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  • Springer  (12)
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  • 1
    Digitale Medien
    Digitale Medien
    Effect of silver addition on superconductivity in the Bi1.6Pb0.4Sr1.6Ca2Cu3O10−y system (1990)
    Springer
    Journal of materials science 1 (1990), S. 30-33 
    Details
    ISSN: 1573-482X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik , Maschinenbau
    Notizen: Abstract Silver/superconductor composites containing 0 to 80 vol% silver have been prepared and their properties determined. Optimum heat treatment at sintering temperatures (∼ 800° C) under low oxygen pressures produces material with high critical current density and improves physical properties. Magnetic susceptibility measurements have been found to be consistent with resistivity results. In order to retain a single high-T c phase with increasing silver content, decreased oxygen partial pressures are required. Using the normal-state resistivity of these composites, a percolation threshold at a silver volume fraction of ∼43% was observed, while zero resistivity measurements show that a continuous superconducting network can be obtained with up to ∼80 vol% silver. The critical current density of 21 vol% silver-doped samples was found to be 1520 A cm−2 at 77.3 K, compared to 260 A cm−2 for an undoped sample.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00716013
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  • 2
    Digitale Medien
    Digitale Medien
    Analytical block-diagonalization of matrices using unit spherical tensors (1993)
    Springer
    Journal of mathematical chemistry 14 (1993), S. 391-403 
    Details
    ISSN: 1572-8897
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: Abstract A new method for block-diagonalizing large Hamiltonian matrices, in closed form, is described. The method is based on (i) a general unitary transformation due to Slichter, and (ii) Fano's unit spherical operatorsÛ Q K (I i,I i). The method is illustrated with a simple three spin 1/2 dipolar coupled spin system, characterized by off-block-diagonal unit spherical tensorsÛ 0 2 (3/2,1/2,α) andÛ 0 2 (3/2,1 /2′,α). In addition, it is pointed out that any Hamiltonian matrix can be re-labelled in terms of fictitious spin labels, enabling a wide variety of unit spherical tensors to be used in block-diagonalization. For example, a single spin 5/2 matrix can be re-labelled using three spin labels 1/2, 1/2′, and 1/2″, respectively. Thus the tensor algebra required to block-diagonalize a 6 x 6 matrix is determined solely by the properties of the Pauli spin matrices. Finally, it is shown that re-labelling within the unit spherical tensor framework provides a unifying framework for standard basis operators, fictitious spin 1/2 and 1 operators, and others. The fictitious spin 1 / 2 unit spherical operators discussed in this paper differ from those of Vega and Pines.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01164478
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  • 3
    Digitale Medien
    Digitale Medien
    Irreducible half-integer rank unit spherical tensors (1994)
    Springer
    Journal of mathematical chemistry 15 (1994), S. 367-387 
    Details
    ISSN: 1572-8897
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: Abstract A new class of half-integer rank spherical tensors is introduced. The motivation for investigating this new class of tensors originated from a desire to be able to partition matrices using mixtures of fictitious integer and half-integer spin labels. However, it is shown that they can also be used as annihilation/creation operators for spin-1/2, 3/2, etc., particles. In particular, half-integer rank tensors can be used to add/subtract a spin-1/2 particle from a given ensemble. Thus they can be viewed as the natural generalization of the raising and lowering operatorsI ±, in that they change bothI andM, simultaneously. The concept of a “universal rotator” is introduced and it is demonstrated that half-integer rank tensors obey the same contractional and rotational properties as their integer counterparts, but with half-integer rank. In addition, it is shown that half-integer rank tensors can be used to factorize the Pauli spin matrices. Finally, an example of the use of half-integer rank tensors in the block-diagonalization of a simple 3 x 3 matrix is presented and discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01277571
