Related papers: On the spectral relations for multitime correlatio…
In this paper, we summarize the technique of using Green functions to solve electrostatic problems. We start by deriving the electric potential in terms of a Green function and a charge distribution. We then provide a variety of example…
By introducing multipe-site correlation functions, we propose a hierarchical Green function approach, and apply it to study the characteristic properties of a 2D square lattice Hubbard model by solving the equation of motions of a…
Homogeneous and inhomogeneous biharmonic equation are considered on the $n$-dimensional unit sphere. The Green function is given as a series of Gegenbauer polynomials. In the paper, explicit representations of the Green function are found…
The spectral functions are studied in conjunction with the dyadic Green's functions for various media. The dyadic Green's functions are found using the eigenfunction expansion method for homogeneous, inhomogeneous, periodic, lossless,…
In this work, we consider the inverse scattering transform and multi-solition solutions of the sextic nonlinear Schr\"{o}dinger equation. The Jost functions of spectrum problem are derived directly, and the scattering data with $t=0$ are…
In this work, we generalize previous results about the Fractionary Schr\"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate…
Starting from the recently proposed dynamical exchange-correlation field framework, the equation of motion of the diagonal part of the many-electron Green function is derived, from which the spectral function can be obtained. The resulting…
A general formula for the orbital magnetic moment of interacting electrons in solids is derived using the many-electron Green function method. The formula factorizes into two parts, a part that contains the information about the…
The equilibration of two coupled reservoirs is studied using a Green function approach which is suitable for future development with the closed time path method. The problem is solved in two parameterizations, in order to demonstrate the…
We derive a set of relations among the thermal components of the 3-point function and its spectral representations at finite temperature in the real-time formalism. We then use these to explicitly calculate the 3-point spectral densities…
A Response Function Theory and Scattering Theory applicable to the study of physical properties of systems driven arbitrarily away from equilibrium, specialized for dealing with ultrafast processes and in conditions of space resolution…
Equal-time Green's function is used to derive a three-dimensional integral equation from the Bethe-Salpeter equation. The resultant equation, in the absence of anti-particles, is identical to the use of time-ordered diagrams, and has been…
A nonlinear generalization of the Fluctuation-Dissipation Theorem (FDT) for the n-point Green functions and the amputated 1PI vertex functions at finite temperature is derived in the framework of the Closed Time Path formalism. We verify…
The problem of calculating real-time correlation functions is formulated in terms of an imaginary-time partial differential equation. The latter is solved analytically for the perturbed harmonic oscillator and compared with the known exact…
In Green's function theory, the total energy of an interacting many-electron system can be expressed in a variational form using the Klein or Luttinger-Ward functionals. Green's function theory also naturally addresses the case where the…
A general form of multi-channel Bethe-Salpeter equation is considered. In contradistinction to the hitherto applied approaches, our coupled system of equations leads to the simultaneous solutions for all relativistic four-point Green…
In a recent letter [Phys. Rev. Lett. 131, 216401] we presented the multichannel Dyson equation (MCDE) in which two or more many-body Green's functions are coupled. In this work we will give further details of the MCDE approach. In…
We introduce a quasiclassical Green function approach describing the unitary yet irreversible dynamics of quantum systems effectively acting as their own environment. Combining a variety of concepts of quantum many-body theory, notably the…
Accurate modeling of the electronic structure of warm dense matter is a challenging problem whose solution would allow a better understanding of material properties like equation of state, opacity, and conductivity, with resulting…
Multispecies reaction-diffusion systems, for which the time evolution equation of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time…