On higher order estimates in quantum electrodynamics.
On quantum weyl algebras and generalized quons
The model of generalized quons is described in an algebraic way as certain quasiparticle states with statistics determined by a commutation factor on an abelian group. Quantization is described in terms of quantum Weyl algebras. The corresponding commutation relations and scalar product are also given.
On recurrence relations for radial wave functions for the -th dimensional oscillators and hydrogenlike atoms: analytical and numerical study.
On representations of Lie algebras of a generalized Tavis-Cummings model.
On rotation and vibration motions of molecules
On some periodic Hartree-type models for crystals
On the classical non-integrability of the Hamiltonian system for hydrogen atoms in crossed electric and magnetic fields
Hydrogen atoms placed in external fields serve as a paradigm of a strongly coupled multidimensional Hamiltonian system. This system has been already very extensively studied, using experimental measurements and a wealth of theoretical methods. In this work, we apply the Morales-Ramis theory of non-integrability of Hamiltonian systems to the case of the hydrogen atom in perpendicular (crossed) static electric and magnetic uniform fields.
On the classification of the Lie algebras .
On the current of large atoms in strong magnetic fields
In this talk I will discuss recent results on the magnetisation/current of large atoms in strong magnetic fields. It is known from the work (E. Lieb, J.P. Solovej, and J. Yngvason, “Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions”, Commun. Math. Phys. (1994), no. 161, 77-124) of Lieb, Solovej and Yngvason that the energy and density of atoms in strong magnetic fields are given to highest order by a Magnetic Thomas Fermi theory (MTF-theory) when the magnetic field strength...
On the degenerate multiplicity of the loop algebra for the 6V transfer matrix at roots of unity.
On the essential spectrum of the Jansen-Hess operator for two-electron ions.
On the Hawking wormhole horizon entropy.
On the infrared problem in a model of scalar electrons and massless, scalar bosons
On the Klainerman–Machedon conjecture for the quantum BBGKY hierarchy with self-interaction
We consider the 3D quantum BBGKY hierarchy which corresponds to the -particle Schrödinger equation. We assume the pair interaction is . For the interaction parameter , we prove that, provided an energy bound holds for solutions to the BBKGY hierarchy, the limit points satisfy the space-time bound conjectured by S. Klainerman and M. Machedon [45] in 2008. The energy bound was proven to hold for in [28]. This allows, in the case , for the application of the Klainerman–Machedon uniqueness theorem...
On the leading correction of the Thomas-Fermi model: Lower bound.
On the point limit of the Pauli-Fierz model
On the quantal nature of the Coulomb field
It is shown that the total electric charge, as determined from the Gauss law, is a quantum object. The argument is based on elementary considerations concerning the number of photons, which should be large in a classical situation.
On the thermodynamic limit for Hartree–Fock type models
Operator gauge symmetry in QED.
Orbital stability of standing waves for a class of Schrödinger equations with unbounded potential.