Exact Green Function Research Articles

Full-wave analysis of waveguide-to-microstrip transitions for millimeter wave applications

A “full-wave” solution is presented for the waveguide to microstrip transition. The exact Green's function of the transition is used in a moment method procedure. The behavior of the microstrip transition to a rectangular waveguide is studied with respect to the critical dimensions of the microstrip width, length and backshort location. The convergence characteristics of the full wave analysis method are investigated, along with the current distribution and the input impedance. Results given for the return loss is compared with measurements.

Nonequilibrium time-dependent functional theory for coupled interacting fields.

We develop a nonequilibrium time-dependent functional theory of coupled interacting fields in terms of the Liouvillian quantum field dynamics. In this theory the expectation values of the appropriate field operators are treated as the functional variables. Thus, the formalism proposed here goes beyond the existing time-dependent density-functional method, in that we now have a mixed-state multivariable dynamical theory. A large class of condensed matter problems, with the given initial condition that the system be in thermodynamic equilibrium and subjected to time-dependent external forces, can now be examined. In particular, we formulate the self-consistent coupled equations for the electron, ion, and the electromagnetic fields. The above formalism provides a firm physical and mathematical basis for time-dependent dynamical simulation procedures such as those envisaged in the Car-Parrinello approach by replacing the fictitious Lagrangian by a precise action principle. The theory involves a certain functional representing the mutual interactions and correlations among these fields. In parallel with this, we also generalize the Baym \ensuremath{\Phi}-derivable method in many-body theory to investigate the class of problems mentioned above. This involves a functional of the exact one-particle Green functions. We compare the two methods and suggest the use of the latter in the former scheme as a way of going beyond the simple mean-field schemes. We illustrate the utility of the framework by citing a variety of illustrative examples.

Seismic response of three-dimensional alluvial valleys for incident P, S, and Rayleigh waves

A simplified indirect boundary-element method (BEM) is presented. It is used to compute the seismic response of three-dimensional alluvial valleys under incident P, S , and Rayleigh waves. The method is based on the integral representations for scattered elastic waves using single-layer boundary sources. This approach is called indirect BEM in the literature as the sources strengths should be obtained as an intermediate step. Scattered waves are constructed at the boundaries from which they radiate. Therefore, this method can be regarded as a numerical realization of Huygens' principle. Boundary conditions lead to a system of integral equations for boundary sources. A simplified discretization scheme is used. It is based on the approximate rectification of the surfaces involved using circles for the numerical and analytical integration of the exact Green's function for the unbounded elastic space. Various examples are given for three-dimensional problems of scattering and diffraction of elastic waves by soft elastic inclusion models of alluvial deposits in an elastic half-space. Results are displayed in both frequency and time domains. These results show the significant influence of locally generated surface waves in seismic response, and they evince three-dimensional effects.

Full-wave analysis and design of a new double-sided branch-line coupler and its complementary structure

A new double-sided branch-line coupler using microstrip lines as input/output lines and slotlines as branches is analyzed and designed. The even-odd mode theory is first used to analyze the ideally simplified circuit model and to find out the preliminary circuit dimensions. Based on these dimensions, the full-wave spectral domain approach (SDA) is employed to accurately simulate the circuit performance. By the formulation of the exact Green's function in the spectral domain, the effects of surface wave and radiation phenomena are accurately accounted for. Experimental data agree very well with the SDA simulation results. It is found that the even-odd mode theory which neglects discontinuities between lines is not enough to design a coupler. The SDA code can then be used to accurately simulate and optimize the circuit performance. The complementary structure with slotlines as input/output lines and microstrip lines as branches is also investigated both theoretically and experimentally. It is noticed that the radiation and leakage from the two double-ended branches for all structures will deteriorate the circuit performance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Standard model CP-violation and baryon asymmetry (I). Zero temperature

We consider quantum effects in a world with two coexisting symmetry phases, unbroken and spontaneously broken, as a result of a first order phase transition. The discrete symmetries of the problem are discussed in general. We compute the exact two-point Green function for a free fermion, when a thin wall separates the two phases. The Dirac propagator displays both massive and massless poles, and new CP-even phases resulting from the fermion reflection on the wall. We discuss the possible quark-antiquark CP-asymmetries produced in the Standard Model (SM) for the academic T = 0 case. General arguments indicate that an effect first appears at order α W in the reflection amplitude, as the wall acts as a source of momentum and the on-shell one-loop self-energy cannot be renormalized away. The asymmetries stem from the interference of the SM CP-odd couplings and the CP-even phases in the propagator. We perform a toy computation that indicates the type of GIM cancellations of the problem. The behaviour can be expressed in terms of two unitarity triangles.

