Related papers: Formal and Precise Derivation of the Green Functio…
The functional integral method can be used in quantum mechanics to find the scattering amplitude for particles in the external field. We will obtain the potential scattering amplitude form the complete Green function in the corresponding…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
We present a spectral weight conserving formalism for Fermionic thermal Green's functions that are discretized in imaginary time and thus periodic in imaginary ("Matsubara") frequency. The formalism requires a generalization of the Dyson…
In this paper, we employ the generalized Bloch theory to rediscover the generalized Brillouin zone theory and follow this way to obtain the Green's function of the non-Hermitian system. We focus on a classical chiral model and give the…
We consider thermal $n$-point Green functions in the framework of quantum field theory at finite temperature. We show how analytic continuations from imaginary to real energies relate these functions originally defined in the imaginary-time…
Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…
In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are…
We revisit the volume Green's function integral equation for modelling light scattering with discretization strategies as well as numerical integration recipes borrowed from finite element method. The merits of introducing finite element…
A method for the computation of scattering data and of the Green function for the one-dimensional Schr\"{o}dinger operator $H:=-\frac{d^2}{dx^2}+q(x)$ with a decaying potential is presented. It is based on representations for the Jost…
The irregular solutions of the stationary Schr\"odinger equation are important for the fundamental formal development of scattering theory. They are also necessary for the analytical properties of the Green function, which in practice can…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…
The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…
The scattering theory of electron transport allows for a compact and powerful description in terms of $\check{g}^2 = 1$ Green functions, so-called circuit theory of quantum transport. A scatterer in the theory is characterized by an action,…
We investigate scalar and spinor field theories in a constant magnetic field at finite temperature and chemical potential. In an external constant magnetic field the exact solution of the two-point Green functions are obtained by using the…
We formulate the dynamical mean field theory directly in the continuum. For a given definition of the local Green's function, we show the existence of a unique functional, whose stationary point gives the physical local Green's function of…
This article is concerned with a mathematical tool, the Associated Transfer Matrix T, which proves useful in the study of a wide class of physical problems involving multilayer heterostructures. General properties of linear, second order…
We consider a scattering problem generated by the Sturm-Liouville equation on a tree which consists of a equilateral compact subtree with a lead (a half-infinite edge) attached to this compact subtree. We assume that the potential on the…
In this paper, we give a simple diagrammatic identification of the unique combination of the causal n-point vertex functions in the real time formalism that would coincide with the corresponding functions obtained in the imaginary time…
A first-principles derivation is given of the imaginary part of a Green's function in real-time thermal field theory. The analysis and its conclusions are simpler than in the usual circled-vertex formalism. The relationship to Cutkosky-like…
We introduce the Green's functions technique as an alternative theory to the quantum regression theorem formalism for calculating the two-time correlation functions in open quantum systems. In particular, we investigate the potential of…