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  • 4
    Digitale Medien
    Digitale Medien
    Some analytical results for spin 1/2 spin systems. III: The benzene ring (1996)
    Springer
    Journal of mathematical chemistry 20 (1996), S. 285-299 
    Details
    ISSN: 1572-8897
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: Abstract In two earlier papers on multiply connectedABCD spin 1/2 spin systems, it was shown that it is possible to simplify the calculation of (i) the time dependent density matrixϱ(t), and (ii) the time evolution of high-order multiple quantum operators, evolving in the presence of differing Zeeman offsets, scalar coupling and dipolar interactions, by subdividing the Hamiltonian $$\mathcal{H}$$ into $$(\mathcal{H}_1 + \mathcal{H}_2 )$$ , where $$\mathcal{H}_1 $$ , is a suitable linear combination of the constants of the motion. In this paper, these techniques are applied to the benzene ring with particular emphasis on high-order multiple-quantum NMR experiments, and their interpretation in terms of specific wavefunctions. In particular, it is shown that excellent agreement between theory and experiment can be obtained for the energy splittings witnessed in the Δm = +4,+5 MQ-NMR transitions, with minimum effort.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01165349
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  • 5
    Digitale Medien
    Digitale Medien
    Some analytical results forABC, ABCD, andXBCD coupled spin 1/2 systems. I (1996)
    Springer
    Journal of mathematical chemistry 19 (1996), S. 353-364 
    Details
    ISSN: 1572-8897
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: Abstract By choosing a suitable linear combination of the constants of the motion $$H_1 $$ , it is shown that the calculation of the density matrixρ(t) can be simplified by subdividing the Hamiltonian $$H$$ into $$(H_1 + H_2 )$$ . In particular, this technique can be used to obtain closed form solutions for the eigenfunctions and eigenvalues of spin 1/2ABC andXBCD spin systems, evolving in the presence of Zeeman offsets, scalar coupling and dipolar interactions. In general, the eigenvalues and eigenvalues of $$H_1 $$ are very transparent, while those of $$H_2 $$ require more effort. Nevertheless, simplifications can be made. Firstly, the effective size of the Hamiltonian matrix $$H_2 $$ which needs to be considered, is reduced fromN ×N to at least (N − 2) × (N − 2), while forXBC ... systems it is reduced to (N − 4) × (N − 4). Secondly, the highest rank and highest/lowest order tensor operators available to the spin ensemble are constants of the motion under $$H_2 $$ . Finally, by exploiting the fact that $$J_z $$ is a good quantum number, it is possible to block-diagonalize the $$H_2 $$ matrix into no more than 3 × 3 matrices.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01166725
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  • 6
    Digitale Medien
    Digitale Medien
    Some analytical results forABC, ABCD, andXBCD coupled spin 1/2 systems. II (1996)
    Springer
    Journal of mathematical chemistry 19 (1996), S. 365-374 
    Details
    ISSN: 1572-8897
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: Abstract In the preceding paper, it was shown that the calculation of the density matrixρ(t) for multiply connectedABC, etc., spin 1/2 spin systems can be greatly simplified by subdividing the Hamiltonian $$H$$ into $$(H_1 + H_2 )$$ , where $$H_1 $$ is a suitable linear combination of the constants of the motion. In this paper, a framework for the determination of the time evolution of high-order multipolar quantum states is presented and discussed. It is shown that the necessary mathematical labour is reduced to a minimum by (i) exploiting the fact that $$J_z $$ is a good quantum number, and (ii) using the theory of partitioned matrices. For example, it is shown that for a generaln-coupled spin 1/2 system, the spin dynamics of the $$Q = \pm K_{max} ( \pm K_{max} \mp 1)$$ multipolar states, whereK max is the maximum tensorial rank, can be determined without the need to diagonalize the full 2 n × 2 n Hamiltonian matrix, wheren is the number of spins. In fact, to describe the time evolution of the $$Q = ( \pm K_{max} \mp 1)$$ multipolar states it is only necessary to diagonalize twon ×n matrices at most. Finally, some cautionary remarks are made concerning the use of the “weak-coupling approximation”.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01166726