Mutual impedance between skewed patch antennas

This paper considers the mutual impedance between skewed rectangular microstrip patch antennas as a function of the skew angle. The analysis is done using the exact Green's function for the patch and the method of moments to solve for the field. The theoretical results obtained are compared with published experimental results. >

Exact results on the multi-channel Kondo effect from conformal field theory

We review some of the exact results, obtained from conformal field theory for the non-Fermi-liquid fixed point in the multi-channel single-impurity Kondo model. These include thermodynamics, transport, stability and robustness of the non-Fermi-liquid, exact Green's functions, enhancement of pair-correlations and crossover behavior. The physical origin of the non-Fermi-liquid behavior is a generalization of spin-charge separation.

Universal subgap optical conductivity in quasi-one-dimensional Peierls systems.

Quasi-one-dimensional Peierls systems with quantum and thermal lattice fluctuations can be modeled by a Dirac-type equation with a Gaussian-correlated off-diagonal disorder. A powerful new method gives the exact disorder-averaged Green function used to compute the optical conductivity. The strong subgap tail of the conductivity has a universal scaling form. The frequency and temperature dependence of the calculated spectrum agrees with experiments on KCP(Br) and trans-polyacetylene.

Smooth contact of orthotropic laminates by rigid cylinders

An analytical method is developed to investigate the contact behavior of an Orthotropic laminate indented by a frictionless cylinder. The method is derived from an exact Green's function, which is based on the anisotropic elasticity theory in the plane strain condition. The contact response of a laminate is characterized into small and large contact stages depending on conformation of the curvatures between the indenter and the laminate in the contact region. The large contact stage occurs after conformation of the curvatures, resulting in less stress concentration in the laminate. It is found that the large contact stage readily develops when large indenters or large laminate span-to-thickness ratios are used. Also, the effect of slight misalignment of an indenter on the contact response of the laminate is significant. On the other hand, a change of laminate stacking sequence has an insignificant effect on the force-indentation relationship.

An indirect boundary element method applied to simulate the seismic response of alluvial valleys for incident P, S and Rayleigh waves

AbstractA boundary integral formulation is presented and applied to model the ground motion on alluvial valleys under incident P, S and Rayleigh waves. It is based on integral representations for the diffracted and the refracted elastic waves using single‐layer boundary sources. This approach is called indirect BEM in the literature as the sources' strengths should be obtained as an intermediate step. Boundary conditions lead to a system of integral equations for boundary sources. A discretization scheme based on the numerical and analytical integration of exact Green's functions for displacements and tractions is used. Various examples are given for two‐dimensional problems of diffraction of elastic waves by soft elastic inclusion models of alluvial deposits in an elastic half‐space. Results are displayed in both frequency and time domains. These results show the significant influence of locally generated surface waves in seismic response and suggest approximations of practical interest. For shallow alluvial valleys the response and its resonant frequencies are controlled by a coupling mechanism that involves both the simple one‐dimensional shear beam model and the propagation of surface waves.

Recursive-Green's-function analysis of wave propagation in two-dimensional nonhomogeneous media.

An alternative method is presented for computing wave propagation in two-dimensional nonhomogeneous media. The method is based on computing the exact Green's function for a domain using a recursive Green's-function approach. In comparison with the finite-difference time-domain method, our approach requires substantially less memory and computational time, enabling the modeling of larger and more complex domains. The method is validated by comparing with exact analytical solutions and is found to be highly accurate.

Exact Green's functions of generalized Fibonacci lattices

We study the electronic properties of the generalized Fibonacci lattices generated by the inflation rule ( A, B) → ( AB n , A) with n > 1. A unified real-space renormalization-group scheme is presented for calculating the exact local Green's function at any given site. Analysis suggests that there are extended states in these lattices. Furthermore, the appearance of the extended states and the smoothness of the local density of states depends on the system parameters, implying that these exists a state transition phenomenon similar to that of the incommensurate Harper's model.

