On the role of the normalization factors and of the pseudo-metric in crypto-Hermitian quantum models.
On the semi-classical approximation of the solution of the Heisenberg equation with spin
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
Opening gaps in the spectrum of strictly ergodic Schrödinger operators
We consider Schrödinger operators with dynamically defined potentials arising from continuous sampling along orbits of strictly ergodic transformations. The Gap Labeling Theorem states that the possible gaps in the spectrum can be canonically labelled by an at most countable set defined purely in terms of the dynamics. Which labels actually appear depends on the choice of the sampling function; the missing labels are said to correspond to collapsed gaps. Here we show that for any collapsed gap,...
Opérateurs de Schrödinger avec champs magnétiques faibles et constants
Opérateurs -pseudodifférentiels à flot périodique
Oscillateur quartique et méthodes semi-classiques
Oscillations of a polarizable vacuum.
Oscillatory Integrals and the Method of Stationary Phase in Infinitely Many Dimensions, with Applications to the Classical Limit of Quantum Mechanics. I.
symmetric Schrödinger operators: reality of the perturbed eigenvalues.
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
Perron-Frobenius operators and the Klein-Gordon equation
For a smooth curve and a set in the plane , let be the space of finite Borel measures in the plane supported on , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on . Following [12], we say that is a Heisenberg uniqueness pair if . In the context of a hyperbola , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the...