Green Functions Of Operators Research Articles

Estimates on Green functions of second order differential operators with singular coefficients

We investigate the Green functions G(x,x^{\prime}) of some second order differential operators on R^{d+1} with singular coefficients depending only on one coordinate x_{0}. We express the Green functions by means of the Brownian motion. Applying probabilistic methods we prove that when x=(0,{\bf x}) and x^{\prime}=(0,{\bf x}^{\prime}) (here x_{0}=0) lie on the singular hyperplanes then G(0,{\bf x};0,{\bf x}^{\prime}) is more regular than the Green function of operators with regular coefficients.

Theory of current-voltage asymmetries in double quantum dots

An explanation for the asymmetries in the current-voltage characteristics in mesoscopic quantum systems weakly coupled to reservoirs is proposed. Thus, it is suggested that inelastic scattering between the states in the interacting region dynamically redistributes the tunneling rate through the system. This redistribution functions non-uniformly for negative and positive bias voltages. Based on a diagrammatic technique for non-equilibrium many-body operator Green functions, an expression is presented that accounts for these scattering effects between the states. The theory is consistent with recent experimental data on mesoscopic systems.

Theory of spin filtering through quantum dots

Using a nonequilibrium diagram technique for Hubbard operator Green functions combined with a generalization of the transfer Hamiltonian formalism, we calculate the transport through a magnetic quantum dot system with spin-dependent couplings to the contacts. In specific regimes of the parameter space the spin-dependent tunnel current becomes more than 99.95% spin polarized, suggesting that a device thus constructed can be used in spin-filter applications. First-principles electronic structure calculations show the existence of nanostructured systems, such as, e.g., ${\mathrm{M}\mathrm{g}\mathrm{O}/\mathrm{F}\mathrm{e}/\mathrm{P}\mathrm{d}}_{5}/\mathrm{F}\mathrm{e}/\mathrm{M}\mathrm{g}\mathrm{O}$ (001), with the desired properties in the direction of the current.

Relating Green’s functions in axial and Lorentz gauges using finite field-dependent BRS transformations

We use finite field-dependent BRS transformations (FFBRS) to connect the Green functions in a set of two otherwise unrelated gauge choices. We choose the Lorentz and the axial gauges as examples. We show how the Green functions in axial gauge can be written as a series in terms of those in Lorentz gauges. Our method also applies to operator Green’s functions. We show that this process involves another set of related FFBRS transformations that is derivable from infinitesimal FFBRS. We suggest possible applications.

New methods for the renormalisation of composite operator green functions

New methods are developed for the renormalisation of composite operator Green functions, based on the idea of non-linear source renormalisation. The anomalous dimension in the renormalisation group equattion (RGE) for the generating functional becomes a non-linear function of the sources, and extra terms are therefore induced in the RGEs for the Green functions. These methods are applied to the operator product expansion, and a simple RGE for the Wilson coefficients is presented. Applications are made to Green functions of conserved and anomalous currents.

Self-consistent many-body theory for the standard basis operator Green's functions

We propose a self-consistent many-body theory for the standard basis operator Green's functions and obtain an exact Dyson-type matrix equation for the interacting many-level systems. A zeroth order approximation, which neglects all the damping effects, is investigated in detail for the anisotropic Heisenberg model, the isotropic quadrupolar system and the Hubbard model. In the case of the anisotropic Heisenberg ferromagnet with both exchange and single-ion anisotropy the low-temperature renormalization of the spin-waves for the uniaxial ordering agrees with the Bloch-Dyson theory. For the spin-1 easy-plane ferromagnet, the critical parameters for the phase transition at zero temperature are determined and compared with other theories. The elementary excitation spectrum of the spin-1 isotropic quadrupolar system is calculated and compared with the random phase approximation and Callen-like decoupling schemes. Finally, the theory is applied to the study of the single-particle excitation spectrum of the Hubbard model.

Inelastic neutron cross section for a magnetic impurity in a Heisenberg ferromagnet

The inelastic neutron cross section is calculated for a Heisenberg ferromagnet containing either a ferromagnetically or an antiferromagnetically coupled impurity. This is achieved by constructing the appropriate total spin operator Green functions from their equations of motion and using a decoupling scheme that renders the analysis equivalent to employing the linear spin-wave approximation It is shown that the cross section as a function of neutron energy change exhibits peaks when the condition for an impurity mode is satisfied. The cross sections contain both diffuse and coherent terms. The former are of direct experimental interest and are discussed in detail for both types of impurity.