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Fractals, Dissipation and Coherent States

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Quantum Interaction (QI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7620))

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Abstract

Self-similarity properties of fractal structures, including the logarithmic spiral, are related to quantum dissipative dynamics, generalized squeezed coherent states and noncommutative geometry in the plane. The rôle played by the fractal Hamiltonian which actually turns out to be the fractal free energy is discussed. Time evolution characterized by the breakdown of time-reversal symmetry is controlled by the entropy. Coherent boson condensation induced by the generators of the coherent states is shown to control the formation of fractals. Vice-versa, coherent generalized states are recognized to possess self-similar fractal structure. The global nature of fractals appears to emerge from irreversible coherent local deformation processes.

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Authors and Affiliations

  1. Dipartimento di Fisica “E. R. Caianiello” and Istituto Nazionale di Fisica Nucleare, Universitá di Salerno, I-84084, Fisciano, Salerno, Italy

    Giuseppe Vitiello

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  1. Giuseppe Vitiello
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Editors and Affiliations

  1. Indiana University, 47405, Bloomington, IN, USA

    Jerome R. Busemeyer

  2. Conservatoire National des Arts et M’etiers, 75003, Paris, France

    François Dubois

  3. Paris School of Economics, 75014, Paris, France

    Ariane Lambert-Mogiliansky

  4. University of Padua, 35131, Padua, Italy

    Massimo Melucci

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Vitiello, G. (2012). Fractals, Dissipation and Coherent States. In: Busemeyer, J.R., Dubois, F., Lambert-Mogiliansky, A., Melucci, M. (eds) Quantum Interaction. QI 2012. Lecture Notes in Computer Science, vol 7620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35659-9_7

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  • DOI: https://doi.org/10.1007/978-3-642-35659-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35658-2

  • Online ISBN: 978-3-642-35659-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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