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 $B$ modelled by the Pauli Hamiltonian, with fixed total angular momentum with respect to magnetic field axis. All three Hamiltonians describe $N$ electrons and a fixed nucleus where the Coulomb interaction has been replaced by $B$-dependent one-dimensional effective (vector valued) potentials but without magnetic field.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 $\mathbb{R}^n$, 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

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 $H^+_2$ 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 $He_2^{3+}$ 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 $H(\hbar)=-\hbar^2d^2/dx^2+V(x)$ 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