Full Green Function Research Articles

A cosmological Slavnov-Taylor identity

We develop a method for treating the consistency relations of inflation that includes the full time-evolution of the state. This approach relies only on the symmetries of the inflationary setting, in particular a residual conformal symmetry in the spatial part of the metric, along with general properties which hold for any quantum field theory. As a result, the consistency relations that emerge, which are essentially the Slavnov-Taylor identities associated with this residual conformal symmetry, apply very generally: they are true of the full Green's functions, hold largely independently of the particular inflationary model, and can be used for arbitrary states. We illustrate these techniques by showing the form assumed by the standard consistency relation between the two and three-point functions for the primordial scalar fluctuations when they are in a Bunch-Davies state. But because we have included the full evolution of the state, this approach works for a general initial state as well and does not need to have assumed that inflation began in the Bunch-Davies state. We explain how the Slavnov-Taylor identity is modified for these more general states.

Orbital magnetization of correlated electrons with arbitrary band topology

Spin-orbit coupling introduces chirality into electronic structure. This can have profound effects on the magnetization induced by orbital motion of electrons. Here we derive a formula for the orbital magnetization of interacting electrons in terms of the full Green's function and vertex functions. The formula is applied within dynamical mean-field theory to the Kane-Mele-Hubbard model that allows both topological and trivial insulating phases. We study the insulating and metallic phases in the presence of an exchange magnetic field. In the presence of interactions, the orbital magnetization of the quantum spin Hall insulating phase with inversion symmetry is renormalized by the bulk quasi-particle weight. The orbital magnetization vanishes for the in-plane antiferromagnetic phase with trivial topology. In the metallic phase, the enhanced effective spin-orbit coupling due to the interaction sometimes leads to an enhancement of the orbital magnetization. However, at low doping, magnetization is suppressed at large interaction strengths.

Complexity penalized hydraulic fracture localization and moment tensor estimation under limited model information

In this paper, we present a novel technique for micro-seismic localization using a group sparse penalization that is robust to the focal mechanism of the source and requires only a velocity model of the stratigraphy rather than a full Green's function model of the earth's response. In this technique, we construct a set of perfect delta detector responses, one for each detector in the array, to a seismic event at a given location and impose a group sparsity across the array. This scheme is independent of the moment tensor and exploits the time compactness of the incident seismic signal. Furthermore, we present a method for improving the inversion of the moment tensor and Green's function when the geometry of seismic array is limited. In particular, we demonstrate that both Tikhonov regularization and truncated SVD can improve the recovery of the moment tensor and be robust to noise. We evaluate our algorithm on synthetic data and present error bounds for both estimation of the moment tensor as well as localization. Furthermore we discuss the estimated moment tensor accuracy as a function of both array geometry and fault orientation.

Self-energy effects in the Polchinski and Wick-ordered renormalization-group approaches

I discuss functional renormalization group (fRG) schemes, which allow for non-perturbative treatment of the self-energy effects and do not rely on the one-particle irreducible functional. In particular, I consider the Polchinski or Wick-ordered scheme with amputation of full (instead of bare) Green functions, as well as more general schemes, and establish their relation to the ‘dynamical adjustment propagator’ scheme by Salmhofer (2007 Ann. Phys., Lpz. 16 171). While in the Polchinski scheme the amputation of full (instead of bare) Green functions improves treatment of the self-energy effects, the structure of the corresponding equations is not suitable to treat strong-coupling problems; it is also not evident how the mean-field solution of these problems is recovered in this scheme. For the Wick-ordered scheme, fully or partly excluding tadpole diagrams one can obtain forms of fRG hierarchy, which are suitable to treat strong-coupling problems. In particular, I emphasize the usefulness of the schemes, which are local in the cutoff parameter, and compare them to the one-particle irreducible approach.

Scattering of a spherical wave by a small sphere: An elementary solution

Wave scattering by objects that are small compared to the wavelength (Rayleigh scattering) is usually studied for plane incident waves. However, knowledge of the full Green's function of the problem becomes necessary when the separation of scatterers from either an interface or each other is comparable to the scatterers' dimensions. Here, an elementary analytic solution is derived for diffraction of a spherical sound wave by a small, soft sphere. The approximate solution is obtained from asymptotic expansions of an exact solution, holds everywhere outside the sphere, and reduces to classical results due to Kelvin and Rayleigh in appropriate special cases.

