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...
Perturbation of an eigen-value from a dense point spectrum : a general Floquet hamiltonian
Perturbative expansions in quantum mechanics
We prove a analytic versal deformation theorem in the Heisenberg algebra. We define the spectrum of an element in the Heisenberg algebra. The quantised version of the Morse lemma already shows that the perturbation series arising in a perturbed harmonic oscillator become analytic after a formal Borel transform.
Perturbative treatment of the evolution operator associated with Raman couplings.
Planar binary trees and perturbative calculus of observables in classical field theory
Planarizable supersymmetric quantum toboggans.
Point canonical transformation versus deformed shape invariance for position-dependent mass Schrödinger equations.
Points tournants et résonances de Stark-Wannier
Pointwise bounds on the asymptotics of spherically averaged -solutions of one-body Schrödinger equations
Polynomial boundedness of eigensolutions and the spectrum of Schrödinger operators.
Positivity of Lyapunov exponents for Anderson-type models on two coupled strings.
Preuve de la conjecture de Lieb-Thirring dans le cas des potentiels quadratiques strictement convexes
Problème de Cauchy global pour des systèmes de Dirac-Klein-Gordon
Problème spectral de Sturm-Liouville : le cas de l'oscillateur quartique
Proof of a conjecture about atomic and molecular cores related to Scott's correction.
Proof of the ionization conjecture in a reduced Hartree-Fock model.