Related papers: On the Green's function and iterative solutions of…
By using the generating function formula for the product of two q-Hermite polynomials q-deformation of the Feynman Green function for the harmonic oscillator is obtained.
The solution of some equations involving functional derivatives is given as a series indexed by planar binary trees. The terms of the series are given by an explicit recursive formula. Some algebraic properties of these series are…
A state-preserving quantum counting algorithm is used to obtain coefficients of a Lanczos recursion from a single ground state wavefunction on the quantum computer. This is used to compute the continued fraction representation of an…
Loop quantum gravity and cosmology are reviewed with an emphasis on evaluating the dynamics, rather than constructing it. The three crucial parts of such an analysis are (i) deriving effective equations, (ii) controlling the theory's…
Response functions are a fundamental aspect of physics; they represent the link between experimental observations and the underlying quantum many-body state. However, this link is often under-appreciated, as the Lehmann formalism for…
In this paper, the Green's function and decomposition technique is proposed for solving the coupled Lane-Emden equations. This approach depends on constructing Green's function before establishing the recursive scheme for the series…
In this paper, we present a quantum computational method to calculate the many-body Green's function matrix in a spin orbital basis. We apply our approach to finite-sized fermionic Hubbard models and related impurity models within Dynamical…
After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop quantum cosmology, and a computation of…
We compute the Green's function for the Hodge Laplacian on the symmetric spaces M\times\Sigma, where M is a simply connected n-dimensional Riemannian or Lorentzian manifold of constant curvature and \Sigma is a simply connected Riemannian…
If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Green's operator can be constructed in terms of a continued fraction. As an…
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…
We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain $\Omega \subseteq \mathbb{R}^n$, $n \geq 3$, under the assumption that…
In loop quantum cosmology, non-perturbative quantum gravity effects lead to the resolution of the big bang singularity by a quantum bounce without introducing any new degrees of freedom. Though fundamentally discrete, the theory admits a…
We discuss similarities and differences between Green Functions in Quantum Field Theory and polylogarithms. Both can be obtained as solutions of fixpoint equations which originate from an underlying Hopf algebra structure. Typically, the…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…
Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain simple representations for the Green's function of the Dirac-Oscillator and Dirac-Coulomb problems. This is accomplished…
We show that the Green's functions in non-linear gauge in the theory of perturbative quantum gravity is expressed as a series in terms of those in linear gauges. This formulation is also holds for operator Green's functions. We further…
Accurate modeling of the electronic structure of warm dense matter is a challenging problem whose solution would allow a better understanding of material properties like equation of state, opacity, and conductivity, with resulting…
In this work we revise the most recent developments concerning the study of first order problems regarding differential equations with involutions. We take into account two cases: the case of initial conditions and constant coefficients and…
We present a quantum-classical hybrid implementation of the Liouvillian recursion method to compute many-body Green's functions using a quantum computer. From an approximate ground state preparation circuit, this algorithm produces the…