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Single-particle resonances are crucial for exotic nuclei near and beyond the drip lines. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold becomes very important and can lead…
Quantum many-body systems in thermal equilibrium can be described by the imaginary time Green's function formalism. However, the treatment of large molecular or solid ab inito problems with a fully realistic Hamiltonian in large basis sets…
This paper aims at extending our previous work on the solution of the one-dimensional Dirac equation using the Tridiagonal Representation Approach (TRA). In the approach, we expand the spinor wavefunction in terms of suitable square…
An exact path integral treatment of a particle in a deformed radial Rosen-Morse potential is presented. For this problem with the Dirichlet boundary conditions, the Green's function is constructed in a closed form by adding to V_{q}(r) a…
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…
We derive semiclassical approximations for wavefunctions, Green's functions and expectation values for classically chaotic quantum systems. Our method consists of applying singular and regular perturbations to quantum Hamiltonians. The…
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,…
We deduce the dynamic frequency-domain-lattice Green's function of a linear chain with properties (masses and next-neighbor spring constants) of exponential spatial dependence. We analyze the system as discrete chain as well as the…
Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations…
We have employed our recently developed Green's function formalism to study the dielectric behavior of a model membrane, formed by two periodic interfaces separating two media of different dielectric constants. The Maxwell's equations are…
This is a supplementary material of our recent paper\cite{yangPRB}, where a class of exactly solvable S=1 quantum Ising spin models were studied based on the hole decomposition scheme. Here we provide some details for the Green functions,…
We determine the generating function of the harmonic oscillator by a new method. Using this generating function we derive the eigenfunctions of the moment p. We find that the normalization of these eigenfunctions is a real and not complex…
We consider a small interacting sample coupled to several non-interacting leads. Initially, the system is at thermal equilibrium. At some instant $t_0$ the system is set into the so called partition-free transport scenario by turning on a…
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…
Access to magnetic excitation spectra of single atoms deposited on surfaces is nowadays possible by means of low-temperature inelastic scanning tunneling spectroscopy. We present a first-principles method for the calculation of inelastic…
We calculate the eigenstates of a diatomic molecule in a range of model mean-field potentials, and evaluate the evolution of their associated Raman spectra with field strength. We demonstrate that dramatic changes in the appearance of the…
Neural operators, which learn mappings between the function spaces, have been applied to solve boundary value problems in various ways, including learning mappings from the space of the forcing terms to the space of the solutions with the…
Within the framework of non-relativistic quantum mechanics, the ro-vibrational energy spectra of the improved deformed exponential-type potential model are obtained using the Greene-Aldrich approximation scheme and an appropriate coordinate…
The complete system of the B-spline solutions for the Dirac equation with the parity-nonconserving (PNC) weak interaction effective potential is obtained. This system can be used for the accurate evaluation of the radiative corrections to…
We present the multi-channel Dyson equation that combines two or more many-body Green's functions to describe the electronic structure of materials. In this work we use it to model photoemission spectra by coupling the one-body Green's…