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  • 1
    Electronic Resource
    Electronic Resource
    Analysis of the Knight shift for liquid alkali alloys (1969)
    Springer
    The European physical journal 222 (1969), S. 253-260 
    Details
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Knight shift for binary alkali systems in the liquid phase is analyzed in terms of a simple augmented plane wave approximation (A.P.W.). A proper normalization of the electron wave functions combined with the concentration dependence of the Pauli susceptibility gives a reasonable prediction of the Knight shift of both components as a function of concentration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01392124
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  • 2
    Electronic Resource
    Electronic Resource
    The thermodynamic limit for long-range random systems (1983)
    Springer
    Journal of statistical physics 32 (1983), S. 141-152 
    Details
    ISSN: 1572-9613
    Keywords: Subadditive ergodic theorem ; random interactions ; longrange interactions ; dipolar coupling ; free energy ; correlation length
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Long-range spin systems with random interactions are considered. A simple argument is presented showing that the thermodynamic limit of the free energy exists and depends neither on the specific random configuration nor on the sample shape, provided there is no external field. The argument is valid for both classical and quantum spin systems, and can be applied to (a) spins randomly distributed on a lattice and interacting via dipolar interactions; and (b) spin systems with potentials of the formJ(x 1,x 2)/|x 1 -x 2| αd , where theJ(x 1,x 2) are independent random variables with mean zero,d is the dimension, and α 〉 1/2. The key to the proof is a (multidimensional) subadditive ergodic theorem. As a corollary we show that, for random ferromagnets, the correlation length is a nonrandom quantity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01009426
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  • 3
    Electronic Resource
    Electronic Resource
    Nonlinear neural networks. I. General theory (1988)
    Springer
    Journal of statistical physics 50 (1988), S. 231-257 
    Details
    ISSN: 1572-9613
    Keywords: Neural networks ; spin glasses ; learning rules ; clipped and other nonlinear synapses ; synaptic kernel ; spectral theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A neural network is called nonlinear if the introduction of new data into the synaptic efficacies has to be performed through anonlinear operation. The original Hopfield model is linear, whereas, for instance, clipped synapses constitute a nonlinear model. Here a general theory is presented to obtain the statistical mechanics of a neural network with finitely many patterns and arbitrary (symmetric) nonlinearity. The problem is reduced to minimizing a free energy functional over all solutions of a fixed-point equation with synaptic kernelQ. The case of clipped synapses with bimodal and Gaussian probability distribution is analyzed in detail. To this end, a simple theory is developed that gives the spectrum ofQ and thereby all the solutions that bifurcate from the high-temperature phase.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01022994
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  • 4
    Electronic Resource
    Electronic Resource
    An inequality for trace ideals (1980)
    Springer
    Communications in mathematical physics 76 (1980), S. 143-148 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We prove an inequality for trace ideals which relates the difference of two positive operators to the difference of their square roots. Inequalities involving operator-monotone functions more general than the square root, are considered as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01212822
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  • 5
    Electronic Resource
    Electronic Resource
    Universal upper bound for the tunneling rate of a large quantum spin (1988)
    Springer
    Communications in mathematical physics 119 (1988), S. 213-219 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An upper bound is derived for the tunneling rate of a spin with large spin quantum numberS. The bound isuniversal in the sense that it does not depend on the specific form of the anisotropy (i.e., the potential barrier). The method of proof relies on the exponential localization theorem of Fröhlich and Lieb and lends precise support to a rather suggestive interpretation put forth in a WKB analysis of van Hemmen and Sütő. The resulting bound agrees with their expression for the tunneling rate in the limit of largeS.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01217739
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  • 6
    Electronic Resource
    Electronic Resource
    Hebbian learning reconsidered: Representation of static and dynamic objects in associative neural nets (1989)
    Springer
    Biological cybernetics 60 (1989), S. 457-467 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract According to Hebb's postulate for learning, information presented to a neural net during a learning session is stored in the synaptic efficacies. Long-term potentiation occurs only if the postsynaptic neuron becomes active in a time window set up by the presynaptic one. We carefully interpret and mathematically implement the Hebb rule so as to handle both stationary and dynamic objects such as single patterns and cycles. Since the natural dynamics contains a rather broad distribution of delays, the key idea is to incorporate these delays in the learning session. As theory and numerical simulation show, the resulting procedure is surprisingly robust and faithful. It also turns out that pure Hebbian learning is by selection: the network produces synaptic representations that are selected according to their resonance with the input percepts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00204701
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  • 7
    Electronic Resource
    Electronic Resource
    Martingale approach to neural networks with hierarchically structured information (1988)
    Springer
    The European physical journal 71 (1988), S. 261-271 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A modified version of a model with hierarchically structured information, originally proposed by Parga and Virasoro, is studied in the context of martingale theory. The number of generations is allowed to be arbitrary but fixed. In the calculation of the storage capacity both the patterns and all their ancestors have to be taken into account as retrieval states. Due to the martingale property, the free energy greatly simplifies and for the retrieval states is shown to reduce to the one of the Hopfield model. So the storage capacity and retrieval quality of both models are identical. Numerical stimulations confirm the theoretical predictions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01312798
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  • 8
    Electronic Resource
    Electronic Resource
    A note on the diagonalization of quadratic boson and fermion hamiltonians (1980)
    Springer
    The European physical journal 38 (1980), S. 271-277 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We take advantage of the symmetry present in quadratic boson and fermion hamiltonians to give a short and simple derivation of their diagonalizations. This is of particular relevance to bosons. Both procedures are critically evaluated and a striking resemblance is pointed out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01315667
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  • 9
    Electronic Resource
    Electronic Resource
    The relevance of theA 2-term in the Dicke maser hamiltonian (1980)
    Springer
    The European physical journal 38 (1980), S. 279-285 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the multi-mode Dicke maser model, and analyze the conditions under which theA 2-term may be dropped from the hamiltonian. As far as the dynamics is concerned, theA 2-term may be dropped at the very beginning. As far as thermodynamics is concerned, there is mostly no need to keep theA 2-term. An exception is the case where one of the two states involved in the two-level atom approximation, is the atomic ground state. In general, however, dropping theA 2-term is an irrelevant modification. This result is obtained by partly diagonalizing the hamiltonian and applying the results of Hepp and Lieb.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01315668
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  • 10
    Electronic Resource
    Electronic Resource
    The mattis random magnet as an isotopically disordered harmonic crystal (1980)
    Springer
    The European physical journal 40 (1980), S. 55-59 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The elementary excitations in a Heisenberg-Mattis random ferromagnet are studied. A solution is obtained by mapping the original problem onto a classical one, viz. determining the eigenfrequencies and eigenmodes of an isotopically disordered harmonic crystal with masses plus and minus one. The latter problem is much more amenable to an exact analysis. In contrast to previous work we find little evidence that spin waves do exist in one dimension.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01295070
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