H2 molecule in strong magnetic fields

The Pauli-Hamiltonian of a molecule with fixed nuclei in a strong constant magnetic field is asymptotic, in norm-resolvent sense, to an effective Hamiltonian which has the form of a multi-particle Schr\"odinger operator with interactions given by one-dimensional \delta-potentials. We study this effective Hamiltonian in the case of the H2 -molecule and establish existence of the ground state. We also show that the inter-nuclear equilibrium distance tends to 0 as the field-strength tends to infinity

Spectral fluctuations of Schr\"odinger operators generated by critical points of the potential

Starting from the spectrum of Schr\"odinger operators on $\mathbb{R}^n$, we propose a method to detect critical points of the potential. We argue semi-classically on the basis of a mathematically rigorous version of Gutzwiller's trace formula which expresses spectral statistics in term of classical orbits. A critical point of the potential with zero momentum is an equilibrium of the flow and generates certain singularities in the spectrum. Via sharp spectral estimates, this fluctuation indicates the presence of a critical point and allows to reconstruct partially the local shape of the potential. Some generalizations of this approach are also proposed.\medskip keywords : Semi-classical analysis; Schr\"odinger operators; Equilibriums in classical mechanics.Comment: 18 pages, Final versio

The Atomic Slide Puzzle: Self-Diffusion of an Impure Atom

In a series of recent papers van Gastel et al have presented first experimental evidence that impure, Indium atoms, embedded into the first layer of a Cu(001) surface, are not localized within the close-packed surface layers but make concerted, long excursions visualized in a series of STM images. Such excursions occur due to continuous reshuffling of the surface following the position exchanges of both impure and host atoms with the naturally occuring surface vacancies. Van Gastel et al have also formulated an original lattice-gas type model with asymmetric exchange probabilities, whose numerical solution is in a good agreement with the experimental data. In this paper we propose an exact lattice solution of several versions of this model.Comment: Latex, 4 pages, 2 figures, to appear in Phys. Rev. E (RC

Quantum ergodicity for Pauli Hamiltonians with spin 1/2

Quantum ergodicity, which expresses the semiclassical convergence of almost all expectation values of observables in eigenstates of the quantum Hamiltonian to the corresponding classical microcanonical average, is proven for non-relativistic quantum particles with spin 1/2. It is shown that quantum ergodicity holds, if a suitable combination of the classical translational dynamics and the spin dynamics along the trajectories of the translational motion is ergodic.Comment: 20 pages, no figure

Nothing moves a surface: vacancy mediated surface diffusion

We report scanning tunneling microscopy observations, which imply that all atoms in a close-packed copper surface move frequently, even at room temperature. Using a low density of embedded indium `tracer' atoms, we visualize the diffusive motion of surface atoms. Surprisingly, the indium atoms seem to make concerted, long jumps. Responsible for this motion is an ultra-low density of surface vacancies, diffusing rapidly within the surface. This interpretation is supported by a detailed analysis of the displacement distribution of the indium atoms, which reveals a shape characteristic for the vacancy mediated diffusion mechanism that we propose.Comment: 4 pages; for associated movie, see http://www-lion.leidenuniv.nl/sections/cm/groups/interface/projects/therm

On a semiclassical formula for non-diagonal matrix elements

Let $H(\hbar)=-\hbar^2d^2/dx^2+V(x)$ be a Schr\"odinger operator on the real line, $W(x)$ be a bounded observable depending only on the coordinate and $k$ be a fixed integer. Suppose that an energy level $E$ intersects the potential $V(x)$ in exactly two turning points and lies below $V_\infty=\liminf_{|x|\to\infty} V(x)$. We consider the semiclassical limit $n\to\infty$, $\hbar=\hbar_n\to0$ and $E_n=E$ where $E_n$ is the $n$th eigen-energy of $H(\hbar)$. An asymptotic formula for $$, the non-diagonal matrix elements of $W(x)$ in the eigenbasis of $H(\hbar)$, has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.Comment: LaTeX2

A One-Dimensional Model for Many-Electron Atoms in Extremely Strong Magnetic Fields: Maximum Negative Ionization

We consider a one-dimensional model for many-electron atoms in strong magnetic fields in which the Coulomb potential and interactions are replaced by one-dimensional regularizations associated with the lowest Landau level. For this model we show that the maximum number of electrons is bounded above by 2Z+1 + c sqrt{B}. We follow Lieb's strategy in which convexity plays a critical role. For the case of two electrons and fractional nuclear charge, we also discuss the critical value at which the nuclear charge becomes too weak to bind two electrons.Comment: 23 pages, 5 figures. J. Phys. A: Math and General (in press) 199

Van de grond : verkenning mogelijkheden voor het inzetten van publieke grond voor maatschappelijke doelen in Eemland

Eemland is één van de beste weidevogelgebieden van Nederland. Veel boeren doen al aan agrarisch natuurbeheer, maar de groei is eruit. Agrarische natuur- en landschapsvereniging Ark & Eemlandschap zou graag meer in handen hebben dan de subsidieregeling SNL om boeren te stimuleren om mee te doen. Zij ziet in grondgebruiksrecht een potentiële extra beloning, juist omdat grond schaars is. Hoge grondprijzen en een lage grondmobiliteit zijn typische problemen van stadsrandgebieden zoals Eemland. Ark & Eemlandschap zou grond in bezit bij overheden en maatschappelijke organisaties graag inzetten om extra groenblauwe diensten te stimuleren. Voor het verdelen van de publieke grond kan worden gedacht aan een grondbank als organisatievorm. Ark & Eemlandschap wil namelijk met de grondbank publieke grond in pacht uitgeven, in ruil voor extra agrarisch natuurbeheer (of klompenpaden) op grond die de boer al in gebruik of in bezit heeft. Op deze manier wil Ark & Eemlandschap boeren verleiden om bijvoorbeeld op voor de weidevogel gunstige plekken agrarisch natuurbeheer te gaan doen

Force-velocity relation and density profiles for biased diffusion in an adsorbed monolayer

In this paper, which completes our earlier short publication [Phys. Rev. Lett. 84, 511 (2000)], we study dynamics of a hard-core tracer particle (TP) performing a biased random walk in an adsorbed monolayer, composed of mobile hard-core particles undergoing continuous exchanges with a vapor phase. In terms of an approximate approach, based on the decoupling of the third-order correlation functions, we obtain the density profiles of the monolayer particles around the TP and derive the force-velocity relation, determining the TP terminal velocity, V_{tr}, as the function of the magnitude of external bias and other system's parameters. Asymptotic forms of the monolayer particles density profiles at large separations from the TP, and behavior of V_{tr} in the limit of small external bias are found explicitly.Comment: Latex, 31 pages, 3 figure