Large transverse field tunnel splittings in the Fe_8 spin Hamiltonian

The spin Hamiltonian that describes the molecular magnet Fe$_8$ has biaxial symmetry with mutually perpendicular easy, medium, and hard magnetic axes. Previous calculations of the ground state tunnel splittings in the presence of a magnetic field along the hard axis are extended, and the meaning of the previously discovered oscillation of this splitting is further clarified

Comparisons of soil suction induced by evapotranspiration and transpiration of S. <i>heptaphylla</i>

For a given evapotranspiration (ETr), both soil evaporation and plant transpiration (Tr) would induce soil suction. However, the relative contribution of these two processes to the amount of suction induced is not clear. The objective of this study is to quantify ETr- and Tr-induced suction by a selected tree species, Scheffllera heptaphylla, in silty sand. The relative contribution of transpiration and evaporation to the responses of suction is then explored based on observed differences in Tr- and ETr-induced suction. In total, 12 test boxes were used for testing: 10 for vegetated soil with different values of leaf area index (LAI) and root area index (RAI), while two were for bare soil as references. Each box was exposed to identical atmospheric conditions controlled in a plant room for monitoring suction responses over a week. Due to the additional effects of soil evaporation, ETr-induced suction could be 3%–47% higher than Tr-induced suction, depending on LAI. The significance of evaporation reduced substantially when LAI was higher, as relatively less radiant energy fell on the soil surface for evaporation. For a given LAI, the effects of evaporation were less significant at deeper depths within the root zone. The effects of RAI associated with root-water uptake upon transpiration were the dominant process of ETr affecting the suction responses.</jats:p

Oscillatory Tunnel Splittings in Spin Systems: A Discrete Wentzel-Kramers-Brillouin Approach

Certain spin Hamiltonians that give rise to tunnel splittings that are viewed in terms of interfering instanton trajectories, are restudied using a discrete WKB method, that is more elementary, and also yields wavefunctions and preexponential factors for the splittings. A novel turning point inside the classically forbidden region is analysed, and a general formula is obtained for the splittings. The result is appled to the \Fe8 system. A previous result for the oscillation of the ground state splitting with external magnetic field is extended to higher levels.Comment: RevTex, one ps figur

Quenched Spin Tunneling and Diabolical Points in Magnetic Molecules: II. Asymmetric Configurations

The perfect quenching of spin tunneling first predicted for a model with biaxial symmetry, and recently observed in the magnetic molecule Fe_8, is further studied using the discrete phase integral (or Wentzel-Kramers-Brillouin) method. The analysis of the previous paper is extended to the case where the magnetic field has both hard and easy components, so that the Hamiltonian has no obvious symmetry. Herring's formula is now inapplicable, so the problem is solved by finding the wavefunction and using connection formulas at every turning point. A general formula for the energy surface in the vicinity of the diabolo is obtained in this way. This formula gives the tunneling apmplitude between two wells unrelated by symmetry in terms of a small number of action integrals, and appears to be generally valid, even for problems where the recursion contains more than five terms. Explicit results are obtained for the diabolical points in the model for Fe_8. These results exactly parallel the experimental observations. It is found that the leading semiclassical results for the diabolical points appear to be exact, and the points themselves lie on a perfect centered rectangular lattice in the magnetic field space. A variety of evidence in favor of this perfect lattice hypothesis is presented.Comment: Revtex; 4 ps figures; follow up to cond-mat/000311

Spin Tunneling in Magnetic Molecules: Quasisingular Perturbations and Discontinuous SU(2) Instantons

Spin coherent state path integrals with discontinuous semiclassical paths are investigated with special reference to a realistic model for the magnetic degrees of freedom in the Fe8 molecular solid. It is shown that such paths are essential to a proper understanding of the phenomenon of quenched spin tunneling in these molecules. In the Fe8 problem, such paths are shown to arise as soon as a fourth order anisotropy term in the energy is turned on, making this term a singular perturbation from the semiclassical point of view. The instanton approximation is shown to quantitatively explain the magnetic field dependence of the tunnel splitting, as well as agree with general rules for the number of quenching points allowed for a given value of spin. An accurate approximate formula for the spacing between quenching points is derived

Efficient algorithms for tensor scaling, quantum marginals and moment polytopes

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our algorithm provides an efficient weak membership oracle for the associated moment polytopes, an important family of implicitly-defined convex polytopes with exponentially many facets and a wide range of applications. These include the entanglement polytopes from quantum information theory (in particular, we obtain an efficient solution to the notorious one-body quantum marginal problem) and the Kronecker polytopes from representation theory (which capture the asymptotic support of Kronecker coefficients). Our algorithm can be applied to succinct descriptions of the input tensor whenever the marginals can be efficiently computed, as in the important case of matrix product states or tensor-train decompositions, widely used in computational physics and numerical mathematics. We strengthen and generalize the alternating minimization approach of previous papers by introducing the theory of highest weight vectors from representation theory into the numerical optimization framework. We show that highest weight vectors are natural potential functions for scaling algorithms and prove new bounds on their evaluations to obtain polynomial-time convergence. Our techniques are general and we believe that they will be instrumental to obtain efficient algorithms for moment polytopes beyond the ones consider here, and more broadly, for other optimization problems possessing natural symmetries

Macroscopic Quantum Tunneling of a Domain Wall in a Ferromagnetic Metal

The macroscopic quantum tunneling of a planar domain wall in a ferromagnetic metal is studied based on the Hubbard model. It is found that the ohmic dissipation is present even at zero temperature due to the gapless Stoner excitation, which is the crucial difference from the case of the insulating magnet. The dissipative effect is calculated as a function of width of the wall and is shown to be effective in a thin wall and in a weak ferromagnet. The results are discussed in the light of recent experiments on ferromagnets with strong anisotropy. PACS numbers:75.60.Ch, 03.65.Sq, 75.10.LpComment: 13page

Achieving Good Angular Resolution in 3D Arc Diagrams

We study a three-dimensional analogue to the well-known graph visualization approach known as arc diagrams. We provide several algorithms that achieve good angular resolution for 3D arc diagrams, even for cases when the arcs must project to a given 2D straight-line drawing of the input graph. Our methods make use of various graph coloring algorithms, including an algorithm for a new coloring problem, which we call localized edge coloring.Comment: 12 pages, 5 figures; to appear at the 21st International Symposium on Graph Drawing (GD 2013

Dichloro(diphenylarsino)ruthenium(III) & Its Reactions with Some Nitrogen Donors

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