Related papers: On the Green's function and iterative solutions of…
With resonances treated as eigenstates of a non-Hermitian quantum Hamiltonian, the task of localization of the complex energy eigenvalues is considered. The paper is devoted to the reduced version of this task in which one only computes the…
Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several conceptual and technical difficulties…
Following the introduction of the invariant distance on the non-commutative C-algebra of the quantum group SU_q(2), the Green function and the Kernel on the q-homogeneous space M=SU(2)_q/U(1) are derived. A path integration is formulated.…
Loop quantum gravity is a mature theory. To proceed to explicit calculations in cosmology, it is necessary to make assumptions and simplifications based on the symmetries of the cosmological setting. Symmetry reduction is especially…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
We introduce a classical fractional particle model in $\mathbb{R}^{n}$, extending the Newtonian particle concept with the incorporation of the fractional Laplacian. A comprehensive discussion on kinetic properties, including linear momentum…
The spectral properties of the quantum mechanical system consisting of a quantum dot with a short-range attractive impurity inside the dot are investigated in the zero-range limit. The Green function of the system is obtained in an explicit…
The $\beta\gamma$ system is generalized by complex(rational) powers of the fields, which leads to a corresponding extension on the Fock space. Two different approaches to compute the Green functions of the physical operators are proposed.…
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…
A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schroedinger equation. Specially a new expression of the perturbed energy is…
A method is given to obtain the Green's function for the Poisson equation in any arbitrary integer dimension under periodic boundary conditions. We obtain recursion relations which relate the solution in d-dimensional space to that in…
After introducing the basic ingredients of Loop Quantum Cosmology, I will briefly discuss some of its phenomenological aspects. Those can give some useful insight about the full Loop Quantum Gravity theory and provide an answer to some…
In this work, we present a new result which concerns the derivation of the Green function relative to the time-independent Schrodinger equation in two dimensional space. The system considered in this work is a quantum particle that have an…
We present a method to compute the many-body real-time Green's function using an adaptive variational quantum dynamics simulation approach. The real-time Green's function involves the time evolution of a quantum state with one additional…
Let $L$ be a second-order, homogeneous, constant (complex) coefficient elliptic system in ${\mathbb{R}}^n$. The goal of this article is provide a qualitative and quantitative study of the nature of the Green function associated with the…
A modification of the spiked harmonic oscillator is studied in the case for which the perturbation potential contains both an inverse power and a linear term. It is then possible to evaluate trial functions by solving an integral equation…
In this article, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: Firstly, we…
A relativistic Green function approach to the inclusive quasielastic (e,e') scattering is presented. The single particle Green function is expanded in terms of the eigenfunctions of the nonhermitian optical potential. This allows one to…
The \textsc{Greens} library is presented which provides a set of C++ procedures for the computation of the (radial) Coulomb wave and Green's functions. Both, the nonrelativistic as well as relativistic representations of these functions are…
We relate topological properties of non-Hermitian systems and observables of quantum open systems by using the Keldysh path-integral method. We express Keldysh Green's functions in terms of effective non-Hermitian Hamiltonians that contain…