On the factorization criterion for quantum statistics
On the Fröhlich-Spencer-Estimate in the theory of anderson localization.
On the global Cauchy problem for some non linear Schrödinger equations
On the heat trace of the magnetic Schrödinger operators on the hyperbolic plane.
On the Index of Callias-type Operators.
On the large order asymptotics of general states in semiclassical quantum mechanics
On the nonrelativistic limit of the Dirac hamiltonian
On the number of bound states of a bosonic N-particle Coulomb system.
On the relative fundamental solutions for a second order differential operator on the Heisenberg group
Let Hₙ be the (2n+1)-dimensional Heisenberg group, let p,q ≥ 1 be integers satisfying p+q=n, and let , where X₁,Y₁,...,Xₙ,Yₙ,T denotes the standard basis of the Lie algebra of Hₙ. We compute explicitly a relative fundamental solution for L.
On the relativistic calculation of the Lamb shift
A relativistic calculation of the Lamb shift, using the classical field created by the Dirac transition currents, is proposed.
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,...