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  • 1
    Electronic Resource
    Electronic Resource
    Aperiodic tilings with non-symmorphic space groups p2jgm (1988)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 44 (1988), S. 678-688 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: As an illustrative application of the general theory of quasicrystallographic space groups a non-symmorphic aperiodic tiling is constructed with space group p2Jgm using a generalization of the grid method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388003733
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  • 2
    Electronic Resource
    Electronic Resource
    The two-dimensional quasicrystallographic space groups with rotational symmetries less than 23-fold (1988)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 44 (1988), S. 197-211 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The crystallographic concepts of lattice and space group are extended to describe materials with crystallographically forbidden point groups, and a complete classification of all two-dimensional space groups with rotational order less than 23 is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767387010511
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  • 3
    Electronic Resource
    Electronic Resource
    Pitfalls of the relaxation time approximation: Hydrodynamic sound in a multicomponent Fermi liquid (1985)
    Springer
    Journal of low temperature physics 59 (1985), S. 115-121 
    Details
    ISSN: 1573-7357
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract When transport in a Fermi liquid is treated in the relaxation time approximation, the quasiparticle energy appearing in the local equilibrium distribution must have the form determined by the nonequilibrium distribution function. Sometimes this requirement is overlooked and the equilibrium quasiparticle energy is used. In applications to unpolarized normal3He the resulting error can be repaired by a simple rescaling of the relaxation rates 1/τ1 by the Fermi liquid corrections 1+F l/(2l+1). The distinction between the two forms of the relaxation time approximation is thus of little consequence, and quantities independent of the relaxation time are entirely unaffected. We point out that more significant damage results from using this wrong relaxation time approximation in a multicomponent (or spin-polarized single-component) Fermi liquid. In particular, it is essential to use the correct form to derive the velocity of hydrodynamic sound, even though the incorrect form also satisfies all the conservation laws, and even though the sound velocity is independent of the relaxation time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00681507
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  • 4
    Electronic Resource
    Electronic Resource
    Bravais classes for the simplest incommensurate crystal phases (1992)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 48 (1992), S. 515-532 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Through the reformulation of crystallography that treats periodic and quasiperiodic structures on an equal footing in three-dimensional Fourier space, a novel computation is given of the Bravais classes for the simplest kinds of incommensurately modulated crystals: (3 + 3) Bravais classes in the cubic system and (3 + 1) Bravais classes in any of the other six crystal systems. The contents of a Bravais class are taken to be sets of ordinary three-dimensional wave vectors inferred from a diffraction pattern. Because no finer distinctions are made based on the intensities of the associated Bragg peaks, a significantly simpler set of Bravais classes is found than Janner, Janssen & de Wolff [Acta Cryst. (1983). A39, 658–666] find by defining their Bravais classes in higher-dimensional superspace. In our scheme, the Janner, Janssen & de Wolff categories appear as different ways to describe identical sets of three-dimensional wave vectors when those sets contain crystallographic (3 + 0) sublattices belonging to more than a single crystallographic Bravais class. While such further discriminations are important to make when the diffraction pattern is well described by a strong lattice of main reflections and weaker satellite peaks, by not making them at the fundamental level of the Bravais class, the crystallographic description of all quasiperiodic materials is placed on a single unified foundation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767392000448
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  • 5
    Electronic Resource
    Electronic Resource
    Space groups of trigonal and hexagonal quasiperiodic crystals of rank 4 (1994)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 50 (1994), S. 72-85 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: As a pedagogical illustration of the Fourier-space approach to the crystallography of quasiperiodic crystals, a simple derivation is given of the space-group classification scheme for hexagonal and trigonal quasiperiodic crystals of rank 4. The categories, which can be directly inferred from the Fourier-space forms of the hexagonal and trigonal space groups for periodic crystals, describe general hexagonal or trigonal quasiperiodic crystals of rank 4, which include but are not limited to modulated crystals and intergrowth compounds. When these general categories are applied to the special case of modulated crystals, it is useful to present them in ways that emphasize each of the subsets of Bragg peaks that can serve as distinct lattices of main reflections. These different settings of the general rank-4 space groups correspond precisely to the superspace-group description of (3 + 1) modulated crystals given by de Wolff, Jannsen & Janner [Acta Cryst. (1981), A37, 625–636]. As a demonstration of the power of the Fourier-space approach, the space groups for hexagonal and trigonal quasiperiodic crystals of arbitrary finite rank are derived in a companion paper [Lifshitz & Mermin (1994). Acta Cryst. A50, 85–97].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767393006300