Superfluid nucleon matter in and out of equilibrium and weak interactions

The Larkin-Migdal approach to a cold superfluid Fermi liquid is generalized for a non-equilibrium system. The Schwinger-Keldysh diagram technique is applied. The developed formalism is applicable to the pairing in the states with arbitrary angular momenta. We consider the white body radiation problem by calculating probabilities of different direct reactions from a piece of a fermion superfluid. The closed diagram technique is formulated in terms of the full Green's functions for systems with the pairing correlation. The cutting rules are used to classify the diagrams representing one-nucleon, two-nucleon, etc. processes in the matter. The important role of multi-piece diagrams for the vector-current conservation is demonstrated. In the case of equilibrated systems, dealing with dressed Green's functions, we demonstrate correspondence between calculations in the Schwinger-Kadanoff-Baym-Keldysh formalism and the ordinary Matsubara technique. As an example we consider neutrino radiation from the neutron pair breaking and formation processes in case of a singlet pairing. Necessary correlation effects are included. The in-medium renormalization of normal and anomalous vertices is performed.

Exact Crossover Green Function in the Two-Channel and Two-Impurity Kondo Models

Symmetry-breaking perturbations destabilize the critical points of the two-channel and two-impurity Kondo models, thereby leading to a crossover from non-Fermi liquid behavior to standard Fermi liquid physics. Here we use an analogy between this crossover and one occurring in the boundary Ising model to calculate the full crossover Green function analytically. In remarkable agreement with our numerical renormalization group calculations, the single exact function applies for an arbitrary mixture of the relevant perturbations in each model. This rich behavior resulting from finite channel asymmetry, interlead charge transfer, and/or magnetic field should be observable in quantum dot or tunneling experiments.

Two loop renormalization of the n = 2 Wilson operator in the RI′/SMOM scheme

We compute the anomalous dimensions of the flavour non-singlet twist-2 Wilson operators in the RI'/SMOM scheme at two loops in an arbitrary linear covariant gauge. In addition we provide the full Green's function for these operators inserted in a quark 2-point function at the symmetric subtraction point. The three loop anomalous dimensions in the Landau gauge are also derived.

Regge field theory in zero transverse dimensions: loops versus “net” diagrams

Toy models of interacting Pomerons with triple and quaternary Pomeron vertices in zero transverse dimension are investigated. Numerical solutions for eigenvalues and eigenfunctions of the corresponding Hamiltonians are obtained, providing the quantum solution for the scattering amplitude in both models. The equations of motion for the Lagrangians of the theories are also considered and the classical solutions of the equations are found. Full two-point Green functions ("effective" Pomeron propagator) and amplitude of diffractive dissociation process are calculated in the framework of RFT-0 approach. The importance of the loops contribution in the amplitude at different values of the model parameters is discussed as well as the difference between the models with and without quaternary Pomeron vertex.

Topological Order Parameters for Interacting Topological Insulators

We propose a topological order parameter for interacting topological insulators, expressed in terms of the full Green's functions of the interacting system. We show that it is exactly quantized for a time-reversal invariant topological insulator, and it can be experimentally measured through the topological magneto-electric effect. This topological order parameter can be applied to both interacting and disordered systems, and used for determining their phase diagrams.

Underestimation of body waves and feasibility of surface-wave reconstruction by seismic interferometry

Interferometry is an approach to extract the Green's function between two receivers as if the virtual source is at one of the receiver locations. The Green's function which is the response to an impulsive source, accounts for the wave propagation in the medium between the two receivers. It is commonly thought that Green's function estimates obtained from interferometry accurately represent the full Green's function, but this is not always the case. In fact, the accuracy of the retrieved Green's function, which consists of the surface and body waves, is in practice restricted by the limited distribution of the sources of field fluctuations. We demonstrate the importance of adequate source distribution for the accuracy of the retrieved Green's function, using examples from interferometry applications. In these examples, sources are controlled (as in exploration seismology) or uncontrolled (as in crustal seismology).

