146 research outputs found
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 , 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 be a Schr\"odinger operator on the real
line, be a bounded observable depending only on the coordinate and
be a fixed integer. Suppose that an energy level intersects the potential
in exactly two turning points and lies below
. We consider the semiclassical limit
, and where is the th
eigen-energy of . An asymptotic formula for , the
non-diagonal matrix elements of in the eigenbasis of , 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
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