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An extension of the fermionic particle--particle propagator is presented, that possesses similar algebraic properties to the single--particle Green's function. In particular, this extended two--particle Green's function satisfies Dyson's…
We improve on Fourier transforms (FT) between imaginary time $\tau$ and imaginary frequency $\omega_n$ used in certain quantum cluster approaches using the Hirsch-Fye method. The asymptotic behavior of the electron Green's function can be…
A review of electronic dynamics of single-impurity and many-impurity Anderson models is contained in this report. Those models are used widely for many of the applications in diverse fields of interest, such as surface physics, theory of…
We present a Green's function formulation of the quantum defect embedding theory (QDET) where a double counting scheme is rigorously derived within the $G_0 W_0$ approximation. We then show the robustness of our methodology by applying the…
We provide an in-depth examination of the $GW$ approximation of Green's function many-body perturbation theory by detailing both its theoretical and practical aspects in the realm of quantum chemistry. First, the quasiparticle context is…
We extend the self-consistent Green's functions formalism to take into account three-body interactions. We analyze the perturbative expansion in terms of Feynman diagrams and define effective one- and two-body interactions, which allows for…
We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on $\mathbb{Z}^d$ with power-law long-range hopping and analytic cosine type potentials. As applications, we prove the arithmetic version of…
Sub-wavelength arrays of quantum emitters offer an efficient free-space approach to coherent light-matter interfacing, using ultracold atoms or two-dimensional solid-state quantum materials. The combination of collectively suppressed…
Measurable spectra are theoretically very often derived from complicated many-body Green's functions. In this way, one calculates much more information than actually needed. Here we present an in principle exact approach to construct…
We present a quantum optics theory, numerical calculations, and experiments on coupled quantumdots in semiconductor nanowire waveguides. We first present an analytical Green function theory tocompute the emitted spectra of two coupled…
We extend the recently developed Quantum Quasi-Monte Carlo (QQMC) approach to obtain the full frequency dependence of Green functions in a single calculation. QQMC is a general approach for calculating high-order perturbative expansions in…
We propose a framework to construct the ground-state energy and density matrix of an N-electron system by solving selfconsistently a set of single-particle equations. The method can be viewed as a non-trivial extension of the Kohn-Sham…
Widths of low-lying states in nuclei are of the order of 30 MeV. These large widths are a consequence of the strong interactions leading to a strongly correlated many body system at the typical densities of nuclear matter. Nevertheless…
Green's function in non-Hermitian systems has recently been revealed to be capable of directional amplification in some cases. The exact formulas for end-to-end Green's functions are significantly important for studies of both non-Hermitian…
To obtain the basis for combining various many-body techniques to QED in a consistent manner, we investigate the theory of quantum electrodynamical self-consistent fields. The reserch interest was born mainly of the electronic structure…
We investigate the influence of a time dependent, homogeneous electric field on scattering properties of non-interacting electrons in an arbitrary static potential. We develop a method to calculate the (Keldysh) Green's function in two…
Including finite-temperature effects from the electronic degrees of freedom in electronic structure calculations of semiconductors and metals is desired; however, in practice it remains exceedingly difficult when using zero-temperature…
The Koopman operator provides a linear framework to study nonlinear dynamical systems. Its spectra offer valuable insights into system dynamics, but the operator can exhibit both discrete and continuous spectra, complicating direct…
We address the problem of finding self-consistent parquet equations for two-body correlated Greens functions that arise out of a cumulant expansion. The general theory as developed for non-relativistic electron systems reproduces the…
The eigenstate thermalization hypothesis provides to date the most successful description of thermalization in isolated quantum systems by conjecturing statistical properties of matrix elements of typical operators in the (quasi-)energy…