A diagrammatic approach to spin algebras

A reduction formula for the thermal average of the time-ordered product of spin operators for a magnetic moment in a field H is presented. The reduction formula and the spin algebra are used to compute the magnetization. The procedure provides the basis for a diagrammatic approach to interacting spin systems.     

Twisted group algebras I

A generalization of the group algebra of a locally compact group is studied, by expressing the group algebra of a central group extension as the direct sum of closed *-ideals each one of which is isomorphic to such a twisted group algebra. In particular, the representation theory of such algebras is associated with the theory of projective representations by studying the representations of the group algebra of the group extension and the associated unitary representations of the group extension.     

Twisted group algebras II

Wendel showed that norm non-increasing isomorphisms between the group algebras of locally compact groups could be expressed in terms of group characters and topological isomorphisms. His results are extended to twisted group algebras. In particular, by applying a generalisation ofWendel's main result to twisted group algebras over the same group, it is shown that the number of such algebras is equal to the number of orbits in a 2-cohomology group overG under the action of the automorphism group ofG. An application to the twisted group algebra defined byWeyl's form of the canonical commutation relations is considered.     

Particles of nonzero rest mass and spin algebras

We construct a family of parametrized spin-Z_α algebras from the (canonical) spin-S and (helicity)spin-Z ones in the case of irreducible unitary representations [m, s] of the Poincaré group. The parameter α refers to a rotation angle around the third axis. Equivalences of such constructions are given through a family of unitary transformations containing, for definite values of α, well established and very useful transformations. General formulas referring to the so-called Shirokov-Foldy form of the Poincaré generators and to typical Shirokov's operators are given explicitly.     

Multiple spin echoes in inhomogeneously broadened NMR systems

New types of spin echoes produced by refocusing the magnetic moments dephased during a long rf excitation pulse are observed in inhomogeneously broadened NMR systems. The experimental results are in good agreement with the theoretical predictions.     

The spin holonomy group in general relativity

It has recently been shown by Goldberg et al. that the holonomy group of the chiral spin-connection is preserved under time evolution in vacuum general relativity. Here, the underlying reason for the time-independence of the holonomy group is traced to the self-duality of the curvature 2-form for an Einstein space. This observation reveals that the holonomy group is time-independent not only in vacuum, but also in the presence of a cosmological constant. It also shows that once matter is coupled to gravity, the conservation of holonomy is lost.When the fundamental group of space is non-trivial, the holonomy group need not be connected. For each homotopy class of loops, the holonomies comprise a coset of the full holonomy group modulo its connected component. These cosets are also time-independent. All possible holonomy groups that can arise are classified, and examples are given of connections with these holonomy groups. The classification of local and global solutions with given holonomy groups is discussed.     

Norms in group algebras of finite groups under inducing

We compare norms of an element of a group algebra of a normal subgroup of a finite group in a representation of the normal subgroup and the corresponding induced representation (under the natural embedding of the group algebra of the normal subgroup in the group algebra of the entire group).     

On the theory of NMR spin echoes in solids

A general expression in terms of two-time correlation functions is derived for the spin echo responses to 90°-τ-β⁰_φ pulse sequences of quadrupolar spins coupled through dipolar interactions. The second moments of the correlation function are calculated for a system of spin one nuclei and shown to be in accordance with the experimental observations. Furthermore, results are presented for the fourth moments.     

NMR study of spin dynamics in disordered Heisenberg paramagnets

The spin dynamics in the disordered paramagnets KMg_1?xMn_xF₃ and Zn_1?xMn_xF₂ were investigated using the F¹⁹ NMR. Linewidths and relaxation rates of those distinct classes of F¹⁹ nuclei that have different numbers of nearest neighbor magnetic ions were obtained as a function of concentration x. The particular importance of the isolated magnetic ion to the low frequency spectral density was established.     

Braid group action and quantum affine algebras

We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop-like generators of the algebra are obtained which satisfy the relations of Drinfel'd's new realization. Coproduct formulas are given and a PBW type basis is constructed.     

Generating spin turbulence through nonlinear excitation in liquid-state NMR

Chaotic dynamics of a water magnetization in a 600 MHz NMR spectrometer was generated by a radiation damping-based electronic feedback. Erratic induction signal was observed for several tens of seconds. The analysis of the data shows that this chaotic behaviour can be ascribed to spin turbulence in the sample and that a simpler model based on the three-dimensional Bloch equations modified to include a feedback field may not account for the experimental data.     

NMR study of the spin polarization in dilute Al-Mn alloys

The spatial dependence of the spin density oscillations σ(r) around Mn impurities in Al-Mn dilute alloys has been studied by ²⁷Al four pulse NMR experiments. The concentration dependence of the magnetic broadening $\text{ΔH}{}^{\mathrm{i}}\text{1}\text{2}$ of the ²⁷Al line is found slower than linear. This result, together with the temperature dependence of the magnetic broadening as measured by CW NMR, demonstrates both the preasymptotic depression of σ(r) in Al-Mn and the long range damping of σ(r) associated with the finite mean free path at high T.     

Investigation of spin reorientation phenomena in ferromagnetic MnSb by NMR

A temperature dependence of wall edge and wall centre resonances of ⁵⁵Mn has been carried out in MnSb in the region 77 to 530 K. The data show that the spin reorientation occurs in the temperature region 519 to 524 K. The observed quadrupolar splitting, ν_Q, doubles across the transition. The dc resistivity measurements also show an anomoly in this transition region. It is also found that this transition occurs when the $\text{c}\text{a}$ ratio becomes 1.417 in MnSb and MnBi.     

MAS NMR studies of carbon-13 spin exchange in durene

One- (1-D) and two-dimensional (2-D) carbon-13 NMR exchange measurements in powder samples of isotopically normal durene under magic angle spinning (MAS) are reported. The experiments include rotor synchronized 2-D exchange (RS2DE), 1-D magnetization transfer (MT) and time reverse ODESSA (tr-ODESSA). The latter two experiments were performed as a function of several external parameters, including proton decoupling field during mixing time, sample spinning rate and partly, of temperature. The effects of these parameters on the spin exchange induced by spin diffusion and by chemical, or physical exchange, is discussed. Spin exchange between all types of carbons in the durene molecules occurs on the time scale of seconds. From the dependence of the spin exchange rate on the external parameters it is concluded that the process is dominated by spin diffusion. On the basis of these results an upper limit of 10(-16) cm2 s(-1) can be set for the self-diffusion constant in crystalline durene.