Scattering in three-dimensional fuzzy space

We develop scattering theory in a non-commutative space defined by a $su(2)$ coordinate algebra. By introducing a positive operator valued measure as a replacement for strong position measurements, we are able to derive explicit expressions for the probability current, differential and total cross-sections. We show that at low incident energies the kinematics of these expressions is identical to that of commutative scattering theory. The consequences of spacial non-commutativity are found to be more pronounced at the dynamical level where, even at low incident energies, the phase shifts of the partial waves can deviate strongly from commutative results. This is demonstrated for scattering from a spherical well. The impact of non-commutativity on the well's spectrum and on the properties of its bound and scattering states are considered in detail. It is found that for sufficiently large well-depths the potential effectively becomes repulsive and that the cross-section tends towards that of hard sphere scattering. This can occur even at low incident energies when the particle's wave-length inside the well becomes comparable to the non-commutative length-scale.Comment: 12 pages, 6 figure

Duality constructions from quantum state manifolds

The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS_2/CFT_1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et. al. the corresponding state manifold is seen to be exactly AdS_2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.Comment: 25 Pages, References Adde

Spectrum of the three dimensional fuzzy well

We develop the formalism of quantum mechanics on three dimensional fuzzy space and solve the Schr\"odinger equation for a free particle, finite and infinite fuzzy wells. We show that all results reduce to the appropriate commutative limits. A high energy cut-off is found for the free particle spectrum, which also results in the modification of the high energy dispersion relation. An ultra-violet/infra-red duality is manifest in the free particle spectrum. The finite well also has an upper bound on the possible energy eigenvalues. The phase shifts due to scattering around the finite fuzzy potential well have been calculated

[μ-1,2-Bis(diphenyl­phosphan­yl)-1,2-dimethyl­hydrazine-κ2 P:P′]bis­[chlorido­gold(I)]

The title compound, [Au2Cl2(C26H26N2P2)], is formed from a bidentate phosphine ligand complexed to two linearly coordinated gold(I) atoms. The gold(I) atoms are 3.4873 (7) Å apart. The mol­ecule exhibits a crystallographic twofold rotation axis

[μ-1,2-Bis(diphenyl­phosphan­yl)-1,2-diethyl­hydrazine-κ2 P:P′]bis­[chlorido­gold(I)] tetra­hydro­furan disolvate

The title compound, [Au2Cl2(C28H30N2P2)]·2C4H8O, was synthesized from a bidentate phosphine ligand complexed to two linear gold(I) chloride moieties. The Au(I) atom is in an almost linear coordination with a P—Au—Cl angle of 179.22 (4)°. The complex molecules reside on a twofold rotation axis

Immunology for Clinicians: A ‘Trojan Horse’ approach

A South African website imparts basic immunology information to clinicians and other health care workers

Chlorido{N-[2-(diphenylphosphanyl)- benzyl]-1-(pyridin-2-yl)methanamine-kP} gold(I)

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1,2-Bis(diphenyl­phosphino)-1,2-diethyl­hydrazine

The title compound, C28H30N2P2, adopts a well documented and studied gauche conformation around the hydrazine bond. Bond lengths and angles are in the typical ranges expected for P—N and P—C bonds. A normal hydrazine N—N bond length of 1.426 (3) Å is observed

Poly[[μ2-1,2-bis­(diphenyl­phosphan­yl)-1,2-diethylhydrazine]-μ4-nitrato-μ2-nitrato-silver(I)]

The title compound, [Ag2(NO3)2(C28H30N2P2)]n, crystallizes in polymeric α-helices. Three O atoms from three different nitrate ions in equatorial positions and two Ag atoms at axial positions set up a trigonal bipyramid. These units are linked by the phosphine ligands into endless helical chains that run along the c axis. The crystal used for the data collection was a racemic twin