arXiv subjects

Ilias Chenn

Publications and source records attributed to Ilias Chenn.

3 recordsLinked to original sources

arXiv2022

Approximating the ground state eigenvalue via the effective potential

In this paper, we study 1-d random Schrödinger operators on a finite interval with Dirichlet boundary conditions. We are interested in the approximation of the ground state energy using the minimum of the effective potential. For the 1-d continuous Anderson Bernoulli model, we show that the ratio of the ground state energy and the minimum of the effective potential approaches $\frac{π^2}{8}$ as the domain size approaches infinity. Besides, we will discuss various approximations to the ratio in different situations. There will be numerical experiments supporting our main results for the ground state energy and also supporting approximations for the excited states energies.

math.SP↗

arXiv2022

On the Reduced Hartree-Fock Equations with a Small Anderson Type Background Charge Distribution

We demonstrate that the reduced Hartree-Fock equation (REHF) with a small Anderson type background charge distribution has an unique stationary solution by explicitly computing a screening mass at positive temperature.

math-ph↗

arXiv2021

On a Novel Effective Equation of the Reduced Hartree-Fock Theory

We show that there is an one-to-one correspondence between solutions to the Poisson-Landscape equations and the reduced Hartree-Fock equations in the semi-classical limit at low temperature. Moreover, we prove that the difference between the two corresponding solutions is small by providing explicit estimates.

math.AP↗