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  • 1
    Electronic Resource
    Electronic Resource
    Spherical containment and the Minkowski dimension of partial orders (1993)
    Springer
    Order 10 (1993), S. 227-237 
    Details
    ISSN: 1572-9273
    Keywords: 06A06 ; 52A37 ; Causal order ; spherical (containment) order ; Minkowski dimension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The recent work on circle orders generalizes to higher dimensional spheres. As spherical containment is equivalent to causal precedence in Minkowski space, we define the Minkowski dimension of a poset to be the dimension of the minimal Minkowski space into which the poset can be embedded; this isd if the poset can be represented by containment with spheresS d−2 and of no lower dimension. Comparing this dimension with the standard dimension of partial orders we prove that they are identical in dimension two but not in higher dimensions, while their irreducible configurations are the same in dimensions two and three. Moreover, we show that there are irreducible configurations for arbitrarily large Minkowski dimension, thus providing a lower bound for the Minkowski dimension of partial orders.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01110544
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    From quantum cellular automata to quantum lattice gases (1996)
    Springer
    Journal of statistical physics 85 (1996), S. 551-574 
    Details
    ISSN: 1572-9613
    Keywords: Quantum cellular automaton ; quantum lattice gas ; quantum computation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, we begin an investigation of exactly unitary cellular automata. After proving that there can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in one dimension, we weaken the homogeneity condition and show that there are nontrivial, exactly unitary, partitioning cellular automata. We find a one-parameter family of evolution rules which are best interpreted as those for a one-particle quantum automaton. This model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the Dirac equation. We describe two generalizations of this automaton, the second, of which, to multiple interacting particles, is the correct definition of a quantum lattice gas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02199356
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  • 3
    Electronic Resource
    Electronic Resource
    Lattice gases and exactly solvable models (1992)
    Springer
    Journal of statistical physics 68 (1992), S. 575-590 
    Details
    ISSN: 1572-9613
    Keywords: Lattice gases ; spacetime lattice ; spurious conserved quantities ; solvable models ; Yang-Baxter equation ; disorder solutions ; thermodynamic equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We detail the construction of a family of lattice gas automata based on a model of 't Hooft, proceeding by use of symmetry principles to define first the kinematics of the model and then the dynamics. A spurious conserved quantity appears; we use it to effect a radical transformation of the model into one whose spacetime configurations are equivalent to the two-dimensional states of an exactly solvable statistical mechanics model, the symmetric eight-vertex model with parameters restricted to a disorder variety. We comment on the implications of this identification for the original lattice gas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01341764
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  • 4
    Electronic Resource
    Electronic Resource
    Why do clocks tick? (1993)
    Springer
    General relativity and gravitation 25 (1993), S. 893-900 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Drawing on recent developments in the matrix model approach to string theory and the causal set program for quantum gravity we address the question of the origin of time as one aspect of the phase transition from a topological quantum field theory to a quantum theory of gravity. We construct a model with two phases which can be interpreted as containing clocks which either do not tick or tick exactly once. This demonstrates that while a theory based on causal sets may appear to have inherent notions of time and causality, the existence of a phase transition means, that as Saint Augustine wrote in hisConfessions, “the ‘time’, if such we may call it, when there was no time was not time at all.”
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00759191
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  • 5
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    Why do clocks tick? (1993)
    Springer
    Details
    Publication Date: 1993-09-01
    Print ISSN: 0001-7701
    Electronic ISSN: 1572-9532
    Topics: Physics
    Published by Springer
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  • 6
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    High resolution population estimates from telecommunications data (2015)
    Springer
    Details
    Publication Date: 2015-05-16
    Electronic ISSN: 2193-1127
    Topics: Computer Science
    Published by Springer
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