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  • 7
    Digitale Medien
    Digitale Medien
    Complete solution for two coupled spin-1/2 nuclei evolving under chemical shift and dipolar interaction (1994)
    Springer
    Journal of mathematical chemistry 16 (1994), S. 1-7 
    Details
    ISSN: 1572-8897
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: Abstract The spin dynamics for two coupled spin-1/2 nuclei evolving under isotropic chemical shifts and a dipole-dipole interaction, in the high-field limit, is presented using Fano's unit spherical tensors $$\hat U_Q^K (I_i ,I_j )$$ as a basis set. For simplicity, relaxation effects are ignored. The results are used to discuss the frequently used dipole-dipole approximations for both homonuclear and heteronuclear spin systems. In particular, it is shown that it is possible to analyse NMR spectra of two spin-1/2 systems where the chemical shift differences and the dipolar interactions are of similar magnitude.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01169190
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  • 8
    Digitale Medien
    Digitale Medien
    Irreducible tensor operators and selective/hard single and double resonance experiments in insulators: Applications to NMRON and MQ-NMR (1991)
    Springer
    Hyperfine interactions 62 (1991), S. 255-272 
    Details
    ISSN: 1572-9540
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Recently, pulsed NMRON experiments have been carried out on trace amounts of radioactive54Mn in the antiferromagnet MnCl24H2O at 500 MHz (Le Gros et al. [1]). In this compound, the quadrupole splitting between the two lowest NMR transitions is ≈3 MHz, which precludes the use of non-selective (hard) rf pulses. Yet within the restricted 2*2 manifold, associated with a given transition, the nuclear rotation is “hard”. In this paper, the theory of “selective-hard” NMRON and MQ-NMR experiments is developed within the framework of irreducible tensor operators. In essence, the theory extends the early work of Jaynes [4] to deal with the higher-order multipolar states created during the course of a given NMR experiment. Several new pulsed NMRON and MQ-NMR experiments are proposed. For example, it is demonstrated how “ouble resonance”, “selective-hard” experiments on the pseudo spin-1 manifold spanned by |±1〉 and |0〉 Zeeman states of any integer spinI could be used to extract small chemical shifts in the face of very large quadrupole splittings.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02397707
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  • 9
    Digitale Medien
    Digitale Medien
    A nuclear orientation study of the van Vleck enhanced nuolear antiferromagnet holmium vanadate (1981)
    Springer
    Hyperfine interactions 10 (1981), S. 849-854 
    Details
    ISSN: 1572-9540
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01022021
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  • 10
    Digitale Medien
    Digitale Medien
    High precision54Mn NMRON in antiferromagnetic MnCl2.4H2O, using a new method of nuclear spin cooling in the mK region (1983)
    Springer
    Hyperfine interactions 16 (1983), S. 969-977 
    Details
    ISSN: 1572-9540
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract A practical method of nuclear spin cooling in the mK region, based on dramatic reduction in the spin-lattice relaxation time T1 at the antiferromagnetic-spin flop and spin flopparamagnetic phase transitions, is described. Far lower temperatures (down to 13 mK) than have been obtained to date (∼ 90 mK) are achieved in reasonable times, greatly increasing the sensitivity of NMRON. Following resonance, active isotope spins can be rapidly reset (in times ∼ 1 second) to thermal equilibrium. For54Mn in MnCl2.4H2O, hyperfine parameters A=−203.75 MHz, P=0.155 MHz and the exchange/ crystal field parameter combination Bex + 4¦D¦/gμB=1.355 T have been determined from good agreement between perturbation theory to second order and detailed NMRON results in applied fields parallel to the easy axis in the range 0-0.7 T. Splitting of observed lines in zero applied field (− 3.05 MHz) is mainly due to the pseudo-quadrupole (second order magnetic) interaction. Small third order effects (∼0.05 MHz) have been resolved.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02147400
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