Distributional asymptotic expansions of spectral functions and of the associated Green kernels.
Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator
We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable along the magnetic...
Eigenfunction expansions of functions describing systems with symmetries.
Eigenvalue asymptotics for the Pauli operator in strong nonconstant magnetic fields
We consider the Pauli operator selfadjoint in , . Here , , are the Pauli matrices, is the magnetic potential, is the coupling constant, and is the electric potential which decays at infinity. We suppose that the magnetic field generated by satisfies some regularity conditions; in particular, its norm is lower-bounded by a positive constant, and, in the case , its direction is constant. We investigate the asymptotic behaviour as of the number of the eigenvalues of smaller than...
Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian.
Embedded eigenvalues and resonances of Schrödinger operators with two channels
In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.
Équation de Schrödinger magnétique périodique avec symétrie d'ordre six : mesure du spectre II
Erratum to “Non-trapping condition for semiclassical Schrödinger operators with matrix-valued potentials”.
Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds
We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [29,30,31], a shorter and more transparent proof of which was provided by the author in [41]. The main idea, as in [41], consists...
Essential selfadjointness of the Weyl quantized relativistic hamiltonian
Essential spectrum of multiparticle Brown-Ravenhall operators in external field.
Excess charge for pseudo-relativistic atoms in Hartree-Fock theory.
Exponential decay of two-body eigenfunctions: a review.
Faster than Hermitian time evolution.
Fermi Golden Rule, Feshbach Method and embedded point spectrum
A method to study the embedded point spectrum of self-adjoint operators is described. The method combines the Mourre theory and the Limiting Absorption Principle with the Feshbach Projection Method. A more complete description of this method is contained in a joint paper with V. Jakić, where it is applied to a study of embedded point spectrum of Pauli-Fierz Hamiltonians.
Ferromagnetic integrals, correlations and maximum principles
For correlations of the form (0.2) we consider a critical case and prove power decay upper bounds in terms of the fundamental solution of a certain elliptic operator. This is achieved by improving the use of a maximum principle. We also formulate a general maximum principle and give two applications.
Gaussian Decay of the Magnetic Eigenfunctions.
General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators
This paper is concerned with an extension and reinterpretation of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. We state two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then these results are applied to Dirac operators in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states.
Generalized deformed commutation relations with nonzero minimal uncertainties in position and/or momentum and applications to quantum mechanics.
Generalized Heisenberg algebras, SUSYQM and degeneracies: infinite well and Morse potential.