A quantum mechanical equation H Ψ= E Ψ is composed of three components, viz.,
Hamiltonian H, wave function Ψ, and property E (λ), each of which is confronted with …

This review is devoted to the study of stationary solutions of linear and nonlinear equations
from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as …

While the classification of noninteracting crystalline topological insulator phases by
equivariant K-theory has become widely accepted, its generalization to anyonic interacting …

We show local and global well-posedness results for the Hartree equation i\partial_t γ=-Δ+
w*\rho_ γ, γ, i∂ t γ=-Δ+ w∗ ρ γ, γ, where γ is a bounded self-adjoint operator on L^ 2 (R^ d) …

This article is concerned with the derivation and the mathematical study of a new mean-field
model for the description of interacting electrons in crystals with local defects. We work with …

This paper, devoted to the study of spectral pollution, contains both abstract results and
applications to some self-adjoint operators with a gap in their essential spectrum, occurring …

This book is devoted to explaining how the causal action principle gives rise to the
interactions of the standard model plus gravity on the level of second-quantized fermionic …

We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting
from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical …

Hartree--Fock theory in quantum mechanics is reviewed, from the proposal of the Hartree--
Fock approximation right after quantum mechanics was formulated to its applications in …

We consider the nonlinear Hartree equation for an interacting gas containing infinitely many
particles and we investigate the large-time stability of the stationary states of the form f (− Δ) …