259 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
Effective Hamiltonians for atoms in very strong magnetic fields
We propose three effective Hamiltonians which approximate atoms in very
strong homogeneous magnetic fields modelled by the Pauli Hamiltonian, with
fixed total angular momentum with respect to magnetic field axis. All three
Hamiltonians describe electrons and a fixed nucleus where the Coulomb
interaction has been replaced by -dependent one-dimensional effective
(vector valued) potentials but without magnetic field. Two of them are solvable
in at least the one electron case. We briefly sketch how these Hamiltonians can
be used to analyse the bottom of the spectrum of such atoms.Comment: 43 page
Insights into the mechanism of energy transfer with poly(heptazine imide)s in deoximation reaction
Following our previous studies on potassium poly(heptazine imide) (K-PHI) – catalyzed photooxidative [3+2] aldoxime-to-nitrile addition to form 1,2,4-oxadiazoles, we discovered that electron-rich oximes yield the parent aldehydes instead of target products. In this work, the mechanism of this singlet oxygen-mediated deoximation process was established using a series of control reactions and spectroscopic measurements such as steady-state and time-resolved fluorescence quenching experiments. Additionally, singlet-triplet energy gap value was obtained for K-PHI in suspension, and the reaction scope was broadened to include ketoximes
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
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
Multisite PCET with photocharged carbon nitride in dark
A combination of photochemistry and proton coupled electron transfer (PCET) is a primary strategy employed by biochemical systems and synthetic chemistry to enable uphill reactions under mild conditions. Degenerate nanometer-sized n-type semiconductor nanoparticles (SCNPs) with the Fermi level above the bottom of the conduction band are strongly reducing and act more like metals than semiconductors. Application of the degenerate SCNPs is limited to few examples. Herein, we load microporous potassium poly(heptazine imide) (K-PHI) nanoparticles with electrons (e–) and charge balancing protons (H+) in an illumination phase using sacrificial agents. e–/H+ in the K-PHI nanoparticles are weakly bound and therefore could be used in a range of PCET reactions in dark, such as generation of aryl radicals from aryl halides, ketyl radicals from ketones, and 6e–/6H+ reduction of nitrobenzene to aniline. The integration of several features that until now were intrinsic for plants and natural photosynthesis into a transition metal free nanomaterial composed of abundant elements (C, N, and K) offers a powerful tool for synthetic organic chemistry
H^+_2$ in a strong magnetic field described via a solvable model
We consider the hydrogen molecular ion in the presence of a strong
homogeneous magnetic field. In this regime, the effective Hamiltonian is almost
one dimensional with a potential energy which looks like a sum of two Dirac
delta functions. This model is solvable, but not close enough to our exact
Hamiltonian for relevant strenght of the magnnetic field. However we show that
the correct values of the equilibrium distance as well as the binding energy of
the ground state of the ion, can be obtained when incorporating perturbative
corrections up to second order. Finally, we show that exists for
sufficiently large magnetic fields
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
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
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