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We prove the almost sure existence of a pure point spectrum for the two-dimensional Landau Hamiltonian with an unbounded Anderson-like random potential, provided that the magnetic field is sufficiently large. For these models, the probability distribution of the coupling constant is assumed to be absolutely continuous. The corresponding densityg has support equal to $$\mathbb{R} $$ , and satisfies $$$$ , for some ∈ > 0. This includes the case of Gaussian distributions. We show that the almost sure spectrum ∑ is $$\mathbb{R} $$ , provided the magnetic field B≠0. We prove that for each positive integer n, there exists a field strength B n , such that for all B>B n , the almost sure spectrum ∑ is pure point at all energies $$E \leqslant (2n + 3)B - \mathcal{O}(B^{ - 1} ) $$ except in intervals of width $$\mathcal{O}(B^{ - 1} ) $$ about each lower Landau level $$E_m (B) \equiv (2m + 1)B $$ , for m < n. We also prove that for any B≠0, the integrated density of states is Lipschitz continuous away from the Landau energiesE n (B). This follows from a new Wegner estimate for the finite-area magnetic Hamiltonians with random potentials.

X-ray absorption spectroscopy (XAS) was used to follow the evolution of local structural environments around ferric ions during the formation of ferric hydrous oxide gels from 1 M chloride and 0.1 M nitrate solutions. Fe K-XANES and EXAFS confirm that ferric ions remain 6-fold coordinated during this evolution. EXAFS spectra obtained on partially hydrolyzed ferric chloride solutions indicate the presence of aqua-chloro ferric complexes up to OHFe = 2.2. When OHFe < 1 in the solution, iron mainly occurs in trans-[FeCl2(H2O)4]2+ octahedra with Fe-Cl and Fe-O distances of 2.31 and 2.01 A, respectively. With increasing OH availability in the solution, Cl− anions tend gradually to be exchanged for (O,OH,OH2) ligands. Below OHFe = 1, no structural order is detected beyond the first coordination sphere. Above this ratio, two Fe-Fe distances at 3.05 A and 3.44 A are observed and correspond to the presence of edge- and vertex-sharing Fe-octahedra. XAS results show that ferric gels and highly polymerized aqueous species are short-range ordered. The main contribution to disorder in the gels arises from the small size of coherently scattering domains also responsible for their X-ray ‘amorphous’ character. From the initial to the final stage of hydrolysis, particles possess a nearly spherical shape with a minimum average diameter ranging from 10–30 A for polymers formed from chloride and nitrate solutions. As polymerization proceeds, the local order extends to several tens of angstroms and the particle structures becomes progressively closer to that of akaganeite (β-FeOOH) or goethite (α-FeOOH). This local structure is distinct from that of the lepidocrocite (γ-FeOOH)-like structure of ferric gels precipitated after oxidation of divalent Fe solutions. The growth of the crystalline Fe-oxyhydroxides from gels takes place by the progressive long-range ordering in the ferric polymers without modifying the short-range order around Fe.

Several outstanding studies have recently demonstrated the usefulness of XAS in mineralogy and geochemistry. Most significative advances have taken advantage of the structural information that extends beyond the immediate coordination sphere of the x-ray absorber. The diversity of mineralogical problems that can be addressed by XAS are reviewed. Applications encompass: structure of mineral-forming solutions and gels; crystal structure of the mineral, when this is not known already; and site occupancy of impurities that are present.

We show that under suitable non-trapping conditions on the potential V at energy E the Schrodinger operator H = − h 2 Δ + V exhibits no resonance in a neighbourhood of E for small h . We briefly discuss some critical values of E like thresholds or barrier tops.

(1987). On the location of the resonances for schrodinger. Communications in Partial Differential Equations: Vol. 12, No. 2, pp. 201-222.

The variation of the physical parameters in a P.I.N. junction under neutron irradiation, and their evolution by annealing, are studied. An activation energy of 0.5 ev is obtained. (auth)

XAS spectroscopy has been used to study changes in local structure around Fe(III) in going from solution to gel to α-Fe2O3. Both pre-edge structure and EXAFS show that Fe remains 6-coordinated during this evolution. The first polymers in solution appearing above OH/Fe>1 are characterized by the presence of edge-[d(Fe-Fe)=3.05A] and corner-sharing [d(Fe-Fe)=3.44A] octahedra. The minimum particle size of the ferric oxide gel ranges between 20 and 30 A. After 30 min ageing of this gel at 92°C, face-sharing octahedra [d(Fe-Fe)=2.89A] form and are thought to induce hematite nucleation.