Search for magnetic order in undoped and doped spin‐gap systems by μSR

We introduce our μSR investigations of spin‐gap systems, such as, (1) a 2‐leg spin‐ladder material SrCu₂O₃, (2) a Haldane material (S=1 spin‐chain) Y₂BaNiO₅, (3) a spin‐Peierls material CuGeO₃, (4) a spin‐chain# material Sr₆Ca₈Cu₂₄O₄₁. All of these antiferromagnetic spin systems are characterized by a spin‐gap between the singlet ground‐state and the triplet first excited states. In the above‐mentioned materials, we confirmed the absence of magnetic order down to milli‐Kelvin regime, supporting the non‐magnetic feature of the ground‐state. If a spin‐gap system is doped with charges and/or vacancies at the spin site, unpaired spins are induced out of the singlet ground‐state. In some materials, doping completely destroys the singlet ground‐state and induces a bulk magnetic order. We report μSR investigations of doped materials as well, which clarifies the existence/absence of a magnetic order upon doping. This revised version was published online in July 2006 with corrections to the Cover Date.     

Quantum diffusion of the positive muon in the superconducting state of Al

We report low temperature studies of muon diffusion and trapping in Al doped with Li impurities. The trapping rate at Li and the deduced muon diffusion rate increase more rapidly with decreasing temperature in the superconducting state compared with the normal state. The temperature dependence of the quantum diffusion rate in the superconducting state is close to that predicted by the Kondo theory.     

A theoretical examination of substituent effects on the detoxification reaction between glutathione and halogenated methanes

An important metabolic pathway for halogenated methanes is the detoxification reaction with glutathione in the cell cytosol fraction. Experimental studies have shown that the rate of this S_N2 displacement reaction is directly related to the leaving group ability of the dissociating halide; the rate increases in order of the ions F^?, Cl^?, Br^?, and I^? leaving. In this study, we examine the role of the other halomethane substituents on the rate of this reaction for compounds with a common leaving anion. To this end, reaction Cl^? + CY₃Cl → ClCY₃ + Cl^? (Y = H,F,Cl) is examined using ab initio methods. The barrier for this exchange process may arise from requiring an inversion of the CY₃ group in the transition structure, the energy required to homolytically cleave the C? Cl bond, or from unfavorable steric and electronic interactions in the five-coordinated transition structure. Of these three factors, only the third explains the calculated ordering of barrier heights. This suggests that successive halogenation of methane not only increases its activity as a substrate for anaerobic reduction, as was shown earlier, but also decreases its ability to take part in the detoxification reaction with glutathione.     

An exactly soluble model of a system containing arbitrary isotropic bilinear and biquadratic exchange interactions

Stanley's exact results for a Bethe Lattice of classical spins of arbitrary dimensionality are generalized to include an arbitrary biquadratic interaction term. Simple expressions are obtained for both the nearest neighbor dipolar and quadrupolar correlation functions. It is shown that the system never displays long range order at any finite temperature. A modest amount of biquadratic excahnge can even prevent the system from ordering at T = 0°K. However, except for the linear chain, two distinct temperatures are found for the divergence of the dipolar and quadrupolar susceptibilities.     

Super Teichmüller spaces: Punctures and elliptic points

A model for the super Teichmüller space is described and calculated when the super Riemann surfaces no longer have a compact nonsingular body manifold. The bosonic and fermionic dimensions turn out to be the dimensions of the appropriate spaces of automorphic forms, in the case where the body has a finite number of punctures and/or elliptic points.     

2-manifolds of constant curvature, 3-parameter isometry groups and bäcklund transformations

The relationship between the Sine Gordon equation and Riemannian 2-manifolds of constant negative curvature is well known. We point out that it gives rise (locally) to a transitive action of the 3-parameter group SL(2,R) on the manifold. This enables us to elucidate group theoretically the geometry underlying the Bäcklund transformation. The transformation arises by passing from the 2-manifold, a homogeneous space, to 2-submanifolds of SL(2,R) defined by orbits of the solvable subgroup of SL(2,R). A similar approach allows us several other such transformations, for example, transformations linking φ_xx+φ_yy = sinhφ to φ_xx+φ_yy = sinφ and φ_xx+φ_yy = e^2φ to φ_xx+φ_yy = 0.     

Muon spin relaxation measurements of CsC60, RbC60, KC60

Muon spin relaxation (μ⁺SR) measurements of CsC₆₀ and RbC₆₀ have revealed magnetic ordering at 20 K and 15 K respectively, with static internal fields at the muon site of \sim7 G for both samples. No magnetic ordering is seen in KC₆₀ down to 2.5 K. An apparent small increase in muon spin relaxation which had been seen at 70 K in RbC₆₀ is ascribed to an extrinsic effect, originating in muons which stopped in the aluminum sample holder. This revised version was published online in July 2006 with corrections to the Cover Date.     

Optimal economic growth with foreign trade and a learning industry

Ryder (Ref. 1) has developed a simple two-sector macroeconomic model incorporatinglearning by doing as a determinant of the growth of productivity-enhancing experience and its effect on foreign trade. In this paper, optimal foreign trade and capital allocation policies are determined, in the context of the above model, for ranges of the international trade price not considered by Ryder. An extension of Ryder's model to include a dual trade price structure is briefly discussed. A specific numerical example is used to ascertain the configuration of the various features occurring in the extremal fields at different price levels.     

Operation of a conducting PRIZ

The construction and operation of a PRIZ spatial light modulator is reported using semi-transparent electrodes and no insulating layers. Qualitative observations of the dynamic properties of such conducting devices are found to be similar to those reported in the Soviet literature with several exceptions. The devices demonstrated dynamic detection, memory, and oscillatory instability as well as the typical directional filtering and dc suppression of the standard PRIZ which uses insulating layers. This is the first report of a non-Soviet built device of this type.