Electronic ground states of Fe2+_2^+ and Co2+_2^+ as determined by x-ray absorption and x-ray magnetic circular dichroism spectroscopy

The $^6\Pi$ electronic ground state of the Co$_2^+$ diatomic molecular cation has been assigned experimentally by x-ray absorption and x-ray magnetic circular dichroism spectroscopy in a cryogenic ion trap. Three candidates, $^6\Phi$, $^8\Phi$, and $^8\Gamma$, for the electronic ground state of Fe$_2^+$ have been identified. These states carry sizable orbital angular momenta that disagree with theoretical predictions from multireference configuration interaction and density functional theory. Our results show that the ground states of neutral and cationic diatomic molecules of $3d$ transition elements cannot generally be assumed to be connected by a one-electron process

Direct measurement of the soil water retention curve using X-ray absorption

International audienceX-ray absorption measurements have been explored as a fast experimental approach to determine soil hydraulic properties and to study rapid dynamic processes. As examples, the pressure-saturation relation ?(?) for a uniform sand column has been considered as has capillary rise in an initially dry sintered glass column. The ?(?)-relation is in reasonable agreement with that obtained by inverting a traditional multi-step outflow experiment. Monitoring the initial phase of capillary rise reveals behaviour that deviates qualitatively from the single-phase, local-equilibrium regime described by Richards' equation. Keywords: X-ray absorption, soil hydraulic properties, soil water dynamics, Richards' equatio

Direct Observation of High-Spin States in Manganese Dimer and Trimer Cations by X-ray Magnetic Circular Dichroism Spectroscopy in an Ion Trap

The electronic structure and magnetic moments of free Mn$_2^+$ and Mn$_3^+$ are characterized by $2p$ x-ray absorption and x-ray magnetic circular dichroism spectroscopy in a cryogenic ion trap that is coupled to a synchrotron radiation beamline. Our results show directly that localized magnetic moments of 5 $\mu_B$ are created by $3d^5 (^6\mathrm{S})$ states at each ionic core, which are coupled in parallel to form molecular high-spin states via indirect exchange that is mediated in both cases by a delocalized valence electron in a singly-occupied $4s$ derived orbital with an unpaired spin. This leads to total magnetic moments of 11 $\mu_B$ for Mn$_2^+$ and 16 $\mu_B$ for Mn$_3^+$, with no contribution of orbital angular momentum

Division, adjoints, and dualities of bilinear maps

The distributive property can be studied through bilinear maps and various morphisms between these maps. The adjoint-morphisms between bilinear maps establish a complete abelian category with projectives and admits a duality. Thus the adjoint category is not a module category but nevertheless it is suitably familiar. The universal properties have geometric perspectives. For example, products are orthogonal sums. The bilinear division maps are the simple bimaps with respect to nondegenerate adjoint-morphisms. That formalizes the understanding that the atoms of linear geometries are algebraic objects with no zero-divisors. Adjoint-isomorphism coincides with principal isotopism; hence, nonassociative division rings can be studied within this framework. This also corrects an error in an earlier pre-print; see Remark 2.11

Algebraic lattice constellations: bounds on performance

In this work, we give a bound on performance of any full-diversity lattice constellation constructed from algebraic number fields. We show that most of the already available constructions are almost optimal in the sense that any further improvement of the minimum product distance would lead to a negligible coding gain. Furthermore, we discuss constructions, minimum product distance, and bounds for full-diversity complex rotated Z[i]/sup n/-lattices for any dimension n, which avoid the need of component interleaving

Quantum Interference Controls the Electron Spin Dynamics in n-GaAs

Manifestations of quantum interference effects in macroscopic objects are rare. Weak localization is one of the few examples of such effects showing up in the electron transport through solid state. Here we show that weak localization becomes prominent also in optical spectroscopy via detection of the electron spin dynamics. In particular, we find that weak localization controls the free electron spin relaxation in semiconductors at low temperatures and weak magnetic fields by slowing it down by almost a factor of two in $n$-doped GaAs in the metallic phase. The weak localization effect on the spin relaxation is suppressed by moderate magnetic fields of about 1 T, which destroy the interference of electron trajectories, and by increasing the temperature. The weak localization suppression causes an anomalous decrease of the longitudinal electron spin relaxation time $T_1$ with magnetic field, in stark contrast with well-known magnetic field induced increase in $T_1$. This is consistent with transport measurements which show the same variation of resistivity with magnetic field. Our discovery opens a vast playground to explore quantum magneto-transport effects optically in the spin dynamics.Comment: 8 pages, 3 figure

Donaldson-Thomas invariants and wall-crossing formulas

Notes from the report at the Fields institute in Toronto. We introduce the Donaldson-Thomas invariants and describe the wall-crossing formulas for numerical Donaldson-Thomas invariants.Comment: 18 pages. To appear in the Fields Institute Monograph Serie

Level Eulerian Posets

The notion of level posets is introduced. This class of infinite posets has the property that between every two adjacent ranks the same bipartite graph occurs. When the adjacency matrix is indecomposable, we determine the length of the longest interval one needs to check to verify Eulerianness. Furthermore, we show that every level Eulerian poset associated to an indecomposable matrix has even order. A condition for verifying shellability is introduced and is automated using the algebra of walks. Applying the Skolem--Mahler--Lech theorem, the ${\bf ab}$-series of a level poset is shown to be a rational generating function in the non-commutative variables ${\bf a}$ and ${\bf b}$. In the case the poset is also Eulerian, the analogous result holds for the ${\bf cd}$-series. Using coalgebraic techniques a method is developed to recognize the ${\bf cd}$-series matrix of a level Eulerian poset