10 citations · 20 across the 7 of their papers we have counts for
7 papers
Approximating the ground state eigenvalue via the effective potential
Ilias Chenn, Wei Wang, Shiwen Zhang
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…
On a Novel Effective Equation of the Reduced Hartree-Fock Theory
Ilias Chenn, Svitlana Mayboroda, Wei Wang +1
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 te…
On the Reduced Hartree-Fock Equations with a Small Anderson Type Background Charge Distribution
Ilias Chenn, Shiwen Zhang
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 s…
Vortex Lattices and the Bogoliubov-De Gennes Equations
Ilias, Chenn, Israel Michael Sigal
We consider the Bogoliubov-de Gennes equations giving an equivalent formulation of the BCS theory of superconductivity. We are interested in static solutions with the magnetic fiel…
On Derivation of the Poisson-Boltzmann Equation
Ilias, Chenn, Israel Michael Sigal
Starting from the microscopic reduced Hartree-Fock equation, we derive the nanoscopic linearized Poisson-Boltzmann equation for the electrostatic potential associated with the elec…
On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations
Li Chen, Panayotis Smyrnelis, Israel Michael Sigal
We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations of superconductivity, with multiple magnetic flux quanta per a fundamental cell. We also r…
On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations
T. Tzaneteas, I. M. Sigal
Building on earlier work, we have given in our paper in Contemporary Mathematics 535, 195-213, 2011 (referred here as [TS]) a proof of existence of Abrikosov vortex lattices in the…