Related papers: Exact solution for the Green's function describing…
We derive an alternative representation for the $f$-electron spectral function of the Falicov-Kimball model from the original one proposed by Brandt and Urbanek. In the new representation, all calculations are restricted to the real time…
We study many-particle phenomena of propagating multi-mode photons and phonons interacting through Brillouin scattering-type Hamiltonian in nanoscale waveguides. We derive photon and phonon retarded Green's functions and extract their…
Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time dependent Schr\"odinger equation is an important and challenging problem in quantum mechanics and…
We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
The interaction of electrons with quantized phonons and photons underlies the ultrafast dynamics of systems ranging from molecules to solids, and it gives rise to a plethora of physical phenomena experimentally accessible using…
Our purpose in this study was to present an integral-transform approach to the analytical solutions of the Pennes's bioheat transfer equation and to apply it to the calculation of temperature distribution in tissues in hyperthermia with…
Using Wigner transforms of Green functions, we discuss non-equilibrium generalizations of spectral functions and occupation numbers. We develop methods for computing time-dependent spectral functions in conformal field theories…
Comptonization is the process in which photon spectrum changes due to multiple Compton scatterings in the electronic plasma. It plays an important role in the spectral formation of astrophysical X-ray and gamma-ray sources. There are…
We present a time-linear scaling method to simulate open and correlated quantum systems out of equilibrium. The method inherits from many-body perturbation theory the possibility to choose selectively the most relevant scattering processes…
A propagator for the one dimensional time-dependent Schr\"odinger equation with an asymmetric rectangular potential is obtained using the multiple-scattering theory approach. It allows for the consideration of the reflection and…
We formulate and analyze difference equations on graphs analogous to time-independent diffusion equations arising in the study of diffuse scattering in continuous media. Moreover, we show how to construct solutions in the presence of weak…
We show that the Green's function of a two dimensional fermion with a modified dispersion relation and short distance parameter $a$ is given by the Lerch zeta function. The Green's function is defined on a cylinder of radius R and we show…
We study the Wouthuysen-Field coupling at early universe with numerical solutions of the integrodifferential equation describing the kinetics of photons undergoing resonant scattering. The numerical solver is developed based on the weighted…
We propose integral representations and analytical solutions for the propagator of the $1+1$ dimensional Salpeter Hamiltonian, describing a relativistic quantum particle with no spin. We explore the exact Green function and an exact…
We present a new charge self-consistent scheme combining Density Functional and Dynamical Mean Field Theory, which uses Green's function of multiple scattering-type. In this implementation the many-body effects are incorporated into the…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…
The standard solution to time-harmonic electromagnetic scattering problems in homogeneous layered media relies on the use of the electric field dyadic Green's function. However, for small values of the governing angular frequency $\omega$,…
We consider an active Brownian particle in a $d$-dimensional harmonic trap, in the presence of translational diffusion. While the Fokker-Planck equation can not in general be solved to obtain a closed form solution of the joint distribution…
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…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…