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  • 6
    Electronic Resource
    Electronic Resource
    Bravais classes and space groups for trigonal and hexagonal quasiperiodic crystals of arbitrary finite rank (1994)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 50 (1994), S. 85-97 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: To demonstrate the power of the Fourier-space approach to crystallography, the Bravais classes and space groups of hexagonal and trigonal quasiperiodic crystals are derived for lattices of arbitrary finite rank. The specification of the space groups for each Bravais class is given by an elementary extension of the rank-4 case. The conventional classification of incommensurately modulated hexagonal and trigonal crystals, previously derived using the superspace approach for Bravais classes up to rank (3 + 3) [Janner, Janssen & de Wolff (1993). Acta Cryst. A39, 658–666] and for superspace groups of rank (3 + 1) [de Wolff, Janssen & Janner (1981). Acta Cryst. A37, 625–636], is easily extracted from the general classification for modulations of any finite rank.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767393006312
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  • 7
    Electronic Resource
    Electronic Resource
    Space groups of quasicrystallographic tilings (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 538-547 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method is described for producing tilings with various quasicrystallographic space groups, paying particular attention to the two-dimensional space groups pnm1 and pn1m that can exist as distinct possibilities when the order of rotational symmetry n is a power of an odd prime number.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767389003302
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  • 8
    Electronic Resource
    Electronic Resource
    Farkas's Lemma and the nature of reality: Statistical implications of quantum correlations (1984)
    Springer
    Foundations of physics 14 (1984), S. 1-39 
    Details
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A general algorithm is given for determining whether or not a given set of pair distributions allows for the construction of all the members of a specified set of higher-order distributions which return the given pair distributions as marginals. This mathematical question underlies studies of quantum correlation experiments such as those of Bell or of Clauser and Horne, or their higher-spin generalizations. The algorithm permits the analysis of rather intricate versions of such problems, in a form readily adaptable to the computer. The general procedure is illustrated by simple derivations of the results of Mermin and Schwarz for the symmetric spin-1 and spin-3/2 Einstein-Podolsky-Rosen problems. It is also used to extend those results to the spin-2 and spin-5/2 cases, providing further evidence that the range of strange quantum theoretic correlations does not diminish with increasing s. The algorithm is also illustrated by giving an alternative derivation of some recent results on the necessity and sufficiency of the Clauser-Horne conditions. The mathematical formulation of the algorithm is given in general terms without specific reference to the quantum theoretic applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00741645
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  • 9
    Electronic Resource
    Electronic Resource
    Joint distributions and local realism in the higher-spin Einstein-Podolsky-Rosen experiment (1982)
    Springer
    Foundations of physics 12 (1982), S. 101-135 
    Details
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A method is given to determine whether or not the distribution functions describing the two spin measurements in the spin-s Einstein-Podolsky-Rosen experiment are compatible with the existence of distributions describing three spin measurements (not all of which can actually be performed). When applied to the spin-1/2 case the method gives the results of Wigner, or of Clauser, Holt, Horne, and Shimony, depending on whether or not the two-spin distributions are assumed to have the forms given by the quantum theory. Generalizations of the conditions of Wigner or of Clauser et al. to the spin-1 case are explicitly calculated. The spin-3/2 case is examined in some simple geometries to show that an apparently monotonic trend toward local realism as s increases from1/2 to1 is, in fact, violated when s increases from1 to3/2. The analysis is based on a novel representation of the modulus squared of a rotation matrix element. The structure of that matrix element responsible for the restoration of local realism in the classical (large s) limit is identified, but a rigorous treatment of the classical limit is not attempted. The higher-spin results are significantly stronger than those given by Mermin's spin-s Bell inequality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00736844
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  • 10
    Electronic Resource
    Electronic Resource
    Topological analysis of the cores of singularities in 3He-A (1978)
    Springer
    Journal of low temperature physics 33 (1978), S. 117-126 
    Details
    ISSN: 1573-7357
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: The methods of homotopy theory are employed to study the internal (core) structure of singularities. The technique is illustrated by several applications to line singularities in the A-phase of superfluid helium-3.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00117070
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