitive to the spin—orbit interaction constant.