A note concerning the "Feynman integrability" of sets of trajectories
A numerically efficient approach to the modelling of double-Qdot channels
We consider the electronic properties of a system consisting of two quantum dots in physical proximity, which we will refer to as the double-Qdot. Double-Qdots are attractive in light of their potential application to spin-based quantum computing and other electronic applications, e.g. as specialized sensors. Our main goal is to derive the essential properties of the double-Qdot from a model that is rigorous yet numerically tractable, and largely circumvents the complexities of an ab initio simulation....
A polynomial invariant of rational homology 3-spheres.
A possible approach to inclusion of space and time in frame fields of quantum representations of real and complex numbers.
A Pseudo-Algebra of Observables for the Dirac Equation.
A quantum field theoretical representation of Euler-Zagier sums.
A quantum particle in a quadrupole radio-frequency trap
A result about imbedded eigenvalues in the operator valued Friedrichs model
A trace formula for resonances and application to semi-classical Schrödinger operators
On décrit une formule de trace [S] pour les résonances, qui est valable en toute dimension et pour les perturbations à longue portée du Laplacien. On établit une nouvelle application à l’éxistence de nombreuses résonances pour des opérateurs de Schrödinger semi-classiques.
A Two-Particle Quantum System with Zero-Range Interaction
We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.
About poles of the resolvent, in a model for a harmonic oscillator coupled with massless scalar bosons
absence de résonance près du réel pour l’opérateur de Schrödinger
On donne dans cet exposé des bornes inférieures universelles, en limite semiclassique, de la hauteur des résonances de forme associées aux opérateurs de Schrödinger à l’extérieur d’obstacles avec des conditions au bord de Dirichlet ou de Neumann et des potentiels analytiquement dilatables et tendant vers à l’infini. Ces bornes inférieures sont exponentiellement petites par rapport à la constante de Planck.
Absence of geometrical phases in the rotating stark effect
Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others.
Acceleration of material waves in Fermi accelerator.
Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian
Motivated by the theory of superconductivity and more precisely by the problem of the onset of superconductivity in dimension two, many papers devoted to the analysis in a semi-classical regime of the lowest eigenvalue of the Schrödinger operator with magnetic field have appeared recently. Here we would like to mention the works by Bernoff-Sternberg, Lu-Pan, Del Pino-Felmer-Sternberg and Helffer-Morame and also Bauman-Phillips-Tang for the case of a disc. In the present paper we settle one important...
Accurate WKB Approximation for a 1D Problem with Low Regularity
2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20.This article is concerned with the analysis of the WKB expansion in a classically forbidden region for a one dimensional boundary value Schrodinger equation with a non smooth potential. The assumed regularity of the potential is the one coming from a non linear problem and seems to be the critical one for which a good exponential decay estimate can be proved for the first remainder term. The treatment of the boundary conditions brings...
Addendum to “Curves of maximum modulus in coherent state representations”
Adiabatic Evolution of Coupled Waves for a Schrödinger-Korteweg-de Vries System
The effective dynamics of interacting waves for coupled Schrödinger-Korteweg-de Vries equations over a slowly varying random bottom is rigorously studied. One motivation for studying such a system is better understanding the unidirectional motion of interacting surface and internal waves for a fluid system that is formed of two immiscible layers. It was shown recently by Craig-Guyenne-Sulem [1] that in the regime where the internal wave has a large...
Adiabatic expansion approximation solutions for the three-body problem.