On diamagnetism and de Haas-van Alphen effect
On essential selfadjointness of the Weyl quantized relativistic Hamiltonian.
On higher order estimates in quantum electrodynamics.
On -accretive Schrödinger-type operators with singular potentials on manifolds of bounded geometry.
On -sectorial Schrödinger-type operators with singular potentials on manifolds of bounded geometry
We consider a Schrödinger-type differential expression , where is a -bounded Hermitian connection on a Hermitian vector bundle of bounded geometry over a manifold of bounded geometry with metric and positive -bounded measure , and is a locally integrable section of the bundle of endomorphisms of . We give a sufficient condition for -sectoriality of a realization of in . In the proof we use generalized Kato’s inequality as well as a result on the positivity of satisfying the...
On nodal sets and nodal domains on and
We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on . We also construct a solution of the equation in that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.
On nonlinear Schrödinger equations in exterior domains
On orthogonality relations for dual discrete -ultraspherical polynomials.
On phase segregation in nonlocal two-particle Hartree systems
We prove the phase segregation phenomenon to occur in the ground state solutions of an interacting system of two self-coupled repulsive Hartree equations for large nonlinear and nonlocal interactions. A self-consistent numerical investigation visualizes the approach to this segregated regime.
On quantum twist maps and spectral properties of Floquet operators
On recurrence relations for radial wave functions for the -th dimensional oscillators and hydrogenlike atoms: analytical and numerical study.
On resonant scattering for time-periodic perturbations
On some spaces of linear functionals on the algebras for locally compact groups
On Spectral Stability of Solitary Waves of Nonlinear Dirac Equation in 1D⋆⋆
We study the spectral stability of solitary wave solutions to the nonlinear Dirac equation in one dimension. We focus on the Dirac equation with cubic nonlinearity, known as the Soler model in (1+1) dimensions and also as the massive Gross-Neveu model. Presented numerical computations of the spectrum of linearization at a solitary wave show that the solitary waves are spectrally stable. We corroborate our results by finding explicit expressions for...
On the Aharonov-Casher formula for different self-adjoint extensions of the Pauli operator with singular magnetic field.
On the asymptotic properties of quantum dynamics in the presence of a fractal spectrum
On the convergence of SCF algorithms for the Hartree-Fock equations
The present work is a mathematical analysis of two algorithms, namely the Roothaan and the level-shifting algorithms, commonly used in practice to solve the Hartree-Fock equations. The level-shifting algorithm is proved to be well-posed and to converge provided the shift parameter is large enough. On the contrary, cases when the Roothaan algorithm is not well defined or fails in converging are exhibited. These mathematical results are confronted to numerical experiments performed by chemists.
On the curvature and torsion effects in one dimensional waveguides
We consider the Laplace operator in a thin tube of with a Dirichlet condition on its boundary. We study asymptotically the spectrum of such an operator as the thickness of the tube's cross section goes to zero. In particular we analyse how the energy levels depend simultaneously on the curvature of the tube's central axis and on the rotation of the cross section with respect to the Frenet frame. The main argument is a Γ-convergence theorem for a suitable sequence of quadratic energies.
On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions
This paper is intended to provide the reader with a review of the authors’ latest results dealing with the modeling of quantum dissipation/diffusion effects at the level of Schrödinger systems, in connection with the corresponding phase space and fluid formulations of such kind of phenomena, especially in what concerns the role of the Fokker–Planck mechanism in the description of open quantum systems and the macroscopic dynamics associated with some viscous hydrodynamic models of Euler and Navier–Stokes...
On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation