Related papers: On the Green's Function of the almost-Mathieu Oper…
The scattering of a wave obeying Helmholtz equation by an elliptic obstacle can be described exactly using series of Mathieu functions. This situation is relevant in optics, quantum mechanics and fluid dynamics. We focus on the case when…
Green's functions are highly useful in analyzing the dynamical behavior of polynomials in their escaping set. The aim of this paper is to construct an analogue of Green's functions for planar quasiregular mappings of degree two and constant…
We derive the quantum Boltzmann equation (QBE) of composite fermions at/near the $\nu = 1/2$ state using the non-equilibrium Green's function technique. The lowest order perturbative correction to the self-energy due to the strong gauge…
A new approach proposed recently by author for the calculation of Green functions in quantum field theory and quantum mechanics is briefly reviewed. The method is applied to nonperturbative calculations for anharmonic oscillator,…
In this work we calculate the exact Green's function for arbitrary rectangular potentials. Specifically we focus on Green's function for rectangular quantum wells enlarging the knowledge of exact solutions for Green's functions and also…
We derive explicit representation formulae of Green functions for GJMS operators on $n$-spheres, including the fractional ones. These formulae have natural geometric interpretations concerning the extrinsic geometry of the round sphere.…
We study energy functionals associated with quasi-linear Schr\"odinger operators on infinite graphs, and develop characterisations of (sub-)criticality via Green's functions, harmonic functions of minimal growth and capacities. We proof a…
We define a Schr\"odinger operator on the half-space with a discontinuous magnetic field having a piecewise-constant strength and a uniform direction. Motivated by applications in the theory of superconductivity, we study the infimum of the…
We derive equations for the quasiclassical Green's functions $\check{g}$ within a simple model of a two-band superconductor with a spin-density-wave (SDW). The elements of the matrix $\check{g}$ are the retarded, advanced, and Keldysh…
We study semi-martingale obliquely reflected Brownian motion with drift in the first quadrant of the plane in the transient case. Our main result determines a general explicit integral expression for the moment generating function of…
Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multi-orbital systems, these quantities are related to positive semidefinite matrix-valued functions of the…
The correlation spectrum of fully developed one-dimensional mappings are studied near and at a weakly intermittent situation. Using a suitable infinite matrix representation, the eigenvalue equation of the Frobenius-Perron operator is…
The inverse of an $\infty \times \infty$ symmetric band matrix can be constructed in terms of a matrix continued fraction. For Hamiltonians with Coulomb plus polynomial potentials, this results in an exact and analytic Green's operator…
Employing the self-consistent Green's function approach, we studied the temperature dependence of the spin-wave stiffness in diluted magnetic semiconductors. Note that the Green's function approach includes the spatial and temperature…
Exact solutions of Schroedinger and Pauli equations for charged particles in an external stationary electromagnetic field of an arbitrary configuration are constructed. Green functions of scalar and spinor particles are calculated in this…
We developed a set of equations to calculate the electronic Green's functions in a T-shaped multi-quantum dot system using the equation of motion method. We model the system using a generalized Anderson Hamiltonian which accounts for {\em…
A charged particle in a magnetic field possesses discrete energy levels associated with particle rotation around the field lines. A bound complex of particles with a nonzero net charge possesses an analogous levels associated with its…
Nonequilibrium Green's functions provide a powerful tool for computing the dynamical response and particle exchange statistics of coupled quantum systems. We formulate the theory in terms of the density matrix in Liouville space and…
The magnetoelectronic properties of quasi-one-dimensional zigzag graphene nanoribbons are investigated by using the Peierls tight-binding model. Quasi-Landau levels (QLLs), dispersionless Landau subbands within a certain region of k-space,…
A numerical method is developed for calculating the real time Green's functions of very large sparse Hamiltonian matrices, which exploits the numerical solution of the inhomogeneous time-dependent Schroedinger equation. The method has a…