Gilbert damping and current-induced torques on a domain wall: A simple theory based on itinerant3delectrons only

Many electronic theories of Gilbert damping in ferromagnetic metals are based on the $s\text{\ensuremath{-}}d$ exchange model, where localized $3d$ magnetic spins are exchanged-coupled to itinerant $4s$ electrons, which provide the needed spin relaxation. Recently, Tserkovnyak et al. have obtained Gilbert damping from itinerant $3d$ electrons alone, which have their own spin relaxation. We show that simple semiclassical equations of motion for precessing itinerant $3d$ spins predict exactly the same formula $\ensuremath{\alpha}=1/({\ensuremath{\omega}}_{d}{\ensuremath{\tau}}_{sr}^{d})$ for the Gilbert damping constant as the full Green's function quantum treatment by Tserkovnyak et al. Here, ${\ensuremath{\omega}}_{d}$ is the precession frequency of $3d$ spins in the $d\text{\ensuremath{-}}d$ mutual exchange field, and ${\ensuremath{\tau}}_{sr}^{d}$ the $3d$ spin-relaxation time. A correct form for the spin-relaxation torque is crucial for success: The spins relax toward an instantaneous direction which is that of the vector sum of external field and $d\text{\ensuremath{-}}d$ exchange field. Remarkably, $d\text{\ensuremath{-}}d$ exchange torques disappear completely from the equations of motion for the total $3d$ magnetization, and exchange plays only an indirect role through the spin relaxation. This purely $3d$ model is simpler than the traditional $s\text{\ensuremath{-}}d$ model. We also present a theory of current-induced torques on a domain wall, based on the $3d$ model. We find equivalents to the so-called adiabatic and nonadiabatic torques. They are given by formulas similar to those holding for the $s\text{\ensuremath{-}}d$ exchange model.

Green’s function for multielectron ions and its application to radiative recombination involving dielectronic recombinations

We propose a general method to calculate the full Green's function of multielectron atomic ions. The key point exists in the usage of ${L}^{2}$ integrable functions as a complete basis set in a finite region together with an optical potential to guaranty the outgoing scattering boundary condition. In such a way, the cumbersome procedure of adjusting boundary conditions in solving the differential Schr\"odinger equation is avoided. To show the validity of the method, we studied the radiative recombination involving dielectronic recombinations of Be-like Hg $(\text{Z}=80)$ ions. The radiative damping effect is taken into account naturally in the present method. The calculated results reproduce well the asymmetric line profile observed in the experiments.

Building the full fermion-photon vertex of QED by imposing multiplicative renormalizability of the Schwinger-Dyson equations for the fermion and photon propagators

In principle, calculation of a full Green's function in any field theory requires knowledge of the infinite set of multipoint Green's functions, unless one can find some way of truncating the corresponding Schwinger-Dyson equations. For the fermion and boson propagators in QED this requires an ansatz for the full 3-point vertex. Here we illustrate how the properties of gauge invariance, gauge covariance and multiplicative renormalizability impose severe constraints on this fermion-boson interaction, allowing a consistent truncation of the propagator equations. We demonstrate how these conditions imply that the 3-point vertex in the propagator equations is largely determined by the behavior of the fermion propagator itself and not by knowledge of the many higher-point functions. We give an explicit form for the fermion-photon vertex, which in the fermion and photon propagator fulfills these constraints to all orders in leading logarithms for massless QED, and accords with the weak coupling limit in perturbation theory at O({alpha}). This provides the first attempt to deduce nonperturbative Feynman rules for strong physics calculations of propagators in massless QED that ensure a more consistent truncation of the 2-point Schwinger-Dyson equations. The generalization to next-to-leading order and masses will be described in a longer publication.

