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  • 11
    Electronic Resource
    Electronic Resource
    Zur Quantentheorie des Mehrelektronensystems im schwingenden Gitter (1956)
    Springer
    The European physical journal 146 (1956), S. 555-570 
    Details
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Zusammenfassung Das in dem vorangegangenen ersten Teil der Arbeit gewonnene Aufbaugesetz für die Lösung des Mehrelektronensystems im schwingenden Gitter wird auf ein vonFröhlich vorgeschlagenes eindimensionales Supraleitungsmodell angewendet. Es wird eine neue Lösungsfunktion aufgebaut, die die richtige Translationseigenschaft besitzt und einen tieferen Energie-Erwartungswert als dieFröhlichsche Lösungsfunktion liefert. Durch sie wird weiter ein vonKuper gegenüber derFröhlich-schen Lösung gemachter Einwand behoben, daß die stromtragenden Supraleitungszustände nicht orthogonal auf dem Grundzustand sind. Die vonFröhlich festgestellte Energielücke zwischen Zuständen mit kollektiver Elektronenbewegung („Supraleitungszustände“) und solchen mit individueller Elektronenanregung (‚Normalleitungszustände“) bleibt erhalten. Da diese Normalleitungszustände jedoch nicht mehr in Strenge auf dem Grundzustand orthogonal sind, erscheint eine weitere Untersuchung des Modells wünschenswert.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01333180
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  • 12
    Electronic Resource
    Electronic Resource
    Instability in degenerate two-photon running wave laser (1989)
    Springer
    The European physical journal 77 (1989), S. 157-162 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k〉1+r(k=κ/γ⊥,r=γ∥/γ⊥; κ is the cavity loss of the field and γ∥,γ⊥ are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr〈k〈(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01313633
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  • 13
    Electronic Resource
    Electronic Resource
    Generalized Ginzburg-Landau equation for self-pulsing instability in a two-photon laser (1989)
    Springer
    The European physical journal 77 (1989), S. 163-174 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A nonlinear analysis is made for a degenerate two-photon ring laser near its critical point corresponding to a self-pulsing instability by using the slaving principle and normal form theory. It turns out that the system undergoes two kinds of transitions, a usual Hopf bifurcation to a stable or unstable limit cycle and a co-dimension two Hopf bifurcation where the limit cycles disappear. An analytical criterion is given to distinguish the super-from the sub-critical bifurcation. We have also solved the equations numerically to confirm and to supplement our analytical results. In the case of super-critical bifurcation, a period-doubling bifurcation sequence to chaos is also observed with the decrease in pumping.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01313634
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  • 14
    Electronic Resource
    Electronic Resource
    Quasiperiodicity involving twin oscillations in the complex Lorenz equations describing a detuned laser (1990)
    Springer
    The European physical journal 81 (1990), S. 457-461 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Quasiperiodical motion in the complex Lorenz equations describing a detuned laser is shown to consist of twin oscillations: the first oscillation originates from Hopf bifurcation and the second is a parastic oscillation of the first one. Equations for the twin asymptotic oscillations are analytically derived in the center manifold, showing explicitly the parastic property of the second oscillation: its frequency is proportional to the square of the amplitude of the first one. The phase of the second oscillation shows also certainanholonomy which is very similar to the characteristics of Berry's phase. Numerical results show further that the first oscillation follows the sequence of bifurcations from simple periodic through period-doubling to chaos, as one continuously increases the control parameter, whereas the frequency of the parastic oscillation does not change qualitatively during the bifurcation process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390829
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  • 15
    Electronic Resource
    Electronic Resource
    Unbiased determination of forces causing observed processes (1992)
    Springer
    The European physical journal 88 (1992), S. 95-103 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Using measured short time correlation functions of a stochastic process as constraints in the maximum calibre principle of Jaynes, we formulate the joint probability distribution function of the process. The Lagrange multipliers which hereby occur are determined by minimizing a time-dependent form of the (Kullback) information gain. This step can alternatively be interpreted as if our system builds a neural network which “learns” the Lagrange multipliers. Next, we proceed to determine explicit formulas-expressed in terms of the Lagrange multipliers-for the drift and diffusion coefficients appearing in the corresponding Ito-Langevin equation, which describe the forces underlying the process. Computer-simulations of two processes are presented, showing good confirmation of the theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01573843
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  • 16
    Electronic Resource
    Electronic Resource
    Learning the dynamics of two-dimensional stochastic Markov processes (1992)
    Springer
    Open systems & information dynamics 1 (1992), S. 311-326 
    Details
    ISSN: 1573-1324
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Natural Sciences in General
    Notes: Abstract We show that it is possible to “learn” the forces causing an observed two-dimensional stochastic Markov process. Hereby, we extend the ideas presented in our earlier work [1–3], where we discussed one-dimensional processes. Appropriate short-time correlation function measurements are used as constraints in the maximum information principle of Jaynes, allowing us to formulate the joint probability distribution function of the process. This is done using the method of Lagrange multipliers, which we determine by means of a dynamical learning method. Next, we derive explicit formulas expressing the drift- and diffusion coefficients of the Ito-Langevin equation corresponding to the process in terms of the Lagrange multipliers. This provides us with the sought for underlying deterministic and stochastic dynamics. The method was tested on a simulated Ornstein-Uhlenbeck process, showing good confirmation of the theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02228842
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  • 17
    Electronic Resource
    Electronic Resource
    Arbitrariness in nature: synergetics and evolutionary laws of prohibition (2000)
    Springer
    Journal for general philosophy of science 31 (2000), S. 57-73 
    Details
    ISSN: 1572-8587
    Keywords: complex systems ; evolution ; nonlinearity ; pre-determination ; self-organization ; soft management ; structure-attractors ; synergetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Philosophy , Nature of Science, Research, Systems of Higher Education, Museum Science
    Notes: Abstract The philosophical consequences of synergetics, the interdisciplinary theory of evolution and self-organization of complex systems, are being drawn in the paper. The idea of discreteness of evolutionary paths is in the focus of attention. Although the future is open, and there are many alternative evolutionary paths for complex systems, not any arbitrary (either conceivable or desirable) evolutionary path is feasible in a given system. There are discrete spectra of possible evolutionary paths which are determined exclusively by inner properties of the corresponding systems. Synergetics allows us to reveal general laws of self-organization and, therefore, certain limits of arbitrariness of nature in choosing possible paths of evolution as well as in constructing of a complex evolutionary whole. A comparative analysis between the modern synergetic notions and a few ideas of the Western philosophy (F. Nietzsche, N. Hartmann, M. Heidegger) and of the Eastern teachings (Taoism, Buddhism) is made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008369525041
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