Tetrahedron equation and the algebraic geometry
The algebraic Bethe Ansatz and vacuum vectors.
The boundary-value problem for the transport equation with purely Compton scattering.
The Dirac complex on abstract vector variables: megaforms.
The energy of heavy atoms according to Brown and Ravenhall: the Scott correction.
The essential spectrum of relativistic multi-particle operators
The essential spectrum of relativistic one-electron ions in the Jansen-Hess model.
The existence of Ginzburg-Landau solutions on the plane by a direct variational method
The Feynman path integral as an improper integral over the Sobolev space
The gaps in the spectrum of the Schrödinger operator
We obtain inequalities between the eigenvalues of the Schrödinger operator on a compact domain Ω of a submanifold M in with boundary ∂Ω, which generalize many existing inequalities for the Laplacian on a bounded domain of a Euclidean space. We also establish similar inequalities for a closed minimal submanifold in the unit sphere, which generalize and improve Yang-Yau’s result.
The Gauss center research in multiscale scientific computation.
The initial value problem of the Poincaré gauge theory in vacuum. II. First order formalism
The initial value problem of the Poincaré gauge theory in vacuum. I. Second order formalism
The level crossing problem in semi-classical analysis I. The symmetric case
We describe a microlocal normal form for a symmetric system of pseudo-differential equations whose principal symbol is a real symmetric matrix with a generic crossing of eigenvalues. We use it in order to give a precise description of the microlocal solutions.
The level crossing problem in semi-classical analysis. II. The Hermitian case
This paper is the second part of the paper ``The level crossing problem in semi-classical analysis I. The symmetric case''(Annales de l'Institut Fourier in honor of Frédéric Pham). We consider here the case where the dispersion matrix is complex Hermitian.
The magnetic Schrödinger operator and reverse Hölder class
The mathematics of large atoms
The microlocal Landau-Zener formula
The mixed regularity of electronic wave functions multiplied by explicit correlation factors
The electronic Schrödinger equation describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, three spatial dimensions for each electron. Approximating them is thus inordinately challenging. As is shown in the author's monograph [Yserentant, Lecture Notes in Mathematics 2000, Springer (2010)], the regularity of the solutions, which increases with the number of electrons,...
The mixed regularity of electronic wave functions multiplied by explicit correlation factors***
The electronic Schrödinger equation describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, three spatial dimensions for each electron. Approximating them is thus inordinately challenging. As is shown in the author's monograph [Yserentant, Lecture Notes in Mathematics2000, Springer (2010)], the regularity of the solutions, which increases with the number of electrons,...