Topographic effects for incident P, SV and Rayleigh waves

The topographical effects for incident P, SV and Rayleigh waves in an elastic half-space were studied using an integral representation of the diffracted elastic waves in terms of single-layer boundary sources. The free-boundary condition leads to a Fredholm integral equation of the second kind for boundary sources. We used a discretization scheme based on the numerical and analytical integration of exact Green's functions. This approach is called indirect BEM in the literature. However, it provides far more insight on the physics of diffraction problems than the direct approaches. This is because diffracted waves are constructed at the boundaries from which they are radiated. Therefore, this method can be regarded as a numerical realization of Huygens' principle. Various examples that cover extreme cases are presented. It is found that topography may cause significant effects both of amplification and of deamplification at the irregular feature itself and its neighborhood but the absolute level of amplification is generally lower than about 4 times the amplitude of incoming waves. These facts must be taken into account when the spectral ratio technique is used to study topographical response.

Analysis of distributed-feedback lasers using a recursive Green's functional approach

A method is presented for obtaining the exact propagation constants (resonance wavelengths and threshold gains) for distributed-feedback lasers. The method is based on computing the exact Green's function for resonant cavities using a recursive Green's function approach. The net threshold gains of distributed-feedback lasers are calculated and compared with the results obtained using conventional coupled-mode theory. The comparison reveals that coupled-mode theory is weakest for aperiodic structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Full-wave modeling of coplanar waveguide discontinuities with finite conductor thickness

An extended version of the spectral domain approach (SDA) is developed to analyze discontinuities in open coplanar waveguide with finite metallization thickness. By making use of the exact Green's function in the spectral domain, the effects of surface wave and radiation phenomena are accurately accounted for. Both longitudinal and transverse components of the aperture electric fields are used in the analysis to allow modelling of structures with large transverse dimensions at high frequencies. The procedure also includes mode conversion near the discontinuities. As an illustration of the method, analytical steps and computed scattering parameters of the coplanar waveguide short-circuits and transitions are provided and compared against measured data.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Full-wave analysis of a two slot microstrip filter using a new algorithm for computation of the spectral integrals

An integral equation is formulated in the spectral domain for a two slot microstrip filter using the exact Green's function for the grounded dielectric substrate. Using a moment method (MM) procedure, the integral equation has been discretized. The elements of the impedance matrix and the excitation vector are given by two dimensional Sommerfeld-type integrals in closed form. An efficient and accurate numerical integration scheme for computation of the elements is presented. The S parameters obtained from the MM procedure have been found to be in excellent agreement with measurements. >

ON REPRESENTATION OF QUANTUM ACTION FUNCTIONAL

A representation for QA functional is constructed. The representation can be formulated in terms of compact (one-particle—irreducible) Feynman diagrams with special correspondence rules. The main properties are: (1) the representation of the exact vertex requires only a finite number of diagrams, (2) manifest symmetry with respect to permutations of particles. That enables one to develop consistent calculational methods. The resulting set of equations for the exact Green functions and vertices can open a way to approximate nonperturbative solutions.

The exact Green function of a one-dimensional Thue-Morse lattice

A real-space renormalization-group approach for calculating the exact electronic Green function of an infinite Thue-Morse chain is presented. This approach is based on a renormalization transformation introduced according to the self-similar structure of the chain and the recursion relations for the matrix elements of the Green function. Numerical results for the local density of states for the off-diagonal model show the existence of the extended states.

Study of electromagnetic emissive power of moving ionospheric plasma on the basis of universal numerical model constructed on exact expressions

The exact Green's function for the problem of generation of electromagnetic disturbances by vertically inhomogeneous acoustic-gravity waves has been constructed for a homogeneous non-isotropic plasma. Explicit analytical expressions for the calculation of the electromagnetic field have been obtained for an inhomogeneous plane-stratified ionosphere. The results of the numerical evaluation of the Green's function, characterizing the emissive power of real moving ionospheric plasma are given. The influence of the AGW wave vector direction on the effectiveness of the two types of wave disturbance excitation in an ionospheric plasma has been studied.

Exact Dirac propagator in a magnetic “sheet”

We derive the exact fermionic Green function in an idealized magnetic field configuration, which becomes exact in the infinite energy limit. The fields under consideration can be produced, e.g., in peripheral ultrarelativistic heavy-ion collisions.