Passive Sensor Imaging Using Cross Correlations of Noisy Signals in a Scattering Medium

It is well known that the travel time or even the full Green's function between two passive sensors can be estimated from the cross correlation of recorded signal amplitudes generated by ambient noise sources. It is also known that the direction of the energy flux from the noise sources affects the estimation of the travel time. Using the stationary phase method, we show here that the travel time can be effectively estimated when the ray joining the two sensors continues into the noise source region. We extend this analysis to passive sensor imaging of reflectors with different ambient noise source configurations by suitably migrating the cross correlations. If in addition there is multiple scattering in the medium, then reflectors can be imaged with passive sensor networks or arrays by migrating suitable fourth-order cross correlations. Fourth-order cross correlations can also be used with auxiliary passive sensors in order to enhance travel time estimation in a scattering medium.

Calculation of Tyre Noise Radiation with a Mixed Approach

Summary The radiation of tyre noise is computed using a hybrid integral/ beam tracing approach called GRIM. It is simply an integral over the vibrating tyre, of the product of the known velocity by the full Green function which takes into account all the multiple reflections and diffraction between tyre, ground and car body. This Green function can be calculated by means of a beam tracing program named ICARE -which can deal with curved surfaces and multiple diffraction. This approach makes the link between tyre models and reception points well outside the car. In order to deal with small scale phenomena, close to contact, a combined use of BEM and beam tracing is showed to bypass the limitations of both geometrical and BEM approaches. PACS no.43.28.Js

A Self-Consistent Full 3-D Real-Space NEGF Simulator for Studying Nonperturbative Effects in Nano-MOSFETs

In this paper, we present a full 3-D real-space quantum-transport simulator based on the Green's function formalism developed to study nonperturbative effects in ballistic nanotransistors. The nonequilibrium Green function (NEGF) equations in the effective mass approximation are discretized using the control-volume approach and solved self-consistently with the Poisson equation in order to obtain the electron and current densities. An efficient recursive algorithm is used in order to avoid the computation of the full Green function matrix. This algorithm, and the parallelization scheme used for the energy cycle, allow us to compute very efficiently the current-voltage characteristic without the simplifying assumptions often used in other quantum-transport simulations. We have applied our simulator to study the effect of surface roughness and stray charge on the I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> -V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</sub> characteristic of a 6-nm Si-nanowire transistor. The results highlight the distinctly 3-D character of the electron transport, which cannot be accurately captured by using 1-D and 2-D NEGF simulations, or 3-D mode-space approximations.

Various Full Green Functions in QED

We are interested in deriving various full Green functions through general Ward–Takahashi identities (WTIs) for quantized field theories. With the help of a postulate of gauge group parameter, the general local gauge transformation laws preserving the gauge-invariance of the generating functional itself of QED model have been established successfully. By using path-integral technique, the various WTIs with resulting anomaly terms are derived under the gauge transformations. The arising of Jacobian factor from the integration measure gives a viable possibility to express full Green function. As a consequence, the complete expressions of the full vector, the full axial-vector, the full tensor vertex functions and so on are presented respectively by solving the complete set of the WTIs in the momentum space without considering the constraint imposing any Ansatz. In addition, anomaly function also provides an effective means to judge the divergence of variant coupling currents on fields.

Path-integral over non-linearly realized groups and hierarchy solutions

The technical problem of deriving the full Green functions of the elementary pion fields of the nonlinear sigma model in terms of ancestor amplitudes involving only the flat connection and the nonlinear sigma model constraint is a very complex task. In this paper we solve this problem by integrating, order by order in the perturbative loop expansion, the local functional equation derived from the invariance of the SU(2) Haar measure under local left multiplication. This yields the perturbative definition of the path-integral over the non-linearly realized SU(2) group.

On estimating the impulse response between receivers in a controlled ultrasonic experiment

A controlled ultrasonic laboratory experiment provides a detailed analysis of retrieving a band-limited estimate of the Green's function between receivers in an elastic medium. Instead of producing a formal derivation, this paper appeals to a series of intuitive operations, common to geophysical data processing, to understand the practicality of seismic interferometry. Whereas the retrieval of the full Green's function is based on the crosscorrelation of receivers in the presence of equipartitioned signal, an estimate of the impulse response is recovered successfully with 40 sources in a line covering six wavelengths at the surface.