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The analytical solution of neutron transport equation has fascinated mathematicians and physicists alike since the Milne half-space problem was introduce in 1921 [1]. Numerous numerical solutions exist, but understandably, there are only a…

The linear Boltzmann equation with constant coefficients in the three-dimensional infinite space is revisited. It is known that the Green's function can be calculated via the Fourier transform in the case of isotropic scattering. In this…

A Green's function approach to the inclusive quasielastic ($e,e'$) scattering is presented. The components of the nuclear response are written in terms of the single-particle optical model Green's function. The explicit calculation of the…

In non-classical linear transport the chord length distribution between collisions is non-exponential and attenuation does not respect Beer's law. Generalized radiative transfer (GRT) extends the classical theory to account for such…

We present a proof of an exact equivalence of the two approaches that are most used in computing conductance in quantum electron and phonon transport: the wave function matching and Green's functions methods. We can obtain all the…

A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of…

The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then,…

We investigate transport properties of gate-all-around Si nanowires using non-equilibrium Green's function technique. By taking into account of the ionized impurity scattering we calculate Green's functions self-consistently and examine the…

A new expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is…

We generalize the representation of the real time Green's functions introduced by Langreth and Nordlander [Phys. Rev. B 43 2541 (1991)] and Meir and Wingreen [Phys. Rev. Lett. 68 2512 (1992)] in stationary quantum transport in order to…

This review is devoted to the different techniques that have been developed to compute the phase-coherent transport properties of quantum nanoelectronic systems connected to electrodes. Beside a review of the different algorithms proposed…

Here, we are concerned with a new, highly precise, numerical solution to the 1D neutron transport equation based on Cases analytical singular eigenfunction expansion (SEE). While a considerable number numerical solutions currently exist,…

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…

A quantum transport model incorporating spin scattering processes is presented using the non-equilibrium Green's function (NEGF) formalism within the self-consistent Born approximation. This model offers a unified approach by capturing the…

A relativistic Green's function approach to inclusive quasielastic charged-current neutrino-nucleus scattering is developed. The components of the hadron tensor are written in terms of the single-particle Green's function, which is expanded…

We develop a formalism for the evaluation of conduction eigenchannels of atomic-sized contacts from first-principles. The multiple scattering Korringa-Kohn-Rostoker (KKR) Green's function method is combined with the Kubo linear response…

Electrical transport in semiconductor superlattices is studied within a fully self-consistent quantum transport model based on nonequilibrium Green functions, including phonon and impurity scattering. We compute both the drift…

The properties of symmetric nuclear matter are investigated within the Green's functions approach. We have implemented an iterative procedure allowing for a self-consistent evaluation of the single-particle and two-particle propagators. The…

The nonequilibrium Green's function (NEGF) method is often used to predict transport in atomistically resolved nanodevices and yields an immense numerical load when inelastic scattering on phonons is included. To ease this load, this work…

An eigenfunction expansion method involving hypergeometric functions is used to solve the partial differential equation governing the transport of radiation in an X-ray pulsar accretion column containing a radiative shock. The procedure…