On the essential spectrum of the Jansen-Hess operator for two-electron ions.
On the factorization criterion for quantum statistics
On the heat trace of the magnetic Schrödinger operators on the hyperbolic plane.
On the nonrelativistic limit of the Dirac hamiltonian
On the number of bound states of a bosonic N-particle Coulomb system.
On the role of the normalization factors and of the pseudo-metric in crypto-Hermitian quantum models.
On the singular spectrum for adiabatic quasiperiodic Schrödinger operators.
On the spectrum and eigenfunctions of the Schrödinger operator with Aharonov–Bohm magnetic field.
On the spectrum of a discrete non-Hermitian quantum system.
On the spectrum of Robin Laplacian in a planar waveguide
We consider the Laplace operator in a planar waveguide, i.e. an infinite two-dimensional straight strip of constant width, with Robin boundary conditions. We study the essential spectrum of the corresponding Laplacian when the boundary coupling function has a limit at infinity. Furthermore, we derive sufficient conditions for the existence of discrete spectrum.
On Threshold Eigenvalues and Resonances for the Linearized NLS Equation
We prove the instability of threshold resonances and eigenvalues of the linearized NLS operator. We compute the asymptotic approximations of the eigenvalues appearing from the endpoint singularities in terms of the perturbations applied to the original NLS equation. Our method involves such techniques as the Birman-Schwinger principle and the Feshbach map.
On wave functions in quantum mechanics
On wave functions in quantum mechanics. Part 3. A theory of quantum mechanics where wave functions are defined by means of surely fundamental observables
Opérateurs de Schrödinger avec champs magnétiques faibles et constants
Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups
We present an interacting particle system methodology for the numerical solving of the Lyapunov exponent of Feynman–Kac semigroups and for estimating the principal eigenvalue of Schrödinger generators. The continuous or discrete time models studied in this work consists of interacting particles evolving in an environment with soft obstacles related to a potential function . These models are related to genetic algorithms and Moran type particle schemes. Their choice is not unique. We will examine...
Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups
We present an interacting particle system methodology for the numerical solving of the Lyapunov exponent of Feynman–Kac semigroups and for estimating the principal eigenvalue of Schrödinger generators. The continuous or discrete time models studied in this work consists of N interacting particles evolving in an environment with soft obstacles related to a potential function V. These models are related to genetic algorithms and Moran type particle schemes. Their choice is not unique. We...
Periodic Schrödinger Operators with Constant Weak Magnetic Fields
Perturbation of an eigen-value from a dense point spectrum : a general Floquet hamiltonian
Planarizable supersymmetric quantum toboggans.
Polynomial boundedness of eigensolutions and the spectrum of Schrödinger operators.